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1 Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2011 Harmonic Expectation in Twelve-Bar Blues Progressions Bryn Hughes Follow this and additional works at the FSU Digital Library. For more information, please contact

2 THE FLORIDA STATE UNIVERSITY COLLEGE OF MUSIC HARMONIC EXPECTATION IN TWELVE-BAR BLUES PROGRESSIONS By BRYN HUGHES A dissertation submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Summer Semester, 2011

3 The members of the committee approve the dissertation of Bryn Hughes defended on July 1, Nancy Rogers Professor Directing Dissertation Denise Von Glahn University Representative Matthew Shaftel Committee Member Clifton Callender Committee Member Approved: Evan Jones, Chair, Department of Music Theory and Composition Don Gibson, Dean, College of Music The Graduate School has verified and approved the above-named committee members. ii

4 To my father, Robert David Moyse, for teaching me about the blues, and to the love of my life, Jillian Bracken. Thanks for believing in me. iii

5 ACKNOWLEDGEMENTS Before thanking anyone in particular, I would like to express my praise for the Florida State University music theory program. The students and faculty provided me with the perfect combination of guidance, enthusiasm, and support to allow me to succeed. My outlook on the field of music theory and on academic life in general was profoundly shaped by my time as a student at FSU. I would like to express my thanks to Richard Parks and Catherine Nolan, both of whom I studied under during my time as a student at the University of Western Ontario and inspired and motivated me to make music theory a career. I would also like to thank Matthew Royal, with whom I had the pleasure of taking a number of classes, including an introduction to the field of music cognition. Matthew Shaftel, Clifton Callender, and Denise Von Glahn each deserve utmost thanks for serving as committee members for this dissertation. I learned a great deal from each of them throughout my time spent on this project and as a student in their classes before it began. To Nancy Rogers, my dissertation advisor, I owe tremendous gratitude. My decision to pursue a music cognition topic was inspired by a doctoral seminar I took with her at the end of my second year of coursework. Among many other things, in that class I learned that designing experiments can be a creative and fundamentally rewarding experience. I am also grateful for her constructive feedback, her relentless attention to detail, and for her keen ability to concisely and elegantly solve problems. With her guidance, I know that this document is as good as it possibly could have been. I would also like to thank her for serving as an extremely helpful career mentor. Richard Parks and Catherine Nolan inspired me to make music theory a career; Nancy has helped make it a reality. I am greatly indebted to Christian Vaccaro, Ben Gaskins, Ben Zendel, and Dominique Vuvan, all of whom were extremely patient and helpful when answering numerous questions about statistics that I posed to them throughout this project. I would also like to extend thanks to Sally Gross and Lauren Smith for their administrative help during my time as a student at FSU, to Rob Bennett and Neil Anderson-Himmelspach iv

6 for their guidance with audio editing software, and to Leah Harrison, for delivering copies of the dissertation to my committee on my behalf. I would be remiss if I didn t mention the overwhelming support of my family. My mother, Mair Hughes, my stepfather, John George, and my father, Robert David Moyse, have encouraged my musical endeavors for my entire life, and for that I am endlessly thankful. I would also like to thank Kathy and Doug Bracken for their support, and for welcoming me into their family, crazy academic pursuits and all. Finally, I would like to thank express boundless thanks to my spouse and the love of my life, Jillian Bracken. For her honest criticisms, her infinite support and encouragement, and for her belief in me, I am forever grateful. v

7 TABLE OF CONTENTS List of Tables... ix List of Figures... xiii Abstract... xvi CHAPTER ONE: INTRODUCTION... 1 Jimi Hendrix s Hey Joe : Progression or retrogression?... 1 The twelve-bar blues: a case study... 2 Which blues?... 3 Prominent features of the twelve-bar blues... 3 The V-IV-I debate... 5 CHAPTER TWO: HARMONIC FUNCTION AND THE ANALYSIS OF ROCK MUSIC... 7 What is harmonic syntax?... 8 Room-motion theory... 8 Scale-degree theory Function theory Theories of voice leading Summary CHAPTER THREE: HARMONIC FUNCTION AS EXPECTATION Musical grammar Statistical learning Schema theory Expectation Studies of harmonic expectation Expectation and timing Harmonic expectation in twelve-bar blues progressions CHAPTER FOUR: THE EFFECT OF STYLE-PRIMING ON HARMONIC EXPECTATION Experiment 1: Task Hypotheses Participants Stimuli Equipment Design and Procedure Results and Discussion Root-motion theory Comparison with other quantitative ratings of chord pairs Chord content Phrase openings vi

8 Phrase endings Conclusions Summary CHAPTER FIVE: LISTENERS EXPECTATIONS OF THE TIMING OF HARMONIC EVENTS Experiment 2A: Task Hypotheses Participants Stimuli Equipment Design and Procedure Results and Discussion Experiment 2B: Task Hypotheses Participants Stimuli Equipment Design and Procedure Results and Discussion General Discussion Summary CHAPTER SIX: HARMONIC EXPECTATION IN TWELVE-BAR BLUES PROGRESSIONS Experiment 3 Pre-Test Pre-Test Task Pre-Test Hypotheses Pre-Test Participants Pre-Test Stimuli Pre-Test Equipment Pre-Test Design and Procedure Pre-Test Results and Discussion Experiment 3: Task Hypotheses Stimuli Equipment Design and Procedure Results and Discussion Phrase labels The effect of the variable chord on phrase labels Chord location Which chords prompt listeners to abandon a schema? Ratings Did variable chord affect rating? vii

9 Variable chord location The relationship between Experiment 1 and Experiment Phrase labels and ratings Conclusions Summary CHAPTER SEVEN: CONCLUSIONS Comparison of experimental results with previous research Opportunities for further research Summary ILLUSTRATIONS APPENDIX A: PROCTOR S SCRIPTS AND RESPONSE SHEETS Experiment 1: Proctor s script Experiment 2: Proctor s script Experiment 3: Proctor s script APPENDIX B: DOCUMENTATION OF APPROVAL BY THE FLORIDA STATE UNIVERSITY HUMAN SUBJECTS COMMITTEE APPENDIX C: QUESTION ORDER FOR EXPERIMENTS APPENDIX D: EXPERIMENT 1 CHORD SUCCESSION RATINGS REFERENCES BIOGRAPHICAL SKETCH viii

10 LIST OF TABLES 4.1 A summary of trials used in Experiment Main effect of ordered pitch-class intervals (OPCIs) between chord roots on rating (Experiment 1) Mean ratings for data grouped by primary triads used in each succession in Experiment Main effect of primary chord(s) used on rating for data subsets grouped by ordered pitch-class interval (Experiment 1) Main effect of OPCI on rating for successions that did not include multiple primary triads or multiple primary triad roots (Experiment 1) Statistical significance of mean differences between ratings for instances of the same OPCI (Experiment 1) Mean ratings for chords following the tonic, subdominant, and dominant (Experiment 1) Mean ratings for chords approaching tonic, subdominant, and dominant (Experiment 1) A comparison of ratings for diatonic successions used both in Experiment 1 and Krumhansl Correlations between the different ratings of two-chord successions listed in Table 4.9 (Experiment 1) Correlations between Lerdahl s chord distance measurement and mean ratings for all successions used in Experiment A comparison of mean ratings for diatonic and non-diatonic successions (Experiment 1) A Comparison of mean ratings for diatonic, mixture, and chromatic successions (Experiment 1) A comparison of mean ratings for successions grouped by style and type of succession (diatonic, non-diatonic) (Experiment 1) A comparison of mean ratings for successions grouped by style and type of succession (diatonic, mixture, other chromatic) (Experiment 1) ix

11 4.16 The effect of the type of succession (diatonic vs. non-diatonic) on ratings among successions with diatonic chord roots (Experiment 1) A comparison of mean ratings for successions grouped by first chord (Experiment 1) A comparison of means for successions beginning with primary triads (Experiment 1) A comparison of means for successions grouped by closing chord (Experiment 1) A comparison of mean ratings for successions that close with primary triads (Experiment 1) Cross-tabulation of question type (recorded or synthesized) and accuracy (correct or incorrect) for the pre-test (Experiment 3) A cross-tabulation of phrase (beginning, middle, or end) and accuracy (correct or incorrect) for the pre-test (Experiment 3) A summary of the stimulus groups for the trials used in Experiment A cross-tabulation of stimulus group and phrase label (Experiment 3) The p-values of chi-square tests of all pairs of stimulus groups (labeled A through G) (Experiment 3) The p-values of chi-square tests for all pairs of listener-assigned phrase labels within stimulus groups (Experiment 3) Overall frequency distribution of phrase labels for all variable chords (Experiment 3) The p-values of chi-square tests for all variable chords in stimuli interpreted as either Phrase 2 or Phrase 3 (Experiment 3) Distribution of phrase labels organized by Chord 1 (Experiment 3) Distribution of phrase labels organized by Chord 2 (Experiment 3) Distribution of phrase labels organized by Chord 3 (Experiment 3) Cross-tabulation of Chord 1 and Phrase Label for Stimulus Group A (Experiment 3) x

12 6.13 Cross-Tabulation of Chord 2 and Phrase Label for Stimulus Group B (Experiment 3) Cross-Tabulation of Chord 3 and Phrase Label for Stimulus Group C (Experiment 3) Cross-Tabulation of Chord 1 and Phrase Label for Stimulus Group D (Experiment 3) Cross-Tabulation of Chord 2 and Phrase Label for Stimulus Group E (Experiment 3) Cross-Tabulation of Chord 3 and Phrase Label for Stimulus Group F (Experiment 3) Cross-Tabulation of Chord 2 and Phrase Label for Stimulus Group G (Experiment 3) Ratings for stimulus groups, categorized by significant mean differences (Experiment 3) Chord successions from Experiment 1 and where they appear in Experiment 3 (located by Stimulus Group) Correlations between mean ratings for the I-* succession heard in stimulus groups from Experiment 3 and the ratings for the succession I-* from Experiment Correlations between mean ratings for the IV-* succession heard in stimulus groups from Experiment 3 and the ratings for the succession IV-* from Experiment Correlations between mean ratings for the V-* succession heard in stimulus groups from Experiment 3 and the ratings for the succession V-* from Experiment Correlations between mean ratings for the *-I succession heard in stimulus groups from Experiment 3 and the ratings for the succession *-I from Experiment Correlations between mean ratings for the *-IV succession heard in stimulus groups from Experiment 3 and the ratings for the succession *-IV from Experiment xi

13 6.26 Correlations between mean ratings for the *-V succession heard in stimulus groups from Experiment 3 and the ratings for the succession *-V from Experiment Mean Ratings for all variable chords in Stimulus Group A, grouped by phrase label response Mean Ratings for all variable chords in Stimulus Group B, grouped by phrase label response Mean Ratings for all variable chords in Stimulus Group C, grouped by phrase label response Mean Ratings for all variable chords in Stimulus Group D, grouped by phrase label response Mean Ratings for all variable chords in Stimulus Group E, grouped by phrase label response Mean Ratings for all variable chords in Stimulus Group F, grouped by phrase label response Mean Ratings for all variable chords in Stimulus Group G, grouped by phrase label response C.1 Question order for Experiment 1, Group 1 (Blues) C.2 Question order for Experiment 1, Group 2 (Classical) C.3 Durations in seconds for trials used in Experiments 2A and 2B C.4 Question order for Experiment 2A, Group 1 (With Drums) C.5 Question order for Experiment 2A, Group 2 (Without Drums) C.6 Question order for Experiment 2B C.7 Question order for Experiment D.1 Mean ratings for all successions in Experiment xii

14 LIST OF FIGURES 1.1 Howlin Wolf/Willie Dixon, Little Red Rooster, first verse Chord progression for (Sittin On) The Dock of the Bay, by Otis Redding Plot of mean ratings for data grouped by ordered pitch-class interval in Experiment Plot of mean ratings for chord successions in Experiment 1 grouped according to the number and type of primary triads used Plot of mean ratings for data grouped by root motion by ascending minor second/descending minor seventh (Experiment 1) Plot of mean ratings for data grouped by root motion by ascending perfect fourth/descending perfect fifth (Experiment 1) Plot of mean ratings for data grouped by root motion by ascending perfect fifth/descending perfect fourth (Experiment 1) Plot of mean ratings for data grouped by root motion by ascending minor seventh/descending major second (Experiment 1) Plot of mean ratings for successions that did not include multiple primary triads or multiple primary triad roots, grouped by OPCI (Experiment 1) Plots of ratings for chords following the tonic, subdominant, and dominant (Experiment 1) Plots of ratings for chords approaching tonic, subdominant, and dominant (Experiment 1) Plot of mean ratings for diatonic and non-diatonic successions (Experiment 1) Plot of mean ratings for diatonic, mixture, and chromatic successions (Experiment 1) Plot of mean ratings for diatonic and non-diatonic Successions in both blues and classical contexts (Experiment 1) Plot of mean ratings for diatonic, mixture, and chromatic successions in both blues and classical contexts (Experiment 1) xiii

15 4.14 Plot of mean ratings for successions with diatonic chord roots (Experiment 1) Plot of mean ratings for successions grouped by opening chord (Experiment 1) Plot of mean ratings for successions beginning with primary triads in both blues and classical contexts (Experiment 1) Plot of mean ratings grouped by closing chord (Experiment 1) Plot of mean ratings for successions ending with primary triads in both blues and classical contexts (Experiment 1) Score of the accompanying drum track used in Experiments 2A and 2B A summary of stimuli used in Experiments 2A and 2B A plot of mean ratings for IV, bvii, and #IV in all timing conditions (Experiment 2A) A plot of mean ratings for typical and atypical timing in all harmonic conditions (Experiment 2A) A plot of mean ratings for typical and atypical timing conditions when the data are grouped by contrasting chord (Experiment 2A) A plot of mean ratings for non-tonic chords when the data are grouped by timing (Experiment 2A) A plot of mean ratings for non-tonic chords in all timing conditions (Experiment 2B) A plot of means for ratings of typical and atypical timing conditions (Experiment 2B) A plot of mean ratings for typical and atypical timing when the data are grouped by non-tonic chord (Experiment 2B) A plot of mean ratings for non-tonic chords when the data are grouped by timing (Experiment 2B) The structure of the standard twelve-bar blues and the excerpts from which all stimuli were constructed (Experiment 3) xiv

16 6.2 A representation of phrase label distribution for each stimulus group (Experiment 3) Mean ratings for variable chords categorized by type: diatonic, mixture, and other chromatic (Experiment 3) Mean ratings for variable chords grouped by the ordered pitch-class interval leading into the variable chord (OPCI-to) (Experiment 3) Mean ratings for variable chords grouped by the ordered pitch-class interval leading out of the variable chord (OPCI-from) (Experiment 3) Mean ratings grouped by Stimulus Group Means plot for Stimulus Group A, grouped by variable chord Means plot for Stimulus Group B, grouped by variable chord Means plot for Stimulus Group C, grouped by variable chord Means plot for Stimulus Group D, grouped by variable chord Means plot for Stimulus Group E, grouped by variable chord Means plot for Stimulus Group F, grouped by variable chord Means plot for Stimulus Group G, grouped by variable chord A.1 Response sheet for Experiment A.2 Response sheet for Experiment A.3 Response sheet used for Experiment 3 Pre-Test and Experiment B.1 Informed Consent Form B.2 IRB Approval Memorandum xv

17 ABSTRACT Music theorists often suggest that harmony in common-practice music is governed by syntax. Cognitive studies have shown that listeners expect chord successions that adhere to syntactical rules pertaining to chord-to-chord connections, metrical placement, and formal organization. There is less agreement among music theorists regarding rules of harmonic syntax in rock music. Some suggest that the syntax is the same for both contexts, while others propose new syntactical rules for rock music. Through three empirical studies, this dissertation addresses listener perception of harmony in rock music and examines the degree to which experimental results support the competing theories of rock harmony. For the purposes of these experiments, the twelve-bar blues scheme a model that has greatly influenced rock music serves as a framework for harmonic practice in the rock idiom. The experiments presented in this dissertation define harmonic syntax in terms of expectation. Although all three experiments engage different facets of expectation, they all share certain design features. Foremost is the rating scale response mode, which allows for global judgments of stimuli and addresses expectation by way of misattribution: a positive rating is understood as reflecting a predicted event. Second, because these experiments intend to investigate possible differences in the expectations produced by rock and common-practice music, the stimuli used in each experiment include several features that firmly establish stylistic context. Together, the three studies aim to contribute insight to the growing body of research that addresses the following four broad questions: 1) Does rock music elicit expectations that are different from those held for common-practice music? 2) Do listeners have graded expectations of harmony in rock music? 3) What is the relationship between expectations of temporality and harmony in a rock music context? 4) Does harmony affect expectations of musical form (or vice versa)? The results of all three experiments provide evidence that trained musicians possess specific graded expectations of harmony when engaged with musical stimuli representative of the rock genre. Although many of these expectations align with those already known for common-practice harmony, each experiment revealed subtle but significant discrepancies between expectations for these two genres of music. Experiment 1 showed that listeners are less accepting of out-of-key successions when they are primed by classical style cues than when they are primed by blues/rock cues. When primed by blues/rock cues, listeners rated primary triads equally when initiating or terminating a succession; however, in identical situations primed with classical cues, xvi

18 listeners showed a preference for tonic and dominant over subdominant harmony. Experiments 2 and 3 showed that listeners have strong and specific expectations of musical phrases within the context of twelve-bar blues schemata. Participants displayed sensitivity to the normative harmonic rhythm and timing in the twelve-bar blues phrase structure (Experiment 2) and largely depended on the normative events of these schemata to orient their listening within the overall twelve-bar form (Experiment 3). Experiment 3 also provided evidence that listeners prefer (presumably because they have stronger expectations for) a four-measure phrase when that phrase conveys a clear orientation within the larger twelve-bar form. xvii

19 CHAPTER ONE INTRODUCTION Jimi Hendrix s Hey Joe : Progression or retrogression? The guitar riff that opens Jimi Hendrix s recording of the song Hey Joe quickly orients the listener within a specific musical environment. The blues-inspired gesture begins on an anacrusis and descends through the minor pentatonic scale from top to bottom, firmly establishing E as a tonal center. E is reconfirmed with the bluesy fivenote gesture: 5-b7-5-b7-1 before delving into the verse proper. The song s text poses a question of its eponymous character ( Hey Joe, where you goin with that gun in your hand? ), further rooting itself in a blues-rock setting through the initiation of a stylistically idiomatic poetic device: the presentation of a question that will likely be answered. The song proceeds in four-measure phrases. 1 Hendrix delivers the vocal line in a rhythmically casual manner, aligning the climax of the poetic phrase with the arrival of the tonic. While the contour of the vocal line certainly emphasizes the arrival of the E- major chord in m. 3, an even more salient force driving the music forward in this phrase is the ascending fifths sequence that supports it: C - G - D - A - E E More broadly, we might represent this progression with Roman numerals as follows: bvi - biii - bvii - IV - I I Such an analysis suggests that this passage is entirely non-functional from the standpoint of common-practice tonality. We might describe this sequence of chords as a retrogression or non-functional static harmony, yet these descriptions fail to convey 1 Throughout this dissertation the term phrase will be used more liberally than it would when referring exclusively to common-practice music. Rock music does not always employ conventional harmonic cadences to delineate formal units; sections are typically demarcated by some combination of textual, timbral, rhythmic, and metrical emphasis. Harmony often factors into this delineation as well (and is indeed a topic central to this dissertation); however, given that numerous chord combinations could be considered cadential in rock music, a harmonic cadence will not be considered a requirement for a formal unit to be called a phrase. 1

20 the growing sense of expectation that an experienced listener feels as the passage transpires. Ultimately, this brief analysis of Hey Joe reveals a seemingly dichotomous pair of perspectives regarding the role of harmonic function in rock music. In its musical context, the chord succession heard in Hey Joe truly sounds like a progression with its connotation of perceived forward motion. Yet, through the lens of common-practice tonality, one can only view the succession as non-functional. This analytical conundrum raises the question that will remain central throughout this dissertation: does harmony convey different musical functions in different musical contexts, or does harmony behave in a universally consistent way? The current music-theoretical literature proposes two distinct answers. 1. Harmony is perceived, transformed, and construed in terms of common-practice syntax (Everett 1999 and 2004). 2. The harmonic language of rock abides by its own set of rules which the listener engages when a musical context is established (Moore 1992 and 1995; Stephenson 2002). The twelve-bar blues: a case study This dissertation investigates harmony in a small but important subset of the rock canon: works employing the twelve-bar blues progression. The twelve-bar blues includes several characteristics that make it an attractive target of study. Foremost is that its corpus features a very high degree of stylistic consistency, reducing the number of potential confounding variables in experimental studies. Additionally, as a harmonic formula with tremendous influence throughout the history of rock, the twelve-bar blues offers an opportunity to speculate about harmonic function in a more general sense as it applies to rock music as a whole. Specifically, features such as the V-IV-I chord succession and three-phrase AAB formal structure have each undergone transformations that link the blues to several pop and rock schemata (Headlam 1997; Carter 2005, 108-9; Doll 2007, 152). More generally, the twelve-bar blues provides a practical means for investigating the epistemological foundation of harmonic function. Do the rules of common-practice harmony apply to music outside of its canon, or do they depend upon cultural and/or stylistic context? The twelve-bar blues is an exemplary non-common-practice schema that is ubiquitous throughout North American 2

21 popular music. Thus, its study offers a unique opportunity for comparison with what we already know about common-practice tonality. It is important to understand the central criteria and common features of the twelve-bar blues, which will serve as the point of departure for later chapters. Which blues? There are certainly numerous features that might influence someone to describe a song as blues, or, more specifically, twelve-bar blues. The standard form rose to prominence in the 1930s as a result of the record industry s desire for a polished and consistent musical structure that fit within the three-minute time restriction of the 78 rpm phonodisc (Keil 1966, 55; Springer 1995, 62). While its roots are in blues, the twelve-bar form quickly transcended genre and eventually became an important idiom in blues, jazz, and rock. In its countless guises, the twelve-bar form offers a rich diversity of harmonic realizations across these musical genres. Some researchers have investigated variations of the twelve-bar form in jazz (Steedman 1984; Alper 2005), and several scholars have noted in a general sense that the twelve-bar form has profoundly impacted rock music from the 1950s through the present (Hamm 1979, 396; Covach 2004, 66-67; Stephenson 2002, 103; Carter 2005, 70), but specific relations to the harmonic practices of rock music have been virtually ignored. This project engages the standard twelve-bar form that directly impacted rock music, as can be heard in the music of Buddy Holly, Bill Haley, Elvis Presley, Little Richard, The Beatles, and hundreds of other musicians and bands. 2 Prominent features of the twelve-bar blues The twelve-bar blues almost invariably consists of three four-measure phrases, each of which can be divided into two-measure sub-phrases. Phrases often form calland-response patterns supported both by the melody and by the text (in the case of a song). The idea of call-and-response is also captured within the sub-phrase. For example, in the Howlin Wolf/Willie Dixon song Little Red Rooster, each line of text transpires over the first two measures of a phrase (see Figure 1.1). Vocal calls are 2 While an examination of the corpus of variations on the twelve-bar blues found in the jazz repertory might provide ample insight into the notion of harmonic function in this context, the stylistic differences between rock and jazz are too great to compare in detail within the scope of this project. In cases where a cross-genre comparison is apt, I will differentiate the two as jazz-blues and blues-rock as appropriate. 3

22 responded to by instrumental riffs that close the phrase. In addition, each line is divided into two parts, resembling a call and response. While the twelve-bar structure of Little Red Rooster may appear simple, there are a few analytical questions that have caused disagreement among even the most highly-trained music scholars. For instance, where does harmonic closure occur? Which factors influence closure? Which harmonies are functional, and how do they function? Using the text and melody as a guide might lead one to hear cadences in mm. 3, 7, and 11. Measure 11 offers the strongest cadence, owing to the additional closure created by the typical poetic and melodic change of the B section following two repetitions of the A section. This interpretation undermines the role of the instrumental response, essentially relegating it to the status of a post-cadential extension. Support for this reading can be found in the numerous songs that essentially follow the twelvebar form but include extended or truncated phrases (such as Johnny Cash s Folsom Prison Blues, in which the last phrase of the form is only three measures long). A different interpretation of the twelve-bar form might locate closure in the fourth measure of each phrase. This reading privileges the consistent four-measure hypermeter of the twelve-bar blues, overriding any sense of harmonic closure achieved in mm.1-8. Measures 9-12 prolong dominant harmony, supported through the frequent occurrence of a V chord in m.12, serving as a turnaround leading to the repeat of m.1. While temporary closure may occur in m. 11, the consistent repetition of the twelve-bar form overpowers this notion, inciting a strong expectation for each ensuing return to m. 1. Jazz improvisation teachers frequently reinforce this kind of phrasing, suggesting that their students play fluidly through the end of each 12-measure section to ensure a smooth connection with the return of the first phrase. Full closure is not achieved until the end of the song, at which point the dominant turnaround is replaced by cadential motion to I (often through a chromatic ascent) in the fourth measure of the last phrase (Stephenson 2002, 62; Carter 2005, 66-70). The analytical issues discussed above can be categorized as location issues. In other words, where do important harmonic events occur? Experiment 2 in Chapter 5 examines the degree to which listeners prefer to hear harmonic events on strong beats, strong hyperbeats, or in specific locations within a twelve-bar blues phrase. Experiment 3 in Chapter 6 engages the question in a larger context, investigating whether listeners associate specific harmonic progressions with certain phrases of the twelve-bar form. 4

23 The V-IV-I debate The third phrase in a blues progression typically contains the most harmonic activity in the form, and there is widespread agreement that the third phrase provides a local climactic moment within each verse. Which harmonies are functional in the third phrase of a twelve-bar blues? This question resides at the center of nearly every scholarly debate regarding harmonic function in rock music. Several analysts argue that the V chord found in m. 9 is functional: it prepares the return to I in m. 11, and in combination these chords provide the necessary musical gesture to evince closure. The stepwise voice leading and root motion by descending fifth/ascending fourth made possible through the connection of these two chords supports this notion of closure. This interpretation dismisses the IV chord in m. 10 as an incomplete neighboring embellishment of V that softens the resolution to tonic (Covach 2004; Everett 2001, 61; Doll 2007, 151-2). Essentially, this analysis indicates that the harmony in the third phrase of a twelve-bar blues mirrors common practice. 3 However, many musicians contend that interpreting V as the functional dominant misappropriates the rules of common-practice harmony. Could we not consider the V chord a neighboring embellishment of the IV chord? The direct resolution of the IV to the I chord also aligns with the cadential goals of the melody and text. Discussing the Beatles song You ll Be Mine, in which this particular harmonic convention plays an important role, Mark Spicer suggests that V is subservient to the IV chord [which] is clearly in the driver s seat (Spicer 2005, 8). Given that blues emanated from a different musical tradition, is it not plausible that its harmonic events abide by different syntactical rules? Ken Stephenson (2002, 103) goes as far as to assert that this particular cadence represents a new harmonic standard for rock music in which root progressions contrary to the idioms of the common practice, such as V-IV, are customary. Each argument has weaknesses. Misappropriation aside, interpreting V as the operative chord suggests a substantial misalignment of the melodic and harmonic components of the cadence. As David Temperley (2007) points out, this may be an instance of melodic and harmonic independence ( the melodic-harmonic divorce ) 3 Carter 2005 (71) argues that at the background level, V controls the entire harmonic structure of the third phrase. This notion is supported in examples that include a dominant turnaround gesture at the end of phrase 3 (typically in m.12). Furthermore, he asserts that the harmonic trajectory of the twelve-bar form is a large-scale I-IV-V progression that propels the music through the repeat to the beginning of the next verse. Each of these background harmonies serve as goals, supported by their presence on hypermetrical downbeats. 5

24 commonly found throughout the rock repertory. Nevertheless, several songs utilizing the twelve-bar form exhibit melodies that are supported by the IV chord in m. 10. In these cases, interpreting a misaligned cadence would seem to ignore the obvious stability of the IV chord. Conversely, if the motion from IV to I in mm fulfills the structural requirements of a harmonic cadence, how does one differentiate it from the clearly less important but identical gesture found in mm. 6-7 (or even mm. 2-3, given that IV is commonly found in m. 2)? This interpretation suggests that V is superfluous and could be replaced with another chord. 4 Through three empirical studies, this dissertation addresses listener perception of harmony in rock music and examines the degree to which experimental results support the competing theories above. For the purposes of these experiments, the twelve-bar blues scheme a model that has greatly influenced rock music will serve as a framework for harmonic practice in the rock idiom. Chapter 2 provides an overview of the preeminent theories of harmonic function pertaining to common-practice tonality and discusses numerous instances in the literature in which these theories have been applied to rock music. Chapter 3 reframes the notion of harmonic function within theories of expectation drawn from cognitive psychology. Following a survey of the relevant music cognition and psychology literature, I outline the methodological framework used for each of the three experiments. Chapter 4 investigates the issue of whether or not musical style affects listeners expectations of two-chord successions. Chapter 5 addresses the issue of timing in harmonic expectation. Building on the foundation laid by the first two experiments, Chapter 6 engages harmonic expectation and how it influences our sense of form. Chapter 7 presents a summary of the conclusions drawn from each of the three experiments, and reflects upon their implications within the fields of music theory, music cognition, and rock music analysis. 4 Of course, in common-practice music, not all V-I progressions are considered authentic cadences. Cadences require a combination of melodic, harmonic, and metrical features to truly communicate a sense of closure. In the case of the twelve-bar blues, however, the previously mentioned IV-I progressions all occur in the same metrical location (mm.2-3 of a four-bar phrase), and often support similarly constructed melodic lines. 6

25 CHAPTER TWO HARMONIC FUNCTION AND THE ANALYSIS OF ROCK MUSIC As Walter Everett (2004) has shown, popular music from the last fifty years displays a wide range of harmonic tendencies. Amidst this diversity, Everett nevertheless asserts that the tonal norms basic to the pop music from which rock emerged are the same norms common to the system of common-practice tonality (Everett 2004, 3). Indeed, much of Everett s analytical work is grounded in Schenkerian practice and unsurprisingly reflects this assertion. 5 In some cases, Everett expands his conception of harmonic function to include a greater variety of chords within common-practice functional categories. 6 Most times, however, Everett considers non-common-practice harmonic successions to be byproducts of voice leading or instances of non-functionality. For example, Everett remarks that the dominant harmony in the traditional V-IV-I twelve-bar blues cadence is mitigated by an intervening subdominant, which... has no harmonic value but merely softens the resolution to tonic with its contrapuntal stepwise descent (Everett 2004, 18). Importantly, Everett dismisses theories of retrogressive harmonic function as discredited concepts [that] leave unconsidered the ramifications of voice leading upon chord identity, function, embellishment, and harmonic expansion (Everett 2004, 2 footnote). Several authors have stated opposing views. Most adamant among them is Ken Stephenson, who proposes that the harmonic language of rock music is diametrically opposed to the common practice, citing the V-IV-I cadence in particular as an exemplar of this standard (Stephenson 2002, ). He suggests that in blues, and to a greater extent rock music, harmonic progression is created through chord-root motion by descending second, ascending third, and descending fourth in other words, root motion contrary to the tonal norms of the common practice. Setting aside their differing opinions and methodologies, both Everett and Stephenson imply that listeners at least those who are highly trained possess specific expectations of harmonic succession in rock music. In other words, both Everett and Stephenson believe that harmonic function exists in some capacity in rock 5 This is best illustrated in Everett s monumental two-volume book The Beatles as Musicians (1999), which teems with analyses clearly inspired by Schenkerian theory. 6 See the appendix in Everett 1999 ( ), for example. 7

26 music. In contrast, a skeptic might suggest that the harmonic practice of rock music is not at all governed by syntax. Before sorting out the differences between harmonic practices in rock and common-practice music, it is necessary for us to consider exactly what is meant by harmonic syntax. What is harmonic syntax? Principles of harmonic syntax have been presented from various perspectives by numerous authors throughout the history of music theory. Regarding the music of the common practice, four perspectives on harmonic syntax stand out in the literature: rootmotion theory, scale-degree theory, function theory, and voice-leading theory. In order to provide context for later discussions of harmonic theory in rock music, each of these approaches is briefly summarized below. Root-motion theory Rameau s Traité de l harmonie (1722/1971) was the first of many theoretical works to propose that syntactical chord progressions are the result of an appropriate succession of fundamental bass notes, or chord roots. Simply put, Rameau s theory states that chord roots should progress by certain intervals: the descending fifth, descending third, and ascending second (in order of preference). Root motion by ascending fifth, third, or descending second is increasingly undesirable, with the last expressly forbidden by Rameau (Lester 2002, 766-8). Nicholas Meeùs (2002) connects Rameau s work with the theoretical writings of Arnold Schoenberg (1954/1969) and Yizhak Sadai (1980), both of whom similarly categorize chord progressions according to root motion. Meeùs simplifies the ideas posed by these authors and presents them as two categories: dominant progressions typified by descending-fifth root motion, and subdominant progressions typified by ascending-fifth root motion. Meeùs allows descending-third and ascending-second progressions to substitute for descending-fifth progressions. Likewise, he allows ascending-third and descending-second progressions to substitute for ascending-fifth progressions (Meeùs 2000, 7). He rationalizes third substitutions by identifying the parsimonious voice-leading connection between chords with roots a third apart (Meeùs 2000, 6). For instance, the progression I-vi is an acceptable substitute for the stronger descending-fifth progression iii-vi, since I and iii share and can be connected by efficient voice leading. He justifies the second type of substitution (root motion by 8

27 second) by invoking Rameau s double emploi. For Meeùs (and Rameau), progressions by ascending second are understood as instances of harmonic elision. For example, the progression IV-V is considered an elision of the progressions IV-ii (a third substitute) and ii-v (a descending-fifth progression). As Dmitri Tymoczko (2003) points out, implicit to the theory of root motion is the notion that all diatonic harmonies participate equally in the same set of allowable root motions (Tymoczko 2003, 3). Tymoczko finds this problematic because such theories fail to account for the fact that normal tonal phrases tend to begin and end with the tonic chord (Tymoczko 2003, 5). Indeed, Rameau s and Meeùs s theories only withstand collapse when the status of the V-I progression is elevated among other descending-fifth progressions, a point which Rameau justifies through a supplemental discussion of its characteristic voice leading (Tymoczko 2003, 3). Likewise, a pure root-motion theory lacks the discretion necessary to subvert uncommon progressions such as V-iii-I, ii-iii-i, and vii o -iii-i (Tymoczko 2003, 5). Tymoczko rectifies this flaw with a caveat requiring progressions to begin and end on tonic, and he removes the anomalous iii chord altogether. 7 Through a statistical analysis of several tonal Bach chorales and modal Palestrina mass movements, Tymoczko confirms that dominant progressions (as defined by Meeùs) are more typical of tonal music than are subdominant progressions. By contrast, modal music (such as the Palestrina movements) is characterized equally by dominant and subdominant harmonic motions (Tymoczko 2003, 9-10). To some extent, Tymoczko s survey supports Meeùs s original claim that common-practice harmonic syntax originated from a growing preference among composers for dominant progressions (Meeùs 2000, 17). 8 A handful of contemporary music theorists have used principles of root motion to describe harmonic function in rock music. Interestingly, a few of the criticisms aimed at root-motion theory are less problematic when engaging rock music. When arguing about the fundamental differences between common-practice and rock music, Allan Moore (1992) states that common-practice harmony is linear while rock harmony is cyclic (Moore 1992, 74). By linear, Moore means goal-oriented in the sense that 7 However, Tymoczko does allow the mediant triad to be used as part of an elision (Tymoczko 2003, 6). 8 Tymoczko s data reveal three exceptions to Meeùs s assertion that well-formed progressions consist entirely of dominant progressions: I-V, IV-I, and V-IV 6 (essentially a substitute progression for the more common V-vi). Together, these three progressions account for 87% of subdominant progressions found in Tymoczko s data. Although Tymoczko uses these examples as a means of questioning the theoretical completeness of Meeùs s work, he admits that, in a general sense, there is something right about Meeùs s theory regarding the prevalence of dominant progressions in tonal music and the freedom with which tonal composers use them (Tymoczko 2003, 10). 9

28 common-practice phrases tend to convey a sense of motion toward the harmonic terminus of the phrase (usually tonic). As Tymoczko mentions, root-motion theories are less convincing for tonal music because they necessitate the use of a caveat: phrases must end (and usually begin) on tonic harmony. Rock music, on the other hand, tends to be cyclical, in the sense that formal sections (or sometimes entire songs) are structured in small repeated units of four or eight measures (or occasionally two measures). 9 Since these sections repeat frequently throughout a song, it is less likely that listeners will hear the ends of sections as harmonic goals. Moreover, the identification of tonic is often determined by rhythmic, metrical, or durational emphasis, instead of information gleaned from the operating pitch collection (Moore 1992, 77). Since tonic harmony seems to hold a less prominent (often even ambiguous) place in rock, the restrictions it places upon a root-motion theory of harmonic progression are much less relevant. Chord progressions are more likely to be governed by principles pertaining only to immediately contiguous chords. Thus, in the context of rock music, the use of a root-motion theory may be apt when describing principles of harmonic succession. While Moore poses a convincing argument for using root-motion theory as a guiding principle of rock harmony, he fails to provide a specific description of how such a system would work. He alludes to the lack of tension and release in rock music (an oft-used description of common-practice harmonic function) and how that is represented by rock s preponderance of flatwise harmonic motion (Moore 1992, 80); presumably Moore refers to ascending-fifth progressions from the flat-inflected circle of fifths, such as bvii-iv-i, which occur frequently in rock music. 10 Moore continues by suggesting that many rock sequences could be formed from fifth cycles by substitution of modal-mediant-related chords and elisions of consecutive cyclic steps (Moore 1992, 80). This description neatly coincides with Nicholas Meeùs s rules for subdominant progressions. Incidentally, Meeùs s speculation that subdominant progressions might be better suited to modal music than to tonal music aligns with Moore s claim that rock s musical language is primarily a modal one as opposed to a tonal one (Moore 1992, 76). Several other authors purport that the cyclic nature of rock s formal units nullifies any sense of direction in its harmonic progressions. In his book What to Listen for in Rock, Ken Stephenson posits that most phrases in rock music end with 9 Moore (1992) calls these patterns (77). 10 Everett (1999, 312) calls this particular progression rock defining. Carter (2005, 139) calls it a staple of the repertoire. 10

29 harmonically-open gestures that lack the ability to signify the end of a formal unit or song (Stephenson 2002, 70). 11 Due to this avoidance of harmonic closure, Stephenson recommends identifying chord successions rather than chord progressions (69). Similarly, Alf Björnberg speculates that chord successions are used as harmonic ostinati that are repeated to create a harmonic field within which melodic improvisations may freely operate (Björnberg 1989/2001, 4). Björnberg argues that these ostinati lack the forward-directed teleological character of tension-resolution [in] progressions of common-practice harmony (Björnberg 1989/2001, 14). Philip Tagg takes a clearer stance, suggesting that guitar-based harmony serves neither to provide long-term harmonic direction nor to construct musical narrative but rather to provide a fitting tonal dimension to underlying patterns of rhythm, meter, and periodicity [and] to generate an immediate sense of ongoing tonal movement (Tagg 2003, 13-14; emphasis mine). 12 While some scholars (Everett 2004, Doll 2007) claim that harmonic function is generated by an expected stepwise resolution of specific chord members, Stephenson argues that tendency tones have little influence upon listeners expectations of that chord s harmonic target. He refers specifically to secondary dominant chords in this regard. For instance, Stephenson claims that V/V is seldom followed by V in rock music (Stephenson 2002, 114). He cites several compelling examples in support of this claim. The Beatles Eight Days A Week features a V/V that moves up by minor third to IV. In the Byrds I ll Feel A Whole Lot Better, V/V moves directly to the tonic. Bad, Bad Leroy Brown by Jim Croce includes a V/V that moves to V/vi. According to Stephenson, most other secondary dominants found in rock music behave in a similarly erratic fashion. His culminating example, (Sittin On) The Dock of the Bay by Otis Redding, includes several non-traditional uses of secondary dominants (see Figure 2.1). Stephenson s examples show that chromatically altered chords such as secondary dominants do not resolve in a consistent way throughout the rock repertoire. Stephenson s argument inherently makes a good case for root-motion theory, in which predictions are unaffected by the quality of the chords in question. Even though its #5 does not resolve to the root of the following chord, V/vi-IV is an ascending-second progression that is no more anomalous than its diatonic counterpart iii-iv. Simply put, if 11 Presumably, closure and formal delineation are created through other musical means. 12 Some authors, such as Björnberg, propose (perhaps inadvertently) that harmonic function does not exist in rock music. Instead, sections of music are defined by particular chord progressions, but the transitions between chords within those sections are not governed by any specific set of principles and do not incite any particular expectations of listeners beyond the maintenance of an established pattern. 11

30 two chords have the same root, Stephenson s theory predicts that they will behave in the same way. Like Stephenson, Paul Carter (2005) presents a theory of pop-rock harmony founded upon fundamental bass lines. Carter differentiates progressive from retrogressive motion and suggests that their combination characterizes harmonic practice in pop-rock music. 13 Carter s definition of progression aligns with Meeùs s and Rameau s, but Carter assigns numbers to root motions representing their predictability: P3 for descending fifth, P2 for descending third, and P1 for ascending second. Following Stephenson, Carter proposes that retrogression is commonplace in pop-rock music and is defined by root motions complementary to those used in progressions. Appropriately, Carter also quantifies the predictability of retrogressive motions: R3 for ascending fifth, R2 for ascending third, and R1 for descending second. Thus, chains of chord roots ascending or descending by fourth would yield the most predictable successions, while chains of roots ascending or descending by second would result in unpredictable successions. Overall, root-motion theory is more robust when applied to rock music. The theory s central premise that listeners privilege chord roots over the voice leading of individual parts when hearing harmonic progressions is strongly supported by the preponderance of root-position triads and parallel voice leading in guitar-based repertoire. As Stephenson s examples suggest, the strength of our preference for hearing chord roots even seems to outweigh the presence of secondary leading tones. While its simplicity may not allow for particularly compelling or descriptive analyses, it presents a viable option for explaining our perception of harmonic successions in rock music. Scale-degree theory Scale-degree theory was established by Georg Vogler ( ) and Gottfried Weber ( ) in the early nineteenth century. In their respective theoretical works, Vogler and Weber each ascribed Roman numerals to chords built upon members of the diatonic scale (Bernstein 2002, ). Simon Sechter applied the nomenclature put forth by Vogler and Weber to Rameauvian fundamental bass theory (Bernstein 2002, 788-9). This theoretical infusion made explicit the notion that diatonic 13 Carter (2005) refers to retrogressive motion as regressive motion he uses the terms interchangeably (1). For the sake of clarity, I will only refer to retrogressive motion when discussing Carter s work. 12

31 chords are arranged hierarchically, and that each chord in the system has its own characteristic behavior. Sechter s writings laid the foundation for twentieth-century harmony treatises by Schoenberg, Schenker, and others (Bernstein 2002, 788-9). In contemporary theory textbooks, the tendencies of chords built upon specific scale degrees are often summarized by charts that reveal subtleties simple root-motion theory cannot; for instance, I-V is an acceptable ascending-fifth progression while V-ii is not. Dmitri Tymoczko likens these chord progression charts to first-order Markov models, which, in probability theory, describe the probability of transitions from one state of a system to another (Tymoczko 2003, 13). 14 Tymoczko provides a rational reconstruction of scale-degree theory that consists of a set of probabilities representing the likelihood that any single diatonic chord will move to any other. He obtains his probabilities through a statistical analysis of the Bach chorales, and his results largely support the principles of elementary diatonic harmony (Tymoczko 2003, 15). 15 With a few exceptions, random progressions generated by the model emulate those found in Bach s chorales. While more discriminating than root-motion theory, Tymoczko s model is not flawless. As he admits, the model is prone to generating unstylistic progressions such as I-vi-V-vi-V-vi-V-I. In this example, the presence of a single deceptive resolution is unaffected by any immediately preceding deceptive resolutions. We might describe this theory as having no memory: the probabilities of future events are independent of past events. 16 Similarly, location-specific progressions such as IV-I are also susceptible to misrepresentation by the model. Generated progressions are as likely to include IV-I at a phrase s beginning as at its end. Tymoczko posits that a potential solution would be to add additional states to the model that would account for these and other irregularities (such as idiomatic progressions that are inversion-specific or grammatically unorthodox). Of course, the constant addition of new states to the system complicates the model. Moreover, Tymoczko fails to acknowledge the possibility that harmonic syntax is linked to independent expectations of timing and location. Such factors deserve considerable thought and exceed the explanatory power of a pure scale-degree theory. 14 When applied to harmonic theory, we can interpret state to mean chord. 15 One might choose to criticize Tymoczko s conclusions, since his statistics are drawn from a single musical source. 16 This is true of all first-order Markov models. 13

32 To my knowledge, there has been no attempt at a formal and exhaustive scale-degree-theoretical approach to harmony in rock music. One issue (among many) is that stylistically-consistent investigations, such as Tymoczko s statistical survey of the Bach chorales, are almost impossible when virtually no two scholars agree on a corpus that codifies standard rock harmony similar to the way that Bach s chorales represent standard diatonic harmony. Walter Everett s work on the music of the Beatles includes a table of chord tendencies as they appear throughout The Beatles catalog (Everett 1999, ). In his 2004 article, Everett begins the requisite legwork for a more generalized theory of rock harmony, suggesting six categories for rock music based upon the degree to which a song displays the norms of tonal harmony. David Temperley and Trevor De Clercq s (2011) recently published corpus analysis of rock harmony provides statistical analyses of harmonic progressions used in 100 rock songs. Temperely and De Clercq s findings suggest that rock s harmonic profile differs somewhat from common-practice music; however, the authors admit that the relatively narrow corpus chosen for study may not be entirely representative of rock music as a whole (Temperley and De Clercq 2011, 69). More generalized theories, such as rootmotion theories and function theories, are therefore currently preferred for approaching rock s idiosyncratic harmonic language. Function theory Originally developed by Hugo Riemann (Bernstein 2002, 796), function theory proposes harmonic categories by grouping chords that, while literally constructed of different notes, sound and behave alike (Harrison 1994, 37). Specifically, Riemann s three functional categories were defined by the three primary triads: tonic, subdominant, and dominant. Each category was filled out with diatonic chords that shared two common tones with its constituent primary triad. 17 While the chords consist of distinct elements, the sense of function [that] they communicate is identical (Harrison 1994, 38). As Daniel Harrison explains, function is not something tangible, but rather the result of perceptual judgment on the part of the listener in response to hearing chords (Harrison 1994, 38). Importantly, function is a musical phenomenon entirely dependent upon context: it is meaningless without an established tonal center (Harrison 1994, 37). Typically, functional groups must proceed from subdominant to dominant to tonic. The identification of patterns of functional progression, resulting in 17 Agmon (1995) calls this a prototype-theoretic account of harmonic functions (199). 14

33 the codification of permissible successions, occurred independently in the development of the theory (Tymoczko 2003, 18). The grounds for categorical inclusion in most interpretations of Riemannian function theory are based upon the idea that members of the same category exhibit a certain degree of aural similarity. While this definition allows for a relatively clear rubric for inclusion, it inappropriately equates normative progressions with problematic ones (for instance, ii-iii-i vs. IV-V-I.) An alternative perspective, as Tymoczko points out, would be to group chords according to their most typical targets of resolution. In his reconstruction of function theory, Tymoczko defines categories by again observing the statistical frequency of two-chord diatonic successions in Bach s chorales. For each diatonic chord, Tymoczko supplies a vector of six probabilities that represent the likelihood of that chord moving to any of the remaining diatonic chords. He creates functional categories through a simple comparison of the probability vectors: if two chords vectors show a strong correlation, Tymoczko deems them members of the same functional group (Tymoczko 2003, 19). While Tymoczko s groups avoid the problems encountered in a pure function theory, they also have deficiencies most notably their inability to deal with chords such as IV that commonly serve multiple harmonic roles. In Bach s chorales, IV has a tendency to proceed either to I (as part of a plagal motion) or to V (as a pre-dominant harmony). Its probability vector therefore does not strongly correlate with that of the ii chord, which does not share the same plagal tendencies. Tymoczko s solution is to define two types of IV chords: those that serve a plagal role and those that serve a predominant function. Logically, this results in a strong correlation between the vectors of pre-dominant IV chords and ii chords. To some degree, however, Tymoczko is begging the question: he has parsed the probability vector until it resembles something suitable for a pre-dominant chord because he knows that IV should be pre-dominant. Moreover, the addition of exceptional cases for inclusion into functional groups, such as predominant IV and plagal IV, renders the groups less robust and weakens their explanatory power. Seen in this light, Tymoczko s perspective of function as categories of chords that share the same harmonic targets is merely a simplification of his reconstructed scale-degree theory. 18 Consequently, one could direct the same criticisms of scale-degree theory, discussed above, toward Tymoczko s reconstructed function theory. 18 Tymoczko freely concedes this point in his article (22). 15

34 In his book Harmonic Function in Chromatic Music (1994), Daniel Harrison presents an interpretation of function theory that accounts for the sometimes dual nature of chords functional allegiances. Harrison writes that harmonic function might be not the property of the chordal community as a whole but rather that of the individual constituents of that community (Harrison 1994, 43) in other words, harmonic function is conveyed by scale degrees rather than by chords. For example, the supertonic chord contains two subdominant scale degrees, 4 and 6, that assign it a relatively strong subdominant function. This is especially useful for functionally ambiguous chords such as the submediant and mediant triads, as well as the numerous chromatic chords on which Harrison focuses, such as augmented-sixth chords. Christopher Doll s theory of rock harmony borrows heavily from function theory. Like Harrison, Doll posits that scale degrees, not chords, are the purveyors of harmonic function. Although he acknowledges that the predictive strength of a chord is undeniably tied to numerous musical details, Doll s theory ascribes function according to abstract voice leading in scale-degree space (Doll 2007, 17). Most of Doll s analyses are based on the voice-leading potential projected by the scale-degree content of successive chords, which often goes unrealized on the musical surface. Doll s use of abstract voice-leading allows him to account for the idiomatic parallel motion used to connect chords in guitar-based music. Thus, Doll s theory is more akin to Harrison s work than to the Schenker-inspired analyses of Walter Everett (1999 and 2004), Lori Burns (2000), and others. Doll applies function theory idiosyncratically, suggesting new roles for functional categories, as well as presenting them hierarchically. To Doll, dominant, subdominant, and mediant chords predict tonic chords, and are thus each captured in a higher-level general category called pre-tonic function. Likewise, pre-subdominant, pre-dominant, and pre-mediant chords predict subdominant, dominant, and mediant chords, respectively. Doll permits a chord s membership in a functional category based upon its potential for stepwise resolutions of particular scale degrees. For instance, the motion from 6-5 corresponds to a chord with subdominant function resolving to tonic, while the combined motions of 7-1 and 2-1 or 2-3 correspond to a chord with dominant function resolving to tonic. A chord with mediant function resolves to tonic with the resolution of 7-1 (but not 2-1 or 2-3). Finally, the adjectives authentic, plagal, and mediant are applied to progressions in which the resolutions of chord members emulate his subdominant, dominant, and mediant functions but resolve to non-tonic chords. For example, using Doll s terms, an authentic pre-dominant includes the same pair of ascending and descending steps to the root and third as a dominant to tonic progression, but it moves 16

35 to a dominant chord instead of a tonic. Likewise, a plagal pre-dominant features the same descending step to the fifth of the chord found in subdominant to tonic progressions. Recognizing the ubiquitous b7-1 voice leading heard throughout the rock repertoire, Doll allows the pattern to be included in progressions identified as having dominant function. He calls these rogue dominants to distinguish them from tonal dominants which feature the leading-tone. Similarly, Doll allows b3-1 to substitute for 2-1 in songs that feature harmony drawn exclusively from the minor pentatonic scale. For example, the progression D7-B7 is a rogue dominant progression because its b3 (D) predicts a fall to 1 (B) while its b7 (A) predicts an ascent to 1 (B) (Doll 2007, 24-25). 19 The flexibility of Doll s theory is enticing: it allows for non-common-practice progressions to attain functional status rather than being cast aside as retrogressions. Nevertheless, Doll doesn t simply suggest that every chord has functional value. Indeed, he describes chords with a non-predictive character as neighboring or passing (and thus non-functional). He views retrogression as the delay or softening of a particular progression by an intervening non-functional chord (Doll 2007, 39-41). Depending on the musical situation, the same chords may be assigned different functions. For example, the succession IV-bVII-I could be interpreted authentic predominant, dominant, and tonic. In a different musical situation, the bvii chord could be heard as ornamental within a retrogression: subdominant, non-functional lower neighbor, tonic. Obviously context is highly important when determining harmonic function in Doll s system. 20 Scale-degree and function theories are philosophically different from root-motion theories because they ascribe agency to chords rather than to root relationships. These theories are therefore more discriminating than are root-motion theories: they are able to recognize important differences between successions that have otherwise identical root relationships. 21 Scale-degree and function theories are also much more descriptive than root-motion theories, potentially making them more useful for music analysis. 19 Evidently Doll considers only chord roots when defining exclusively minor pentatonic space. Otherwise, the D# in the B major-minor seventh chord would contradict his categorization of this example. Furthermore, Doll provides no opinion of the seemingly more intuitive voice leading which would maintain A as a common tone between the two chords. 20 Like Walter Everett (2004), Doll develops his theory thorough analysis of numerous musical examples. Similar to Everett s work, Doll s work may be best interpreted as a developing theory, as he does not provide distinct guidelines for determining a chord s function. 21 For instance, scale-degree and function theories do not equate I-V with V-ii, discussed previously. 17

36 Theories of voice leading Several scholars have applied techniques drawn from Schenkerian theory to the analysis of rock music. 22 Chief among them is Walter Everett, who claims that harmony in most rock music features an underlying tonal hierarchy that is embellished through voice-leading patterns, which he often reveals through Schenkerian analyses (Everett 2004, 6). In his 2004 article Making Sense of Rock s Tonal Systems, Everett divides the corpus of rock music from the early 1950s through the present into six categories (labeled 1-6), which he defines by the degree to which their music features commonpractice harmonic and contrapuntal tendencies. Everett considers these features, specifically leading-tone resolution, to be the primary means by which rock music conveys a sense of progression. 23 In his first category, Everett includes music that features thoroughly major-mode or minor-mode systems that resemble those used in the common practice (Everett 2004, 7). Category 2 includes music that is governed exclusively by functional counterpoint. Everett asserts that category 2 chord successions (such as the Hey Joe ascending-fifth sequence) use stepwise voice leading, enabling the music to sound highly deterministic without being truly functional (Everett 2004, 11). Music in Everett s third and fourth categories bear only a fleeting surface-level resemblance to common-practice contrapuntal and harmonic behavior. Finally, Everett places songs that exclusively utilize blues-influenced minor-pentatonic harmonic systems in his categories 5 and 6. In these categories, Everett describes the harmony as entirely non-functional and the voice-leading as severely compromised, stating that tonal centers are established through assertion rather than syntax (Everett 2004, 20). 24 In defining his six categories, Everett purports that as rock music moves further from common-practice tonality, chords become more interchangeable, and harmonic function ceases to impact on our musical expectations. The use of Schenkerian and other reductive techniques in theoretical and analytical writings about rock music has been met with some criticism. Both Allan Moore and Richard Middleton, for instance, claim that Schenkerian analyses privilege 22 In addition to Everett (1999, 2000, 2004), these include Matthew Brown (1997), Lori Burns (1997, 2000), and Timothy Koozin (2000), among many others. 23 This definition was gleaned from Everett s discussion of Paul Simon s The Sounds of Silence, in which he suggests the absence of the leading tone accounts for the lack of pull to the tonic, and the overall absence of any harmonic function at all (Everett 2004, 10). 24 Remarkably, Everett s descriptions of categories 5 and 6 align quite well with Björnberg s (1989/2001) harmonic theory. 18

37 harmony and counterpoint over rhythm and meter, which are often the sole determinants of a tonal center in rock music (Moore 1992, 77; Middleton 1990, 193). 25 As mentioned above, several scholars suggest that much of rock s harmonic palette is modally derived (Moore 1992 and 1999; Björnberg 1989/2001; Tagg 2003; Biamonte 2008) and transpires in repeated cycles that do not allow for the harmonic closure required by Schenkerian theory (Moore 1995, 186-7; Stephenson 2002, 70; Björnberg 1989/2001, 14). Specifically, Moore claims that closure in common-practice music is achieved by the stepwise resolutions of 2 and 7 at cadences. In rock music, these resolutions are often heavily obscured by a misalignment of melody and harmony, 26 and they are notably absent in the numerous songs that use subtonic and/or subdominant harmony as cadential agents (Moore 1995, 186-7). Perhaps most convincing is Moore s contention that rock musicians conceive of harmonies as indivisible units that are rarely governed by principles of voice-leading (Moore 1995, 181) a conjecture recognizing that most composers of rock music are guitarists who frequently connect chords with parallel motion for reasons of convenience and ease of performance on their instrument (Moore 1995, 190). For this reason, Moore considers interior voiceleading strands to be incidental parts that rarely have a linear role (Moore 1995, 190). This belief is echoed by Paul Carter (2005, 133-4) who states that pop-rock music is composed vertically as justification for emphasizing root motion rather than voice leading. Summary In this chapter, I have laid out the main premises of several competing theories of rock harmony. Stephenson and Carter (and, to a lesser extent, Moore) present root-motion theories with three central claims: 1. We attend to a chord s root when listening to harmony in rock music. 2. Harmonic syntax is governed by common intervals formed between successive chord roots. 3. Most importantly, musical style determines which root successions will generate listener expectations. 25 Everett refutes this, suggesting that such claims have been disproved through examples such as the important dominant anacruses in Billy Joel s She s Always a Woman (2004, 7). 26 Moore calls this the melodic-harmonic divorce (1995, 189). The concept was more thoroughly investigated by Temperley

38 Conversely, Everett s and Doll s theories propose that: 1. Counterpoint (perhaps in an abstract guise) is rock s most salient harmonic feature. 2. Harmonic syntax is controlled by voice-leading tendencies determined by tonal hierarchy 3. Rock and common-practice music have similar rules of harmonic syntax. 27 In addition, Björnberg proposes that individual chords possess no inherent functional information and are interchangeable in exclusively modal and pentatonic harmonic systems. 28 While the remainder of this dissertation will engage and scrutinize these premises, it is important to acknowledge the differences in scholarly aims motivating this study and those pursued by the authors surveyed in this chapter. In most cases, the work reviewed above centers on music analysis. This is certainly evident among the Schenker-inspired authors such as Everett, and one could argue that both Stephenson s and Carter s theories are analytically oriented. Christopher Doll s work, although seemingly fueled by the predictive power of functions, essentially requires listeners to make retrospective judgments of abstract voice leading. Thus, Doll s theory is also primarily an analytical endeavor. Analysts tend to publish highly complex, nuanced interpretations of specific musical works that, with careful study, can provide readers with a compelling and enriched musical experience. The experiments presented in this dissertation do not intend to either debunk or to validate analyses. Rather, the goal of this study is to address the fundamental assumptions that lie behind the theories that drive these analyses: do we have harmonic expectations, and if so, what are they? The perspectives reviewed in this chapter suggest some factors that might produce such expectations. The experiments presented in Chapters 4-6 of this dissertation attempt to evaluate the relative merit of each of these claims. 27 As discussed earlier, Doll s theory is clearly more flexible than Everett s. Nevertheless, Doll s functions subsume those recognized in common-practice tonality. 28 Everett s (2004) theories of harmony depend on the style of rock in question. Since his first four categories are firmly based in common-practice tonality, it can be generally said that Everett views rock through a tonal lens. Nevertheless, much like Björnberg, Everett proposes that individual chords are interchangeable in rock music that exclusively uses minor pentatonic harmony. 20

39 CHAPTER THREE HARMONIC FUNCTION AS EXPECTATION In the previous chapter, I outlined several theories of harmony and their applicability to the analysis of rock music. Each theory proposed an analytical explanation of why one chord can move to another. For all of their explanatory power, however, these theories don't attempt to reflect the listener's perspective. How is harmonic knowledge gained? How do harmonic rules manifest themselves in the listening experience? In this chapter, I will review three theories that address the epistemology of music: musical grammar, the theory of statistical learning (specifically the Hick-Hyman law), and schema theory. These theories are not mutually exclusive; parts of each will be used to contextualize my empirical investigation of harmonic function as harmonic expectation. Following a brief survey of pertinent empirical scholarship, I present the experimental framework for the studies of twelve-bar blues progressions that appear in the ensuing chapters. Musical grammar In 1973, Leonard Bernstein delivered a series of lectures about music at Harvard University. He campaigned for a new discipline of music scholarship that engaged the structure of music from the perspective of linguistics. In particular, Bernstein was inspired by the system of generative-transformational grammar championed by Noam Chomsky. Chomskian linguistics attempts to characterize the knowledge required to speak a language. How can we understand a sentence we have never heard before? According to linguistic theory, we have an unconscious knowledge of a system of rules, called a grammar, which enables us to generate possible sentences in a language. Our knowledge of grammar allows us to process and assign meaning to the unfamiliar sentence. Bernstein felt that this theory could potentially offer profound insight into music. The lectures galvanized new interest in interdisciplinary studies combining music and linguistics, perhaps best represented in the music-theoretical literature by Fred Lerdahl and Ray Jackendoff's landmark 1983 publication A Generative Theory of Tonal Music (henceforth, GTTM). In this work, Lerdahl and Jackendoff attempt to describe what we know when we understand the language of music. 21

40 Lerdahl and Jackendoff's theory of musical grammar presumes that we unconsciously understand a set of rules that generates all possible musical structures. Importantly, Lerdahl and Jackendoff qualify their intended meaning of the verb generate in this sense. Chomsky's generative theory does not provide an algorithm that manufactures all grammatical sentences; rather, it assigns structure to sentences. Likewise, Lerdahl and Jackendoff's theory does not compose all possible pieces of tonal music; rather, it provides a structural description of what an experienced listener infers while hearing of a piece of tonal music (Lerdahl and Jackendoff 1983, 6). Such a theory explains what enables us to understand music that we haven't heard before. Moreover, it reflects our ability to identify violations of musical grammar our ability to point out mistakes. This ability is honed with experience gained through our exposure to the ubiquitous music of our culture, which Lerdahl and Jackendoff suggest is common-practice Western tonal music (Lerdahl and Jackendoff 1983, 3-4). The relationship between language and music has also been a central concern among cognitive neuroscientists and cognitive psychologists. Several studies have illustrated that syntactical and harmonic incongruities elicit similar neurophysiological responses in similar locations in the brain (Besson et al 1998; Patel et al 1998). In his review of the corpus of comparative studies of linguistic and musical syntax, Aniruddh Patel suggests that language and music share a common set of syntactical processes (Patel 2003, 674). He claims we have implicit knowledge of principles of syntax which govern our ability to combine structural elements (words) into sequences (sentences) and allow us to detect incongruities in novel sequences. Patel proposes that sentence comprehension involves two distinct components: one that keeps track of predicted syntactic categories ( structural storage ) and one that connects incoming words to their dependent elements heard earlier in the sentence structure ( structural integration ). Both of these components consume neural resources, and this consumption is affected by the distance between elements in the structural hierarchy. Elements close in proximity consume fewer neural resources compared to those that are more distantly connected in the syntactic structure. Moreover, these distances can be quantified, allowing for empirical tests to confirm the system s predictions (Patel 2003, 677). According to Patel, the best music-theoretical parallel to this quantification of our consumption of neural resources during linguistic processing is Fred Lerdahl s model of tonal pitch space (Lerdahl 1988; 2001). In GTTM, Lerdahl and Jackendoff proposed that tonal hierarchy is formed through an understanding of musical events as recursive moments of tension and release specifically, the authentic cadence (Lerdahl and Jackendoff 1983, 214). The tonal pitch space model uses this hierarchy to quantify the 22

41 psychological distance between musical objects (Bigand, Parncutt, and Lerdahl 1996, 127). Among other things, Lerdahl s model represents the distance between any two musical events with a single integer that combines information about pitches, chords, and keys. Moreover, musical events are parsed with tree structures (like diagrams of sentence structures in linguistics) which affect distance measurements in a manner reflecting the music s hierarchy. In any given key, the most important chords are the ones closest in proximity on Lerdahl s model (Bigand, Parncutt, and Lerdahl 1996, 127). The model s distance metric reflects degrees of perceived musical tension (Bigand, Parncutt, and Lerdahl 1996, 128), which, like our processing of linguistic syntax, Patel speculates will correspond to our consumption of neural resources. Most pertinent to the present studies is the distance metric provided by Lerdahl s model. The metric is easily subjected to empirical testing, as demonstrated in a 1996 study reported by Emmanual Bigand, Richard Parncutt, and Fred Lerdahl. Participants were asked to rate the tension produced by the middle chord in a series of three-chord successions that always began and ended with a C-major triad. The results of this experiment showed a significant correlation between the participants ratings of tension and the distance in tonal pitch space between the second chord and the C-major tonic triad (133). While these results are by no means comprehensive or conclusive, they do suggest that Lerdahl s measurements could feasibly represent the processing differences we experience when listening to various chord progressions. The studies discussed above provide some insight into how rules of harmony are manifest in a listening experience. In language and in music, the rules of syntax allow us quickly and accurately to identify grammatical errors. We learn linguistic syntax through exposure and past experience (Lhost and Ashley 2006,1283). As Lerdahl and Jackendoff suggest (1983, 3-4), the ubiquity of common-practice tonal music has nurtured in us a similar understanding of music. Is it possible that other culturally pervasive musics could engender a similar knowledge of syntax? Both Mark Steedman (1984; 1996) and Richard Middleton (1990) speculate that this could be possible for rock music. Borrowing from Lerdahl and Jackendoff, both Steedman and Middleton even suggest that, in rock, the plagal cadence could supplant the authentic cadence at the highest level of recursion. How do listeners gain this knowledge? This question will be addressed in the remaining sections of this chapter. 23

42 Statistical learning Attempting to understand how we obtain knowledge, philosophers throughout history have generally debated from two wide-ranging perspectives: induction and deduction (Huron 2006, 59). Deduction proposes that knowledge is gained by deriving statements from a set of axioms. If the axioms are true, then the derived statements should also be true, as long as one arrives at those statements by logical means. Mathematics is founded upon deductive reasoning, and many music theories also purport to use deductive logic. 29 General statements and axioms formalize these theories; supporting evidence from the repertoire is gathered afterward. Conversely, the process of induction constructs principles through multiple observations of events. Inductive reasoning is plagued with a fundamental problem: no number of consistent observations can absolutely confirm a statement. Despite being inherently fallible, inductive reasoning has its advantages, foremost the ability to adapt to additional experiences and observations. Throughout our lives we experience countless sound events. Over time, we become sensitive to the rates at which these events occur. By induction, we develop an understanding of probabilities for these events, which helps shape our expectations about the future (Huron 2006, 60). Throughout the last fifty years, experimental research has shown that humans are keenly aware of the degree to which various stimuli are present in their environment. W.E. Hick and Ray Hyman studied this phenomenon, independently discovering a relationship between the frequency of occurrence of some stimulus in our environment and the speed at which we are able to process it. For instance, if you were asked to identify the sex of people in a series of photographs, your response time would be fastest when looking at pictures of people you know, slightly slower for pictures of people from your culture that you don t know, and slowest for people from outside of your culture. The reason for this is that we are able to process more familiar, or more frequently occurring, stimuli faster than unfamiliar stimuli. Known as the Hick-Hyman law, this principle can be generalized to many types of stimuli, including musical ones (Huron 2006, 63). The theory of statistical learning suggests that much of our musical knowledge is gained from the frequency of certain musical events in our environment. 30 Several 29 Some examples that come to mind are numerous tuning systems derived from the perfect consonances, Schenkerian theory, and more abstract theories such as Forte s (1973) set theory, and Callender, Quinn, and Tymoczko s theory of chord geometry (2006). 30 In this case, our environment refers to all of our musical experiences, conscious and subconscious. 24

43 music scholars have studied the statistics of music in various ways. Research by Ken ichi Miyazaki (1990) and David Huron and Jasba Simpson (1994) has shown that absolute pitch possessors are able to process the pitch classes associated with white keys on a piano more quickly, presumably because those pitch classes occur more frequently in music a musical instance of the Hick-Hyman law. Jenny Saffran et al (1999) found that participants were quicker and more accurate when identifying the three-pitch sequences that occurred most frequently in seven-minute pitch successions. Other expectations derived from music s statistical regularities include pitch proximity (melodies employ sequences of tones that are close in pitch), step declination (large melodic intervals tend to ascend while small intervals tend to descend), step inertia (melodic steps are followed by steps in the same direction), melodic regression (melodic leaps reverse direction and move towards a mean pitch), and melodic arch (melodies descend at the end of a phrase) (Huron 2006, 73-89). Carol Krumhansl (1990) and Bret Aarden (2003) have both documented that listeners are sensitive to the frequency distribution of scale degrees in tonal music. Krumhansl (1990) extended her investigation to include chord sequences and again revealed a remarkable correlation between listeners' harmonic expectations and the most frequent chords in the common practice. The studies cited above provide simple, well-documented accounts of how statistics can explain our culturally learned musical knowledge. Might certain events occur in rock music more frequently than in common-practice music? I speculate that that they do. Have these events pervaded our musical experience to the point of affecting our understanding and expectations of music? This question is much more difficult to answer. In Western culture, rock music has been ubiquitous for the better part of sixty years, and the blues became increasingly widespread early in the twentieth century. The musical properties upon which most of the aforementioned studies are based have been consistent for much longer and have pervaded a greater number of musical cultures. Nevertheless, other than common-practice Western tonal music, the genre most likely to have influenced the twenty-first-century North American listener's statistical understanding of music is rock. Both a comparison of the relative frequency of harmonic events in rock and classical music and an investigation of whether listeners have different harmonic expectations when listening to rock are warranted. Even if the theory of statistical learning can account for a unique set of harmonic expectations in rock music, it does not offer an explanation of why some people are potentially able to speak two musical languages with different grammatical systems. 25

44 More importantly, how do we know when to activate one musical language over another? Schema theory offers a possible answer to this question. Schema theory In his book A Classic Turn of Phrase, Robert Gjerdingen engages the notion of interpretive context and its significant role in our understanding of music. Musically, interpretive context is perhaps best explained by a (relatively) simple example: stability and instability. Stability and instability are entirely dependent upon context. In certain situations (such as a passage in C major), a C-major triad is highly stable, while in others (such as a passage in B minor), the chord is quite unstable. From a cognitive perspective, how do we understand musical context? Gjerdingen suggests the application of schema theory. Schemata are defined differently in the numerous disciplines in which they are employed. Among psychologists, schemata are considered cognitive structures that are formed on the basis of past experience with objects, scenes, or events and consisting of a set of (usually unconscious) expectations about what things look like and/or the order in which they occur (Gjerdingen 1988, 4; after Jean Mandler). Gjerdingen highlights six characteristics that all schemata share: they have variables they can embed within one another they represent knowledge at all levels of abstraction they represent knowledge rather than definitions they are active processes they function by processing data and evaluating its goodness of fit within the schema itself The input data upon which a schema bases its evaluation of context can otherwise be referred to as a feature. While some features are innately recognized by all people around the world, others are learned through cultural experience (Gjerdingen 1988, 5). Western listeners might learn to identify specific sounds of instruments, chord qualities, scale types, and so on. There are many musical features that are highly context dependent, such as harmonic relationships. For example, if we hear a triple suspension at a final cadence in a chorale, how do we know that the suspended pitches are not part of the cadential tonic chord? According to schema theory, we know this 26

45 because such a chord (root plus the suspended notes) does not exist as a harmonic feature in this particular musical genre. At the outset of the musical experience, various features of the chorale motivated us to invoke common-practice schemata, including harmonic syntax and voice leading, which provide us with a larger interpretive context. Features and schemata have a reciprocal relationship. Features inform schemata selection, which in turn helps to detect additional features. Cognitively, this works like a logical process of elimination. When we encounter a feature, we eliminate all schemata with which that feature is not associated. We continue to accumulate features and eliminate schemata until an appropriate schema becomes apparent. Once this occurs, our chosen schema allows us actively to seek out the remaining features. At this point, the schema achieves a higher level : having established a context for our experience, we are able to begin the process of filling in the blanks (Gjerdingen 1988, 6-7). This process represents our activation of expectations. Studies have shown that listeners activate common-practice schemata in anticipation of musical stimuli. In other words, listeners have certain musical expectations even before hearing a sound. For instance, David Huron studied listeners' interpretations of a single imagined tone. His results showed that in the absence of any musical context, listeners assumed the imagined tone to be the tonic note of a major key (Huron 2006, 207). In a similar experiment, Huron played a single pitch for his participants and asked them to imagine a harmonization of that pitch. The vast majority of listeners imagined an equal-tempered major triad (Huron 2006, 207). Huron's results reveal that most North American listeners preemptively activate representative schemata of the common practice. 31 David Huron explains schema theory from the perspective of evolutionary biology. Recall that schemata represent different sets of expectations that we apply in particular situations. In dire circumstances, quickly and accurately predicting the outcome of events may be a matter of life and death. From a biological standpoint, if expectations are enabled though the implementation of specific schemata, we must quickly apply and (when necessary) switch schemata in response to any given situation. If listeners possess two or more distinct genre-specific sets of musical expectations, how do they know when to apply one particular set rather than another? Schema theory suggests that listeners attend to contextual cues (or features) that eventually influence the 31 It should be noted that major keys and triads are also features present in many non-common-practice musical styles. Indeed, identifying the degree to which these features overlap stylistic boundaries is one of the aims of this dissertation. 27

46 implementation of a particular schema. In these terms, harmonic expectation is represented by the listener's enabling of a higher-level schema activated by the presence of numerous musical features or lower-level schemata. Thus, if distinct harmonic expectations exist for blues and common-practice music, those expectations should be triggered by the presence of idiom-specific musical features. Thus far, I have made little mention of the specific musical features that may trigger various schemata. One reason is that schemata are complex hierarchical models that sometimes defy concrete definitions (consider, for example, common-practice tonal music ). While conceding that high-level schemata may forever remain vague theoretical constructs, we can certainly identify some of their most characteristic and concrete features. In the case of common-practice tonal music, these features would likely include tertian harmony, diatonicism, and the major scale. In contrast, low-level schematic features of blues might be instrumentation (guitar, bass, drums, and a vocalist), so-called blue notes, a shuffle rhythm, and so on. Note that the features at the lowest level of the hierarchy are those that can be most quickly processed. In a fascinating study, Robert Gjerdingen and David Perrott (2008) showed that listeners require as little as 250 milliseconds to correctly identify musical genre, suggesting that the most important information for invoking schemata occurs within the first second of hearing the music and is most likely communicated through features such as timbre, instrumentation, and tuning. Expectation In 1956, Leonard Meyer speculated that music s meaning and emotional content are communicated through the fulfillment and/or denial of expectations (Meyer 1956, 34). Although his investigations were driven by psychological research, including Gestalt principles, his claims remained purely speculative at the time (Huron 2006, 2). When Meyer published his influential book Emotion and Meaning in Music (Meyer 1956), the mind was considered a black box among psychologists (Margulis 2007, ). Fortunately, Meyer s work has inspired numerous studies of expectation over the last fifty years, many of which aim to support and/or recast his theories with empirical evidence (Huron 2006, 3). Studying expectation poses several problems that must be addressed. First, definitions of expectation can be tenuous or vague. Throughout the music theory literature, authors routinely refer to musical expectations as a means of supporting their analytical arguments. While these observations often allow for compelling analyses, 28

47 seemingly ad hoc definitions of expectation can sometimes lead to confusion. In a recent article, Elizabeth Margulis (2007) presents a taxonomical framework with five defining criteria for considering expectation in music (198) 32 : 1. The origin of an expectation may arise from reflexes, conceptual knowledge, mechanisms of statistical learning (as discussed above), logic, or hard-wiring (205). 2. The nature of the expectation can be either conscious or unconscious. Are you aware of the expectation while you re experiencing it, or do you only realize it after that expectation has been violated? (205). 3. The time course of an expectation refers to its duration and temporal specificity. For instance, one could have a long-range expectation for a piece of tonal music to have closure in the home key. The time course of this expectation is long and unspecific regarding the exact moment at which it might be fulfilled. Alternatively, one could have a momentary, time-specific expectation that a dominant seventh chord on the last beat of a measure will resolve to a tonic chord on the first beat of the next measure (206). 4. The object is targeted by the expectation, and could include chords, phrases, melodic pitches, motives, topics, tempi, etc. (206) 5. The fulfillment or denial of an expectation can yield a consequence that impacts our thoughts, emotions, behaviors, or other expectations (206). In his book Sweet Anticipation, David Huron (2006) presents a formal model of expectation abbreviated as the ITPRA model. While the model represents a general theory of expectation, Huron almost exclusively uses musical examples to support his claims. The five components of Huron s model represent the psychological and biological responses that occur when we process an event, musical or otherwise (Huron 2006, 12-14). 1. Imagination Response (pre-outcome). A long-term prediction of the outcome of a future event. Biologically, this forecasting is accompanied by a feeling generated by the body in response to previewing the outcome of a future event. A musical 32 Margulis continues with several analytical examples that promote more thorough discussions of each of these criteria. 29

48 example of this would be our expectation that a tonal piece will end in the home key, and we may imagine the last cadence long before it actually happens. 2. Tension Response (pre-outcome). The mental and corporeal preparation for an anticipated event. Huron describes watching someone who is about to pop a balloon with a needle. One often undergoes motor preparation by tensing up, and perceptual preparation by paying closer attention to all things involved with the anticipated event. In music, a good example would be when a concerto soloist is playing the cadential trill prior to the end of the cadenza. 3. Prediction Response (post-outcome). When a stimulus is accurately predicted, the body provides the reward of a positive (or positively valenced) emotional response. Conversely, when the stimulus is not predicted, the emotional response is negatively valenced. Importantly, confirmation of expected outcomes usually induces a positively valenced response, even when the expected outcome is bad. This facet of Huron s model will be explained in more detail below. 4. Reaction Response (post-outcome). The onset of this response occurs shortly (approximately 150ms) after the outcome of the event and produces an emotional response to the worst-case assessment of the outcome. Huron cites reflexes, such as the startle response or the orienting response, as instances of reaction responses (Huron 2006, 418). 5. Appraisal Response (post-outcome). This is the final and most complex assessment of the outcome that involves conscious thought. It is independent of and not necessarily consistent with the reaction response. Expectation is at least as difficult to measure as it is to define. While numerous methods have been used to investigate expectation, 33 I will only discuss the two that are most pertinent to my study of harmony and the scholarly literature from which it is drawn. Recall the Hick-Hyman law that states the speed of processing a stimulus is inversely proportional to the familiarity of that stimulus (Huron 2006, 415). In addition to providing support for the theory of statistical learning, the law also presents a more general fact about expectation: accurate prediction facilitates perception. In other 33 These include non-verbal response modes such as head turning paradigms, heart-rate monitoring, and brainwave monitoring such as the evoked response potential (ERP) (Huron 2006, 49-52). Other response modes include method of production (Schmuckler 1988, 1989; Larson 1997, 2002) and betting paradigms (Huron 2006, 53-55). 30

49 words, if participants are required to perform some task in response to an event, accurate predictions of that event will enhance their speed and precision when performing the task. Music cognition experiments that measure reaction time tend to present stimuli in two phases: primes and targets. The prime establishes a musical context; the target event immediately follows the prime and is assessed by the listener according to some criterion. For example, in a classic priming experiment, participants hear stimuli consisting of two chords and are asked whether the second chord is in tune or out of tune. In this case, the second chord is the target while the first chord is the prime. On the surface, it may seem that this experiment aims to investigate participants perception of intonation. The real goal, however, is to see whether the relationship between the prime and target chords affects participants ability to make intonation judgments. Since prediction facilitates perception, participants should more quickly and accurately judge the intonation of highly predictable targets. When primed by a G major-minor seventh (GMm7) chord, for instance, a participant might predict that a C-major triad will follow. It is far less likely that this GMm7 chord would lead the participant to predict a C#-minor triad to come next. Asking participants to convey their predictions directly would be complicated and potentially misleading because these predictions are often unconscious and difficult to articulate. Judging the intonation of a chord is a clear forced-choice response that can easily be measured in terms of accuracy and speed. In the above example, if the participant has strong expectations for a C-major target to follow a G Mm7 prime, it will be reflected by the speed and accuracy with which the participant assesses the intonation of the C-major triad. The converse would be true for the C#-major triad: the participant would be slower and less accurate when judging its intonation because it is highly unexpected when following a G-major triad. While several studies have measured the reaction time of listeners asked to judge the intonation of the target chord (Bharucha and Stoeckig 1986 and 1987; Justus and Bharucha 2001), the response task for this approach is not restricted to an intonation judgment. Other investigators have asked participants whether the target chord was consonant or dissonant (Bigand and Pinaeau 1997; Bigand et al 1999; Poulin-Charronat et al 2005), or to identify the timbre of the target chord (Tillman and Lebrun-Guillaud 2006). In each case, chords widely considered to be closely related to the prime were processed faster and with more precision than were unrelated chords. With a few exceptions, each of the studies mentioned above measures a listener s expectations at a specific moment. In Margulis s terms, the time course of these expectations is very specific and very short in duration. The results likely measured expectancy at the prediction phase of Huron s ITPRA model. Experiments investigating 31

50 harmonic expectation in longer musical events, in contrast, are likely assessing participants' appraisal responses. For instance, one might be interested in how the second chord of a five-chord succession impacts a listener's response to the entire stimulus. The investigator would likely want the listener to wait until the five-chord succession transpired before providing a response. A reaction time measurement would be inappropriate in this case, since the time separating the onset of the second chord and the response is so long (recall that reaction response occurs approximately 150ms after the outcome of the event). Reaction time measures are therefore not well suited for these types of experiments, nor are they useful for investigating expectations with longer and less specific time courses. In 1979, Carol Krumhansl and Roger Shepard conducted an experiment in which listeners were presented with a musical context the first seven notes of a C-major scale and assessed the goodness of fit of a single note (the probe tone ) that followed the scale. The results showed that experienced listeners consistently preferred specific pitches (especially members of the tonic triad) in a manner that reflected the traditional models of tonal hierarchy (Krumhansl and Shepard 1979, 592). This was the first of many music cognition experiments that asked listeners to provide ratings in response to musical stimuli. In subsequent studies of harmony, the goodness of fit question has been recast as degree of tension (Bigand, Parncutt, and Lerdahl 1996), the degree of belonging, and degree of completion (Bigand and Pineau 1997; Tillman and Lebrun-Guillaud 2006). One might reasonably wonder what these rating scales have to do with expectation. Recall that in the prediction phase of Huron s ITPRA model, the body produces a positively valenced emotional response when the prediction is correct. In effect, we are rewarded for easily processing a stimulus. When we provide a qualitative assessment of a stimulus, part of our subjective rating reflects this emotional response to the prediction. Although we think we have assessed the stimulus itself, we ve actually confused it with our processing of that stimulus. Psychologists refer to this phenomenon as misattribution (Huron 2006, 135). Our ratings are directly linked with our ability to predict targets, as both Huron (2006; 45, 136) and Aarden (2003, 2) point out. 34 When we claim that a stimulus sounds good, presumably hearing it produced a positive emotional response. 34 While degree of tension and degree of belonging do not directly ask for qualitative judgments, it is plausible that listeners could interpret less tense and belongs as good qualities, while more tense and doesn t belong might have more negative connotations. If participants interpret these descriptions in this way, they may be misattributing their positively or negatively valenced responses as they would with more overt descriptors such as good and bad. 32

51 Both Huron (2006) and Aarden (2003) identify difficulties with probe-tone designs and with the rating scales that accompany them. One problem with this method is that it is quite tedious, requiring a large number of trials (Huron 2006, 46). This can lead to long experiments in which participants could easily fatigue. Using Shepard tones (Shepard 1964) may reduce the number of possible trials by eliminating distinctions in voicing and register among stimuli; on the other hand, the experimenter cannot observe the potential impact of these factors. Perhaps more problematic is the fact that probetone designs require the music to stop and wait for a response, making it difficult for the investigator to discern whether a listener s rating refers to the musical connection between the context and stimulus or to perceptual closure (Huron 2006, 46). Aarden (2003) compared the scale-degree profiles from Krumhansl s early experiments with the distribution of scale degrees throughout a large body of tonal music. He found a strong correlation between Krumhansl s profiles and with the occurrence rates of phrase-terminating scale degrees (Huron 2006, 152). While Krumhansl s profiles do reflect listener s expectations for pitch continuations, it is unclear whether these expectations apply to mid-phrase contexts. In spite of the methodological problems just mentioned, experimental designs using post hoc ratings have been employed successfully by several researchers. In addition to Krumhansl and her collaborators, Bigand, Parncutt, and Lerdahl (1996), Bigand and Pineau (1997), and Tillman and Lebrun-Guillaud (2006) used post hoc rating systems in experimental studies of harmonic expectation. Indeed, Tillman and Lebrun-Guillaud suggest that post hoc judgments may be a better means of revealing interactions between pitch and time (Tillman and Lebrun-Guillaud 2006, ), since these parameters are initially processed independently and are only integrated during later stages of cognitive processing. 35 In Margulis s terms, the nature and time course of our expectations might be more appropriately measured using a subjective assessment. Studies of harmonic expectation Empirical studies of harmony have provided evidence supporting some of the most basic claims of common-practice music theory. In 1982, Carol Krumhansl, Jamshed J. Bharucha, and Edward Kessler reported an experiment in which listeners 35 Tillmann and Lebrun-Guillaud base these claims on their interpretation of research by Peretz and Morais (1989). 33

52 assessed the relatedness of chord pairs in C major, G major, and A minor. Their results revealed that listeners considered chords constructed on the same contextual scale degree to be functionally equivalent. Across keys, chord pairings were rated similarly, regardless of whether the chords or even chord qualities literally matched (Krumhansl, Bharucha, and Kessler 1982, 30). Bharucha and Krumhansl (1983) found similar results in a thorough study of two-chord successions in C major and F-sharp major contexts. In their study, listeners preferences gave more weight to the second chord in the succession and depended strongly on that chord s frequency of occurrence in the tonal repertoire (Krumhansl 1990, 193). These results give credence to the notion that our knowledge of common-practice harmony is a function of statistical learning. More interestingly, Krumhansl assigned values to chord pairs found on Walter Piston s table of root progressions and found a significant correlation between Piston s evaluations and the rating data from her and Bharucha s experiment (Krumhansl 1990, 195), indicating that listeners have a systematic preference for chord progressions considered by Piston to be most common (Krumhansl 1990, 195). In a series of experiments, Bharucha and Stoeckig (1986 and 1987) measured reaction time to investigate harmonic expectancy in two-chord successions. Their results revealed that listeners perform faster and more accurate intonation judgments when chords are in tune and closely related to the prime, and also when chords are mistuned and distantly related to the prime. Given that accurate expectation facilitates perception, Bharucha and Stoeckig ascertained that listeners have strong expectations for well tuned closely related chords. Moreover, listeners showed a bias toward closely related chords, often inaccurately judging them as in tune. 36 The studies discussed above all investigated harmonic expectation in two-chord successions. More recent studies have broadened this context and engaged longer stimuli. Bigand and Pineau (1997) examined the effect of global context on harmonic expectancy by creating stimuli that included the same prime and target pair at the end of an eight-chord sequence. Since stimuli could only be distinguished by the harmonic context created by the first six chords in the sequence, the results could not be attributed to sensory priming. Specifically, each stimulus ended with a G-major triad followed by a C-major triad and the preceding six chords determined the degree to which those chords sounded like a conventional phrase ending (V-I in C major), or an unconventional phrase ending (I-IV in G major). In this case, the prime consisted of all but the final chord and established the musical context in which the participants assess 36 In other words, listeners associated good intonation with goodness of fit. 34

53 the final chord. In a fast-reaction judgment, participants processed conventional progressions more quickly and accurately, suggesting that the influence of global harmonic context may be better understood in the light of current models of tonal cognition instead of sensory priming (Bigand and Pineau 1997, 1105). In other words, our ability to anticipate the next chord in a succession is influenced to some extent by all of the preceding chords that form the tonal context. In a series of follow-up studies, Bigand, Madurell, Tillman, and Pineau (1999) investigated the effect of duration, temporal regularity, and long-range closure on global contexts that again terminated with identical two-chord successions. The results of their first two experiments (addressing duration) showed that the context effect diminished as the length of the prime decreased. This suggests that the processing of the target chord depends on all of the information accumulated from the beginning of the sequence (190). Bigand et al s (1999) culminating experiment engaged expectancy for long-range closure. Chord sequences were split into two phrases separated by a fermata. In all cases, chord sequences ended with a D-major triad followed by a G-major triad. As projected, listeners fastest processing occurred in contexts in which both phrases were firmly in G major and the slowest processing occurred for sequences entirely in D major. In the middle were contexts that began in G major and modulated to D major. The authors claim that this means expectancy occurs at multiple levels: facilitation is best when the target chord is expected at both the high and intermediate levels, reduced when the target chord is expected solely at the high level, and reduced further when it is not expected at either level (193-4). The results of this experiment lend some support to hierarchical theories of tonal music, such as Lerdahl and Jackendoff s GTTM (1983). Expectation and timing In the early development of her model of dynamic attending, Mari Riess Jones claimed that models of expectation (developed prior to her publication in 1981) focused too much on what and not enough on when (Jones 1982a, 36). Generally, Jones argues that these two facets of expectation are inseparable and directly interact with one another. Regarding musical expectation, Jones suggests that listeners can more easily attend to temporally predictable melodic events (Jones 1982b, 11). Similarly, certain melodic events involving contour, melodic interval, and tonal stability combine with rhythmic and metrical accent patterns to create hierarchical temporal regularities or which Jones calls Joint Accent Structures (Jones 1987, 625). While this may seem 35

54 obvious, it touches upon the difficult question of whether temporal events and tonal events interact when listeners form expectations about music. If this is the case, do listeners weigh these factors equally when forming expectations? Furthermore, are listeners expectations formed by a simple additive combination of these factors, or does the musical whole invoke stronger expectancies than the sum of its parts? Several other researchers addressing these questions have reached conflicting conclusions. Gabrielsson (1973) and Monahan and Carterette (1985) found that the effects of rhythmic and pitch dimensions were negatively correlated when listeners judged the similarity of two melodies, suggesting that listeners attend to these musical dimensions separately. Palmer and Krumhansl (1987a) asked listeners to rate the quality of fugue subjects and found that pitch and temporal components had an additive but independent influence on listeners ratings. In a later study, Palmer and Krumhansl (1987b) asked listeners to rate the quality or completeness of a musical phrase presented in either a strictly pitch (isochronous), strictly rhythmic, or a combined pitch/rhythmic domain. They determined that ratings in the combined domain could be predicted as a function of listeners ratings of the same phrases heard in either the separate pitch or rhythmic contexts, again suggesting that these musical domains have an additive relationship as opposed to an interactive one. All of these authors demonstrated that temporal and melodic factors independently influence listeners who are asked to provide similarity or qualitative judgments for a musical stimulus. However, several other researchers have found evidence suggesting an interactive relationship between the temporal and pitch domains. Jones, Boltz, and Kidd (1982) showed that listeners more adeptly discriminated pitch changes when they occurred at important temporal events. Deutsch (1980) showed that participants memory for melodies was enhanced by coinciding pitch and temporal structures; when the pitch and rhythm contexts conflicted, participants were less successful. In a melody-recognition task, Jones (1987) showed that rhythm and contour interact to impact listeners feeling of familiarity with a tune. Marilyn Boltz (1989) attempted to determine whether timing, tonality, or their interaction impacted the perceived completion of a melody. Her results showed main effects both for tonality and for timing, as well as an interaction of those two factors in judgments of completeness. In a 1993 experiment, Boltz again asked listeners to rate the sense of closure conveyed by melodies with variant or invariant metrical structures. In this experiment, Boltz examined the effects of timing and melody on longer-range expectations and found that anticipatory attending only occurred when invariant periodicity coincided with appropriate ending pitches (Boltz 1993, 593). To summarize, the findings of these 36

55 authors suggest that joint expectancies of pitch and timing are stronger than either of those expectancies alone. 37 The majority of experimental studies investigating both pitch and temporal domains have specifically used melodies as musical stimuli. Research pertaining to the potential interaction of harmony and timing is much less widespread. In a 1994 study, Schmuckler and Boltz investigated the influences of the temporal and harmonic domains on expectation. In a series of four experiments, participants heard four-chord phrases that featured common-practice cadences. The phrases were varied with regard to the timing and type of closing chords and also the phrase s temporal periodicity. Depending on the iteration of the experiment, participants responded to these stimuli either rating the fit of the final chord or by indicating (through a two-option forced-choice question) whether or not the final chord belonged in the phrase. Among the most pertinent of Schmuckler s and Boltz s findings was a three-way interaction of ending time, temporal periodicity, and closing chord. In contexts with invariant periodicity, early endings received lower ratings than on-time and late endings, but, perhaps more interestingly, ending time only affected ratings in phrases that concluded with high-expectancy chords. In stimuli with tenuous periodicity, the timing of closing chords had no effect on participants ratings. Similarly, there was a significant interaction between cadence type, periodicity, and ending time. Half and deceptive cadences were judged as more appropriate when they occurred on time or late, while late-arriving authentic cadences actually received slightly higher ratings than on-time authentic cadences. Schuckler and Boltz speculate that this occurs because the strong sense of completion conveyed by the authentic cadence overrides the influence of periodicity or timing. In a 1999 study, Bigand et al investigated the effect of temporal organization on longer-range harmonic expectation. Participants were asked to judge the intonation of the final chord in several two-phrase excerpts that were designed to invoke low-, medium-, and high-level harmonic expectancies. Their results did not show a main effect of temporal organization, but an interaction occurred between temporal organization and harmonic structure. Participants took longer to process chords if those chords were both harmonically and temporally unexpected. The authors interpreted this result as supporting the notion that music cognition is a dynamic context-specific 37 This was first hypothesized by Boltz prior to undertaking her studies (Boltz 1989,15). 37

56 activity that is not guided solely by abstract knowledge of the tonal hierarchy (Bigand et al 1999, 194). 38 Tillman and Lebrun-Guillaud (2006) presented participants with eight-chord successions that varied in harmonic context, 39 periodicity, and timing of the final chord. Participants were asked to judge the timbre of the final chord. The authors results showed that aberrations from the prevailing periodicity, certain harmonic contexts, and early endings caused participants to respond more slowly and less accurately; however, there was no interaction between any of these factors (Tillman and Lebrun-Guillaud 2006, 350). In a series of follow-up experiments, the authors found that the absence of periodicity made future-oriented attending almost impossible. Likewise, the authors speculated that when participants are asked to focus on local-level events (as they were in the first experiment s timbre judgment task) they tend not to be influenced by the global context. When asked to provide subjective judgments of completion, participants are able to better reflect on the musical whole, and their judgments are thus appropriately influenced by an interaction of harmonic context and timing (Tillman and Lebrun-Guillaud 2006, 355). The numerous studies discussed above employed different designs and response modes. It is certainly possible their inconsistent results simply reflect the fact that our cognition of melody, harmony, and rhythm functions according to the specific task at hand. With Palmer s and Krumhansl s work (1987a and 1987b) as a notable exception, experiments that utilized subjective, post-hoc judgment tasks as response modes demonstrated interactive relationship between temporality and pitch (Jones, Boltz, and Kidd 1982; Boltz 1989, 1993; Schmuckler and Boltz 1994; Tillman and Lebrun-Guillaud 2006). Experiments utilizing more objective response modes, such as those that measured reaction time or tested memory, suggested that temporality and pitch have an additive relationship (Gabrielsson 1973; Deutsch 1980; Monahan and Carerette 1985; Tillman and Lebrun-Guillaud 2006). Harmonic expectation in twelve-bar blues progressions The experiments presented in the following three chapters were influenced by many of the studies and theories discussed in this chapter. Although all three 38 This theory is one of the core arguments for Jones s theory of dynamic attending (Jones 1987). 39 In this experiment, all stimuli used the same penultimate and final chords. The harmonic function of these chords was altered by the context established by the first six chords of the succession. 38

57 experiments engage different facets of expectation, they all share certain design features. Foremost is the rating scale response mode, which allows for global judgments of stimuli and addresses expectation by way of misattribution: a positive rating will be understood as reflecting a predicted event. Second, since these experiments intend to investigate possible differences in the expectations produced by blues and common-practice music, the stimuli used in each experiment include several features that firmly establish stylistic context. As Gjerdingen and Perrot (2008) demonstrated, stylistic features quickly activate musical schemata, presumably prompting listeners to engage the appropriate set of stylistically associated expectations. Together, the three studies aim to contribute insight to the growing body of research that addresses the following four broad questions. Does rock music elicit expectations that are different from those held for common-practice music? This question is central to this dissertation and will serve as the driving force for its inquiries, speculations, and conclusions. It certainly lies behind the music-theoretical arguments discussed in Chapter 1; additionally, it remains the elephant in the room for conclusions drawn by much of the aforementioned theoretical and empirical work discussed in this chapter. Lerdahl and Jackendoff claimed that our ability to identify violations of musical grammar is honed by our exposure to the ubiquitous music of our culture (Lerdahl and Jackendoff 1983, 3-4). Common-practice music has undoubtedly pervaded our culture for hundreds of years. Is it possible that alternate musical systems could have reached the same status? Empirical studies have shown that our identification of syntactical errors in music relates to the distributional frequency of events found in the style in which the music is presented. Very few studies have addressed expectations for music with a hierarchy differing from that of commonpractice tonal music. Studies have shown participants to be sensitive to the distribution hierarchy in their native non-european music (Castellano et al 1984; Von Hippel, Huron, and Harnish 2006; Khrumhansl et al 2000). While the expertise of these participants had likely been cultivated by a lifetime of musical experience, both Castellano et al (1984) and Krumhansl et al (2000) found that even non-experts attended to the distributional hierarchy present in the stimuli, even when doing so required them to suppress their prior musical knowledge. Jonaitis and Saffran (2009) found that participants were able to detect mistakes in novel musical systems learned entirely through exposure during the course of an experiment. As a culture, we certainly have been exposed to a greater amount of common-practice music than we have rock music. Nevertheless, rock music has been at the forefront of our musical culture for over sixty years, and, as the experimental evidence suggests, this amount of exposure may be 39

58 sufficient for us to engender an understanding of rock s distributional hierarchy of musical events. It is the aim of this dissertation to investigate whether the idiosyncrasies of rock s harmonic language have impacted our musical expectations to a degree that separates them from those held for common-practice music. Do listeners have graded expectations of harmony in rock music? The majority of studies of harmonic expectation include relatively few chords as stimuli. In priming paradigms, chords used as targets are either very closely or very distantly related to primes. 40 While this allows for a sound experimental design, conclusions have typically been limited to claiming that listeners expect closely related targets to follow closely related primes. However, it has also been demonstrated albeit in decidedly fewer studies that we have graded expectations when presented with various combinations of diatonic triads (Krumhansl 1990; Lhost and Ashley 2006). Bigand, Parncutt, and Lerdahl (1996) included non-diatonic triads and seventh chords along with diatonic triads in their study; however, these chords were always preceded and followed by tonic harmony. The first experiment presented in this dissertation takes these studies as a point of departure. Stimuli include both diatonic and non-diatonic triads preceded or followed by a single primary triad (I, IV, or V). One of its aims is to provide a more detailed description of listeners expectations of harmony when presented with a wider variety of chords than have previously been investigated. The aforementioned results published by both Krumhansl (1990) and Bigand et al (1996) correlated with quantitative models of tonal hierarchy. 41 These metrics will provide a means of comparing the findings of this experiment with those demonstrated by previous empirical studies and illustrated by music-theoretical models. What is the relationship between expectations of temporality and harmony in a rock music context? Some scholars have suggested that rock music operates in fouror eight-measure phrase units within which the harmonic behavior is relatively free (Björnberg 1989/2001). This implies that the structural boundaries of these phrase units should be perceptually salient events demarcated by a change in harmony; a fact that is evident in a vast majority of twelve-bar blues songs (Lhost and Ashley 2006, 1284). 40 Among the most obvious examples of such studies are those by Jamshed Jay Bharucha and his numerous collaborators (Bharucha and Stoeckig 1986; Tekman and Bharucha 1998; Justus and Bharucha 2001). However, even in experiments that did not use a priming paradigm, it has been most common for stimuli used in studies of harmony to include only two levels of this variable (a common chord and an uncommon chord), such as Schmuckler 1989, Steinbaus et al 2006, and others. 41 Krumhansl s metric was based on Piston s table of chord-root progressions. While Piston s table was not expressly quantitative, his strict categorization of chord pairs was suitable enough for calculating statistical correlation. 40

59 Another ubiquitous feature of rock music is the prevalence of common time, with quarter-note beats emphasized by the consistent presence of drums. This emphasis on rhythmic periodicity perhaps explains why melodic and harmonic onsets and termini in rock music are often slightly misaligned with the metrical framework of the song and/or with each other. David Temperley (2007) refers to this phenomenon as the melodicharmonic divorce in rock music. As discussed previously in this chapter, the body of research that has investigated expectation of periodicity, timing, and harmony together has found that disrupted or absent periodicity negates expectations for all but the most salient harmonic events namely authentic cadences (Schmuckler and Boltz 1994; Tillman and Lebrund-Guillaud 2006). Early event onsets are least expected (Tillman and Lebrund-Guillaud 2006) and also affect expectations for long-range temporal regularity, specifically cadences occurring on strong beats in successive phrases (Bigand et al 1999). The second experiment in this dissertation explores the potential effects of periodicity and timing on harmonic expectation in the first two phrases of a twelve-bar blues song. It investigates whether listeners temporal expectations are rigid (strictly adhering to the metrical structure of the schema), graded (higher ratings for metrically strong events among stimuli with atypical timing), or non-existent (no preference for timing among all stimuli). Moreover, it addresses whether temporal disruptions affect listeners harmonic expectations. Is it possible that our expectation for a chord change to occur at a specific location outweighs our expectation of what that chord will be? In other words, is our expectation of timing stronger than our expectation of harmony? Does harmony affect expectations of musical form (or vice versa)? While several studies have investigated the impact of harmony in longer musical contexts (Smith and Melara 1990; Bigand and Pineau 1997; Bigand et al 1999), very few have used contexts that potentially elicit strong expectations themselves. In a 2006 experiment, Elizabeth Lhost and Ric Ashley investigated the impact of chord substitutions on harmonic expectation in twelve-bar blues songs. Stimuli consisted of complete twelve-bar patterns that included a single diatonic chord substitution in one of three locations: m.5, m.9, and m.11. Three substitutions were used in each location and were categorized by the authors as expected, acceptable, or unacceptable chords in these locations. The chords were chosen based on their frequency of occurrence in a corpus of blues songs. Expected chords occurred frequently and consistently in the same location, while unacceptable chords rarely occurred throughout the corpus. Chords were categorized as acceptable if they occurred relatively frequently in the repertoire, but not at that corresponding location. Lhost and Ashley demonstrated that participants had 41

60 graded harmonic expectations, consistently differentiating among the three chord categories. They also found that participants made faster judgments when the chord substitution occurred later in the excerpt, suggesting that harmonic expectations are narrowed when contextual evidence is increased. Participants response times were impacted by location and chord type, though the effect was not consistent across type or location. Nevertheless, Lhost and Ashley concluded that judgments of fit (expectations) are affected by contextual information (the presence of a known musical schema such as a twelve-bar blues form) and not solely by general schematic expectations of Western tonal music (Lhost and Ashley 2006, 1287). Lhost and Ashley s findings raise two points pertinent to the final experiment in this dissertation. The first is that expectations of specific schemata can override more general musical expectations. In their experiment, this was reflected by participants higher ratings for chords expected in specific contexts (such as IV in m.5) over chords that generally receive high ratings in goodness of fit judgments (such as V). My experiment investigates this issue more closely by using as stimuli a greater number of replacement chords (all major and minor triads) in more locations within the twelve-bar blues form. Furthermore, since these stimuli all feature harmonic motion to or from primary triads, the data is apt for comparison with the results of my first experiment. The comparison of ratings for two-chord successions heard in the abstract with ratings for the same successions heard in a longer and more specific musical context will allow for a greater understanding of the role that context plays in harmonic expectation. Second, the experiment investigates whether harmony shapes our expectations of form within the twelve-bar blues. Lhost and Ashley found that participants were more sensitive (and thus reacted more quickly) to harmonic events in the last phrase of the twelve-bar form. Since they only used three chords in each location (and did not use the same chords in each location), Lhost and Ashley were unable to investigate the relationship between these domains in greater detail. 42 Is it possible that specific chords serve to orient the listener within the larger musical structure? For instance, does the presence of V serve as a structural marker for the last phrase in the form, or does it simply sound good in any location because it is highly predictable? To my knowledge, an empirical investigation such as this has yet to be undertaken, and would provide insight into our understanding of multiple levels of harmonic expectation in a form central to the rock idiom. 42 Lhost and Ashley admitted that they may have inappropriately categorized some of the chords used in their experiment (Lhost and Ashley 2006, 1287). My experiment will have no such difficulty, since it uses all major and minor triads as stimuli. 42

61 CHAPTER FOUR THE EFFECT OF STYLE-PRIMING ON HARMONIC EXPECTATION Music theorists, as discussed in previous chapters, often suggest that chord successions in common-practice music are governed by syntax, and cognitive studies have confirmed that listeners expect chord successions that adhere to these syntactical rules. There is less agreement among music theorists regarding principles of chord succession in non-common-practice music, such as blues or rock. Some suggest that the syntax is the same for both contexts, while others propose new syntactical rules for blues/rock music. This study investigates whether listeners have different expectations for chord successions when the chords are presented in two different stylistic contexts: blues/rock music and classical music. Harmonic expectation can be influenced by numerous factors, including chord relatedness (Bharucha and Stoeckig 1986 and 1987; Krumhansl 1990), global harmonic context (Bigand and Pineau 1997), temporal organization (Bigand et al 1999; Tillman and Lebrun-Guillaud 2006), and voice leading (Poulin-Charronnat et al 2005). While the question of stylistic context is not explicitly raised in these studies, it is likely that participants in these experiments interpreted the stimuli as representing common-practice music. As David Huron has noted (Huron 2006, 207), North American listeners tend to activate common-practice musical schemata even in the absence of stylistic context. The current study has two aims. First, it examines listener expectations of two-chord successions that include the so-called primary triads (I, IV, and V); that is, all major and minor triads preceding I, IV, and V, and all major and minor triads following I, IV, and V. 43 Primary triads are central to the harmonic structure of both the twelve-bar blues and common-practice music. Second, the experiment investigates the effect of stylistic context on listeners expectations. To create this musical context, the key for each trial is established by a commercial recording that activates the appropriate stylistic schema. Recall that listeners require less than 200 milliseconds to identify a 43 The decision to limit stimuli to these combinations was one of practicality. It would have been too taxing for participants to hear all possible combinations of major and minor triads. Chromatic chords could have been excluded; however, modally inflected scale degrees (and the chords they are built upon) are important to the blues and rock aesthetic. Given the prominence of the primary triads in the twelvebar blues structure, this was a reasonable compromise. 43

62 musical genre (Gjerdingen and Perrot 2008). Presumably, when participants hear a stylistically clear excerpt, they should be inclined to assess the ensuing harmonic progression in the context provided by the recording. If the data exhibit differences between ratings of identical two-chord successions it would support the theory that listeners may possess two (or more) distinct sets of harmonic expectations. EXPERIMENT 1 Task In this experiment, two groups of subjects (N = 56) listened to pairs of triads and rated how good each harmonic succession sounded. Each triad pair was primed by a brief key-confirming excerpt of either blues/rock or classical music drawn from commercial recordings, always establishing the key of Eb major. Stimuli were presented in blocks corresponding to the musical style of the prime to strengthen listeners notions of stylistic context. Hypotheses Participants will provide high ratings for successions that feature common-practice characteristics such as typical root motion. While both blocks will receive high ratings for this type of harmonic motion, ratings will be higher when these progressions are primed by classical music cues. In common-practice theory, chords with dominant function incite strong expectations for a tonic chord to follow. Christopher Doll describes bvii and biii (which contain the subtonic rather than the traditional leading tone) as rogue dominants in the rock idiom (Doll 2007, 24-25). If these chords have a similar function in rock music, then they should pique the same expectations. Thus, idiomatic blues/rock progressions such as bvii-i, V-IV, and biii-i will receive higher ratings when primed by blues/rock cues. More broadly, a wider variety of chords often lead to tonic harmony in blues/rock music. Thus, in this experiment, successions that end on tonic will receive higher ratings when primed by blues/rock cues. As discussed in Chapter 2, ratings will be interpreted as levels of expectancy in accordance with the concept of misattribution. 44

63 Participants All participants were volunteers enrolled in Music Theory 3 (a required course for undergraduate music majors) at Florida State University. The 33 female and 23 male participants ranged in age from 18 to 23 years (average of years). Stimuli Four representative recordings, two each from the blues/rock and classical repertories, served as contextual cues for the experiment. Boot Hill and Give Me Back My Wig, both by Stevie Ray Vaughn and Double Trouble, were chosen as the representative blues/rock recordings. The first movement of Mozart s Concerto for Two Pianos and Orchestra No. 10 in Eb Major K. 365 and the first movement of Mozart s Symphony No. 1 in Eb major K. 16, recorded by the English Baroque Soloists (conducted by John Eliot Gardiner) and the Academy of St. Martin-in-the-Fields (conducted by Neville Marriner) respectively, were chosen as the representative classical recordings. All recordings included an extended passage that clearly established Eb major as the tonal center. Within stylistic groups, selections were made based on consistency of timbre and idiomatic features. Between stylistic groups, the recordings were chosen for their disparity in this same regard. One excerpt was selected from each recording and edited to a length of 24 seconds. Single two-second clips were selected from each of the 24-second excerpts to be used as shorter cues. The triads that followed these contextual cues were constructed with three Shepard tones to control for any influence of chord inversion or register. 44 Each chord was 750ms in length; successive chords were separated by 500ms of silence. Question prompts, contextual cues, and chord successions were combined with multi-track audio editing software. Any volume differences between the recordings and the synthesized chords were normalized 44 Shepard tones are complex tones that consist of ten octave-related sine tones sounded together. The amplitudes of the sine tones share a logarithmic relationship that results in a fusion that makes it nearly impossible for listeners to discern the sounding octave (Shepard 1964). When triads are constructed with Shepard tones, it is unlikely that listeners can distinguish inversion. 45

64 Equipment Question prompts were synthesized using the MARY Text-to-Speech System. Recordings were transcoded from CD to.wav files with Exact Audio Copy and edited with Audacity. Shepard tones were synthesized with Csound and combined into chords with Audacity. 45 Each stimulus element was then combined, edited, and rendered in REAPER, a multi-track audio editing environment. Finally, all stimuli were compiled and burned onto CD. All of these tasks were completed on a Lenovo R61i laptop computer. During the experiment proper, stimuli were played for participants over a high-quality stereo system in a quiet classroom. Design and Procedure Table 4.1 outlines the design of this experiment. Participants were randomly assigned to one of two groups: group 1 heard only blues/rock cues while group 2 heard only classical cues. Before the experiment proper, participants heard a brief description of the procedure, followed by two practice questions that allowed them to grow accustomed to the speed of the trials and to the rating scale. 46 Trials were presented to listeners in blocks of 67 or 69 trials corresponding to the recordings used in the stimuli. 47 The first key- and style-establishing cue of each block lasted 24 seconds. Subsequent trials in each block used a single two-second cue drawn from the same excerpt. The two-chord successions used in each group were presented in random order across both blocks. The chords used in this experiment included all non-redundant successions of major and minor triads to and from each of the primary triads (I, IV, or V). Overall, 132 successions were used as stimuli. 48 With the inclusion of four non-data questions, 136 trials were heard in each group. Following each trial, participants were given four seconds to rate how good the chord succession sounded on a scale from 1( sounds bad ) to 6 ( sounds good ). After 45 Clifton Callender graciously provided the Csound Shepard tone templates. 46 A transcript of the instructions for this experiment is included in Appendix A. 47 There were 66 trials in each block. In addition, three non-data trials were heard in the first block and one non-data trial was heard in the second block, resulting in 69 and 67 trials per block, respectively. 48 There are three primary triads, twenty-three remaining major and minor triads, and two orderings: 3*23*2=138. Six of these combinations occur twice in the collection of 138: IV-I, I-IV, V-I, I-V, IV-V, and V-IV. The redundancies were removed from the stimuli, leaving 132 unique successions. 46

65 the experiment, participants completed a survey of basic biographical information as well as time spent in university, musical training, primary instruments played, and secondary instruments played. The survey also asked participants to indicate their time spent listening to, performing, composing or arranging, and general interest in ten different musical genres. Results and Discussion The observations presented below are organized in relation to the theoretical systems discussed in Chapters 2 and 3. In each case, the effects of stylistic context are also observed to ascertain any differences in listeners expectations when primed with blues or classical music. Root-motion theory A one-way analysis of variance (ANOVA) revealed a main effect of root motion (p <.001). 49 Table 4.2 and Figure 4.1 show that listeners gave high ratings for successions that included one of the three most prevalent root motions found in major-key common-practice music: descending fifth, descending minor third, and ascending major second. Root motion by ascending perfect fifth and ascending major third also received high ratings; however, it is important to realize that two successions producing ascending fifth root motion involved exclusively primary triads (I-V and IV-I). Overall, listeners strongly preferred successions that included multiple primary triads (p <.001; see Table 4.3 and Figure 4.2); when individual relevant data subsets are grouped by ordered pitch-class interval (OPCI), we can see that successions containing multiple primary triads were rated significantly higher in each case. Table 4.4 and Figures depict the overall ratings grouped by the number of primary triads used as well as the ratings for the individual relevant data subsets grouped by OPCI. Table 4.5 and Figure 4.7 show that, among successions that do not include multiple primary triads or multiple primary triad roots (such as i-iv or v-i), there was a main effect of root 49 Since the chord successions were constructed with Shepard tones, it is perhaps most accurate to refer to the intervals formed between chord roots as ordered pitch-class intervals (OPCIs). For the purpose of drawing a parallel between these results and the idioms of common-practice harmony, I will sometimes refer to root motion by common intervals, such as descending fifths, even though pitch height (and thus, interval direction ) in these successions has no objective meaning. 47

66 motion on ratings (p <.001). 50 Note that these results are nearly identical to those presented in Figure 4.2, suggesting that the presence of multiple primary triads was not solely responsible for listeners high ratings of successions that included common root motion. None of these main effects interacted with stylistic context at the level of significance. While the results revealed that listeners have heightened expectations for certain root progressions, these expectations were significantly affected by scale-degree context. A series of one-way ANOVAs revealed a main effect of first chord on ratings across all data grouped by OPCI. The p-values for these tests are summarized in Table 4.6 and indicate that there were significant differences between ratings within all OPCI groups. These results show that listeners discriminate among specific instances of the same root motion. 51 For instance, descending fifth progressions that began on II, ii, or V (yielding the progressions, II-V, ii-v, V-i, and V-I, respectively) were rated significantly higher than those that began on any other chord. There was no interaction between first chord and style among any of these groups of data. In Chapter 1, I suggested that root motion absent of scale-degree context 52 was a plausible foundation for a theory of rock harmony, since rock progressions tend to be less dependent upon a goal-oriented motion toward the tonic. The significant differences among mean ratings for particular instances of root progressions indicate that successions with equivalent root motion do not incite the same level of expectancy in listeners. Moreover, the lack of significant interaction between first chord and style suggests that root motion alone does not provide a good model for listeners expectations of two-chord successions when primed by either a classical or blues context. Comparison with other quantitative ratings of chord pairs Given that listeners distinguished among specific instances of root progressions, a more detailed statistical analysis of chord combinations was performed. A univariate ANOVA reveals a significant preference for specific chord successions (p <.001). Mean 50 Granted, upon removing these progressions from the data set, only four ascending-fifth successions remained: V-ii, V-II, bvii-iv, and bvii-iv. 51 While it may be tempting to delve deeper into these data subsets, the unbalanced number of successions between subsets makes it difficult to draw more detailed conclusions about specific root motions. 52 Tymoczko calls this scale-degree symmetry (Tymoczko 2003, 3). 48

67 ratings for individual successions grouped by the primary chord on which they started or ended are shown in Table 4.7/Figure 4.8 and Table 4.8/Figure 4.9, respectively. Contrary to my hypotheses, there was no overall significant interaction between first chord, second chord, and style. 53 In order to interpret these results, the mean ratings for select diatonic successions were compared with findings reported by Carol Krumhansl (1990). Krumhansl s experiment, which included only diatonic successions, showed a distinct listener preference for the progressions used most frequently in common-practice music. To support her claims, Krumhansl compared her results with Walter Piston s table of usual root progressions (Piston 1941/1978), which assesses the frequency with which one diatonic chord follows another. For instance, Piston states that ii is followed by V, sometimes followed by IV or vi, and less often followed by I and iii. For the purpose of comparison, Krumhansl assigned values to each entry on Piston s table: 3 to anything labeled followed by, 2 to sometimes followed by, 1 to less often followed by, and 0 otherwise. Krumhansl found that these values significantly correlated with her results. Listener ratings for chord successions examined in this study strongly and significantly correlate with Krumhansl s findings. The mean ratings for each succession observed in Krumhansl, Piston, and my studies are illustrated in Table 4.9; their correlations are shown in Table Interestingly, mean ratings for successions heard in the blues context had a stronger correlation with Krumhansl s results (.829, p <.001) than did successions heard in classical contexts (.816, p <.001). Ratings in both blues and classical contexts correlated most weakly with Krumhansl s ranking of chords found on Piston s table (.622 for blues,.521 for classical). Given that Krumhansl used an adhoc scale to assign these rankings, this result is unsurprising Fred Lerdahl's Tonal Pitch Space model (Lerdahl 1988, 2001) includes a general metric for measuring the perceptual distance between two chords. Defined briefly, the system tallies the number of spaces on the chromatic circle of fifths that separate the keys in which the chords are heard, the number of spaces on the diatonic circle of fifths that separate the scale-degree roots of the chords in question, and the number of common tones shared at four levels of stability (key, triad, root/fifth, and root). The greater the number, the larger the perceived distance is between the two chords. mentioned in Chapter 2, these values correlated with tension ratings provided by As 53 A series of one-way ANOVAs revealed that 9 (out of 132) specific chord combinations were affected by stylistic context. Since there was no overall interaction and no obvious relationship between these specific combinations, they have not been further investigated. A table containing p-values and mean differences between all 132 chord combinations is provided in the Appendix D. 49

68 participants for 50 chord successions heard in an experiment by Bigand, Parncutt, and Lerdahl (1996). Likewise, the results from this experiment significantly correlated with distance measurements based on Lerdahl's system (p <.001). A comparison of correlations between the mean ratings for all successions heard in this experiment (primed by blues, classical, and combined) and distance measurements using Lerdahl's metric is shown in Table Unfortunately, the small sample size in this experiment does not allow us to test the differences among correlations for statistical significance. Most likely, the strength of correlation between the results of this experiment and other quantitative rating systems corresponds with the range of ratings and the number of samples found within each system. The strongest correlation appears to be with Krumhansl s results. Both Piston and Krumhansl only include diatonic chords; thus, when more chords are included (as is the case with the comparison to Lerdahl s ratings), the correlation appears to weaken. With only a few exceptions, stylistic context did not affect listeners ratings of specific chord successions. 55 These results suggest that listeners hold similar expectations of two-chord successions in both common-practice and blues contexts. This is supported by the significant preference for common-practice root motion in both contexts and the strong correlation with Krumhansl s results. To some extent, these expectations reflect theorists generalizations about typical root motion between successive chords. While all of the typical common-practice root progressions (descending fifth, descending third, and ascending second Meeus s dominant progressions ) received high ratings, their presence was not exclusive among the highest-rated chord successions. Ascending-fifth and ascending-third root motion also received high ratings, suggesting that root-motion theory should not be comprised of strictly dominant or strictly subdominant progressions: listeners appear to expect both types in each of these styles. 54 Negative correlation refers to an inverse relationship between two numbers. Thus, larger numbers in Lerdahl s system (representing greater distance and less relatedness ) are reflected by lower ratings. 55 It is certainly possible that the style cue did not sufficiently prime the participants, or that participants were not adequately experienced in both genres. Additional studies will be necessary in order to discern the impact of the neutral timbre of the Shepard tones on the results of this experiment. 50

69 Chord content Overall, listeners rated diatonic successions significantly higher than non-diatonic successions (p <.001; see Table 4.12 and Figure 4.10). As is illustrated by Table 4.13 and Figure 4.11, listeners specifically rated diatonic successions highest, and rated successions that included primary mixture chords 56 higher than successions that included other chromatic chords (e.g., secondary dominants and the Neapolitan). However, a univariate ANOVA comparing the effect of style (blues/rock vs. classical) and succession type (diatonic vs. non-diatonic) on ratings reveals that this preference for diatonic successions was significantly less pronounced in a blues context. Participants gave slightly (but significantly) higher rankings (p =.015) for diatonic successions primed by classical music than they did for diatonic successions primed by blues music. The opposite was true for non-diatonic successions, which were rated higher in a blues context than they were in a classical context (p =.004). These results are presented in Table 4.14 and illustrated in Figure A similar interaction was revealed by a univariate ANOVA comparing style and specific succession type (diatonic, mixture, and chromatic; p =.001). A comparison of mean ratings for these succession types is presented in Table 4.15 and plotted graphically in Figure The findings suggest that in a blues context, listeners are more tolerant of chords from outside of the key. This could be explained by the fact that popular music likely uses chromatic chords more frequently and/or in ways that would be considered unorthodox in the common practice. One could speculate that with a more equal frequency distribution of chromatic and diatonic chords across the repertoire, expectations for diatonic chords could be weakened. In common-practice music that is mostly diatonic, the probabilities of occurrence are more unevenly distributed across the range of possible chords. In Chapter 1, I speculated that the idiomatic chord construction and parallel voice leading in guitar-based rock music might cause listeners to attend to root motion when listening to chord successions in this style. If so, listeners might hear chords with the same root as having essentially the same function: expectations could be similar for ii and II, iv and IV, v and V, and so on. While this notion is compatible with traditional music theory, the argument for rock harmony discussed in Chapter 1 claimed that expectations of root motion would be so strong as to render non-root chord members functionally irrelevant. In other words, chromaticized thirds and fifths would have little 56 Primary mixture chords include i, biii, iv, v, bvi, and bvii. 51

70 impact on our expectations for what chord comes next. The results of this experiment conflict with this hypothesis. In both classical and blues contexts, listeners preferred purely diatonic successions to chromatic successions with diatonic chord roots (p <.001). These findings are illustrated in Table 4.16 and Figure The idea that non-root chord members have little effect upon expectations might suggest that chords containing chromatic pitches with strong harmonic implications, such as secondary dominants, may have much weaker tendencies in a rock setting. This argument s chief proponent is Ken Stephenson (2002), who went so far as to say that in rock music, secondary dominants tend not to resolve to their local tonics. However, in this study listeners rated successions that included a secondary dominant highest when that secondary dominant was followed by its implied target. Although it was the only instance that allowed for investigation, 57 II also known as V/V was rated highest when preceding V (M = 4.55). When approaching I and IV, the mean ratings were significantly lower (M = 3.75 and M = 3.80, respectively; p=.001). Nevertheless, this experiment was not exhaustive enough to make substantial claims about the function of secondary dominant chords in a blues context. Phrase openings Chord successions began with one of four possible openings: I, IV, V, or a non-primary triad. A one-way ANOVA revealed a significant main effect of opening chord category on rating (p <.001): listeners strongly preferred non-primary triad openings to any primary triad opening (see Table 4.17 and Figure 4.15). 58 Overall, no 57 While one could interpret I to be V/IV or IV to be V/bVII, it is perceptually simpler to hear them as diatonic chords. Lerdahl makes the same argument when calculating the distance between pairs of chords in his tonal pitch space model (Lerdahl 2001). Unless context provides reason not to do so, it is preferable to take the simplest path when processing the connection between two chords. Likewise, other chromatic chords heard in the experiment could certainly be interpreted as secondary dominants, but their intended resolutions were never heard throughout the course of the experiment they only resolved to unintended chords. V/V was the only clear secondary dominant used in the trials that resolved both to its intended target and to other chords, thus providing a means for fairly investigating Stephenson s claim. 58 Presumably, this is because listeners preferred chord successions that ended on primary triads. This is not to suggest that listeners generally prefer non-primary triad openings in blues or classical music, but rather it suggests a preference borne out of the design of this experiment. It is reasonable to speculate that listeners consider primary triads to be the most stable and predictable of all triads. This sense of stability and predictability was likely augmented by the frequency at which primary triads occurred throughout this experiment: they were heard at least once in every trial. Since most successions included only a single primary triad, listeners may simply prefer successions to end with (rather than begin on) the most stable and predictable chord in the succession. 52

71 significant differences emerged among primary triad openings; however, an interaction occurred between primary triad openings and stylistic context (p =.014). Among primary triad openings in a classical context, the mean differences showed a significant preference for tonic and dominant openings over subdominant openings. Conversely, in a blues context, listeners rated subdominant openings slightly higher than both tonic and dominant openings, although the differences among ratings were not significant. A comparison of mean ratings appears in Table 4.18 and is illustrated graphically in Figure The distinction between listeners preferences for primary triad openings in classical and blues contexts may reflect the differences between idiomatic phrase openings in the two styles. 59 In common-practice music, phrases most frequently begin with tonic harmony or dominant harmony; openings on other chords are much less typical. Conversely, it is possible that phrases in rock music begin with a greater variety of chords. The twelve-bar blues, for instance, includes three phrases that are defined by three different opening chords. Going beyond the twelve-bar blues, the thirty-two bar song form often includes an eight-measure bridge section (the B section of a typical AABA form) that opens with (and otherwise emphasizes) the subdominant. More generally, bridge sections in rock music frequently begin with an abrupt move to a non-tonic chord that serves as a sectional marker and often as a means of modulation to a contrasting key. Given these stylistic tendencies, it is unsurprising that listeners do not show a preference among primary triad openings in a blues context. Phrase endings A one-way ANOVA revealed that listeners preferred successions ending on primary triads (p <.001). As Table 4.19 and Figure 4.17 illustrate, tonic endings were most preferred, subdominant and dominant endings were rated in the middle, and non-primary endings (that is, chords other than I, IV, and V) were least preferred. There was no significant mean difference between subdominant and dominant endings, but there was significant interaction between closing chord and stylistic context (p =.019). In classical contexts, tonic and dominant endings were preferred over 59 The timbral distinction between the prime and the chord successions suggests that the two-chord successions could be heard as very short phrases, in the loosest sense of the term. Obviously it is quite uncommon for listeners to consider anything that short to be a phrase, regardless of its stylistic context. A future study investigating phrase openings and endings in more realistic musical contexts would be warranted to confirm the findings reported here. 53

72 subdominant endings; in blues contexts, tonic endings were rated highest, whereas subdominant and dominant endings were rated equally. These results are shown in Table 4.20 and Figure The preference for successions primed by classical music to end on tonic or dominant harmony is likely related to the statistical prominence of those two chords among phrase endings in common-practice repertoire. While off-tonic/off-dominant phrase openings do occur, albeit infrequently, off-tonic/off-dominant endings are virtually non-existent in non-modulating phrases such as those used in the experiment. 60 The results for successions heard in a blues context are more difficult to interpret. Phrases ending in tonic or dominant abound in rock music, with dominant endings typically reserved for pre-chorus or bridge sections to prepare the listener for the imminent return of tonic harmony. 61 Rock music often contains sections defined by contrasting harmony that more disparately connects with the tonality of the surrounding sections. Listeners equal preference for dominant and subdominant endings could possibly reflect this tendency; however, these results could simply indicate the general ubiquity of subdominant harmony throughout the repertoire as a whole. Conclusions The strong correlation found between the results of this experiment and other studies (Krumhansl 1990, Lerdahl 2001) suggests that diatonic chords could have similar functions in blues and classical music. It is less clear whether listeners expect non-diatonic chords to follow the same syntactical rules in both contexts. Whether the higher ratings of non-diatonic progressions in blues contexts indicate a greater tolerance for expectancy violations, weaker expectations, or the fulfillment of an entirely different set of harmonic expectations for blues music is a question that would require further investigation through additional experiments Although two-triad successions could be considered tonally ambiguous, it is unlikely that these successions would be confidently interpreted in another key, especially since the tonic was confirmed before each individual trial. 61 This presumes that listeners have not only activated a twelve-bar blues schema, but also a higherlevel rock music or popular music schema in which such endings are more common. 62 As mentioned previously, II-V was the only succession used in this experiment that qualifies as a true instance of a secondary dominant chord resolving to its local tonic. Listeners rated successions that started with II highest when the chord resolved to V in both classical and blues contexts. The remaining non-diatonic major triads, which could each be understood as a secondary dominant, never resolved to their local tonics. While participants did rate these successions higher when they were heard in the blues 54

73 The statistical frequency of specific chord successions in the genres of music studied in this experiment could provide another explanation for the effect of style on listeners ratings of non-diatonic successions. In common-practice music it is typical for non-diatonic chords to be interpreted as secondary dominants that resolve to their target local tonics in instances of tonicization or modulation. It is much rarer to find non-diatonic chords that resolve to non-target chords. As Ken Stephenson has argued, non-diatonic chords traditionally thought of as secondary dominants often resolve to non-target chords in rock music. One such example he cites is Otis Redding s (Sittin On) The Dock Of The Bay, which includes the succession I-III-IV-II in the A section of its AABA form (Stephenson 2002, 116). In this example, both III and II could be considered secondary dominants that resolve to non-targets. 63 Stephenson cites several similar examples that suggest rock music contains more of these types of successions than can be found in common-practice music. Moreover, when a rock song includes non-diatonic harmony (as in the Otis Redding example), the diatonic and non-diatonic content of the song is nearly proportionally equal because the formal sections in rock songs commonly utilize a repeated succession of only three or four chords, with each chord occupying a large portion of the harmony over the course of the song. In comparison, common-practice music typically includes non-diatonic chords in more fleeting situations. Throughout an equivalent duration of music, non-diatonic chords occupy proportionally less time than when they occur in a rock music setting. While this speculation needs to be supported by a thorough survey of the harmonic practice of rock music, we may surmise that the results of this experiment could be a product of statistical learning. Listeners have certain expectations for non-diatonic chord successions in rock music, based on the statistical frequency of non-diatonic progressions in that genre. Since these successions occur less frequently in classical music, listeners expectations are weaker when the successions are presented in that stylistic context. It is possible that voice leading could affect listeners expectations of harmony, especially for non-diatonic chords. In common-practice music, chromatic chords are typically carefully controlled by voice leading. Participants ratings could have been affected by unfulfilled expectations of particular common-practice voice-leading rules. context, ratings might have been different if the stimuli had included more instances of secondary dominants resolving to local tonics. 63 Another interpretation could be that the target chords are simply omitted. If one were to add vi into the second half of the second measure and V into the second half of the fourth measure, the rather conventional progression I-V/vi-vi-IV-V/V-V would result. 55

74 Likewise, listeners could have different expectations of voice leading for guitar-based blues/rock music. In guitar-based blues/rock music, chords are usually connected by parallel voice leading something that is expressly forbidden by the rules of common-practice harmony. Since this experiment used chords constructed with Shepard tones, any notion of outer voices was rendered ambiguous. While this allowed for the control of a potential confound, it could have also removed a schematic feature that listeners would have used to activate the appropriate genre-specific schemata. Moreover, the timbral uniformity of the Shepard tones heard in both contexts, coupled with the timbral disparity between the prime and the chord successions could have also weakened the invoked schema. A future study would likely benefit from using stimuli that feature idiomatic voice leading and timbres that more clearly match the stylistic primes. Such stimuli would likely allow for listeners to invoke more clearly defined schemata and yield more robust ratings for successions heard in the two stylistic contexts. Hierarchical theories of harmony in common-practice music often privilege tonic and dominant chords. Although listeners hold similar expectations for the relationships between successive chords in both style contexts, the results of this experiment suggest that the subdominant harmony has an elevated status in blues/rock music. This likely reflects the statistical prominence of this chord in that repertoire. The results of this study support speculations made by Ken Stephenson (2002), Richard Middleton (1990), and David Temperley (2011), who suggest that subdominant harmony should assume a fundamental role in theories of rock music. Summary Listeners ratings reflected a distinct preference for specific root motion in chord successions primed with both blues and classical music. The ratings for different instances of the same root motion (between various instances of perfect fifths, for example) were significantly different, suggesting that listeners expectations are governed both by root motion and by the scale degrees upon which the chords are built. Overall, listeners rated diatonic successions higher than non-diatonic successions; however, the distinction between diatonic and non-diatonic chords was significantly less pronounced in a blues context. Finally, style affected listeners ratings of the three primary triads; the high rating of the subdominant harmony in a blues context suggests that perhaps this chord should assume a relatively prominent role in theories of blues/rock music. 56

75 CHAPTER FIVE LISTENERS EXPECTATIONS FOR THE TIMING OF HARMONIC EVENTS The experiments described in this chapter investigate the effects of harmony, temporality, and their potential interaction in a blues/rock setting. Some analysts consider chord choice to be considerably less important than the timing of harmonic events in blues/rock music. 64 Mari Riess Jones has argued that timing holds equal footing in the generation of expectation (Jones 1982, 36). Marilyn Boltz goes further, considering temporal structure to be the most important musical dimension in futureoriented attending (Boltz 1993, 586). According to this perspective, listeners hold strong expectations of formal boundaries, which often correspond with higher-level temporal events. Furthermore, listeners may be less sensitive to the specific harmonic events that occur within formal boundaries at hierarchically less important temporal moments. The twelve-bar blues includes three phrase-level formal boundaries that correspond to the A, A, and B sections of the formal design. The present studies address issues of harmony and timing by observing listeners sensitivity to the placement and content of the harmonic event that begins the second phrase of a twelve-bar blues. EXPERIMENT 2A Task In this experiment, participants listened to eighteen-second excerpts, evaluated how good each sounded, and expressed their ratings using a six-point scale. Trials represented possible iterations of the first eight measures of a twelve-bar blues in common time and included a chord change that varied in timing and duration. 64 Stated more strongly, someone believing that there is no established harmonic practice in blues/rock music might reasonably speculate that specific chord choice is irrelevant to this repertoire. 57

76 Hypotheses In accordance with the findings of Schmuckler and Boltz (1994), closely related chord successions will receive higher ratings than will distantly related chord successions, with the highest ratings given to the chord succession most typically associated with this phrase: I-IV-I. Normative timing IV beginning on the downbeat of m.5 and returning to tonic on the downbeat of m.7 will be rated highest, consistent with the theory that listeners expect harmonic events to occur at temporally salient moments in the music. 65 Consistent with the theories of Jones (1987) and Lerdahl and Jackendoff (1983), listeners will prefer progressions that include metrically strong chord changes (distinct from the typical stylistic surface-rhythm emphasis of beats 2 and 4 in blues/rock music). Since the individual stimuli contain relatively little harmonic activity, normative timing will have a greater effect on listener ratings than will chord choice, as Boltz (1993) also speculated. This will be revealed as an interaction between timing and harmony, with less typical chords found in normative locations (such as bvii occurring in mm.5-7) receiving higher ratings than common chords found in atypical locations (such as IV occurring in mm.4-7). Participants 34 Florida State University undergraduate and graduate music majors took part in this study. Participants (18 male, 16 female) ranged in age from years (average age years). Stimuli Trials consisted of eight-measure (32-beat) harmonic progressions representing mm.1-8 of a twelve-bar blues at a tempo of 120 beats per minute. Chords were constructed with Shepard tones to eliminate any effect created by chord inversion or register. Each excerpt began with a rapid fade-in to a one-measure turnaround that established the key (through an emphasis on V) and oriented the listener to the beginning of the form; each excerpt ended with a rapid fade-out. For excerpts that included an accompanying synthesized blues/rock drum pattern (see Figure 5.1), a stylistically appropriate drum-fill emphasizing the downbeat of m.1 was also provided. 65 This theory is particularly associated with Mari Riess Jones s 1987 research. 58

77 Question prompts and harmonic progressions were combined with the drum pattern in a multi-track audio editing environment. Any volume differences between the parts were normalized. Equipment Question prompts were synthesized using the MARY Text-to-Speech System. Shepard tones were synthesized with Csound and combined into chords with Audacity. Each stimulus element was then combined, edited, and rendered in REAPER, a multi-track audio editing environment. All of these tasks were completed on a Lenovo R61i laptop computer. During the experiment proper, stimuli were played for participants over a high-quality stereo system in a quiet classroom. Design and Procedure Figure 5.2 outlines the design of this experiment. Undergraduate students were randomly divided into two groups: group 1 heard trials with a synthesized drum accompaniment while group 2 heard trials without rhythmic accompaniment. Within each group, stimuli were presented in random order. The graduate students were assigned to group 1. After the turnaround that began each trial, all stimuli included a single departure from and return to tonic harmony. The onset, terminus, and contrasting chord used in this event were potentially varied in each stimulus. The non-tonic chords used included the typical choice for this event (IV), a potentially acceptable substitute for IV (bvii), 66 and an unusual substitute for IV (#IV). Onsets and termini of the non-tonic chord were displaced by 1 to 4 quarter notes from their normal locations (the downbeats of m.5 and m.7, respectively); half were earlier than expected, half were later than expected. Chords were sounded with a single attack and sustained. The stimuli in this experiment formed seven groups. Group A varied only the harmony (i.e., the specific contrasting chord). Groups B and C varied both the harmony 66 The decision to deem bvii "potentially acceptable" stems from its ubiquitous mention in scholarly studies of rock harmony (Moore 1992 and 1995, Everett 2000 and 2004, Stephenson 2002, Doll 2007). While the function of this chord is often debated (see Moore 1995 and Everett 2000, for example), neither it nor any other harmony in these experiments is presumed to behave in any particular way. Statistically, bvii is a chord that commonly moves to tonic in blues-influenced rock music, hence it was included here as a potentially viable alternative to IV (another chord that commonly moves to tonic). 59

78 and the onset of the non-tonic chord. Groups D and E varied both the harmony and the terminus of the non-tonic chord. Groups F and G varied the harmony and coordinated the onset and terminus of the non-tonic chord so that its duration consistently remained eight beats. Stimulus group A included 3 excerpts (3 non-tonic chords, no timing displacements) and groups B-G each included 12 excerpts (3 chords*4 different timing displacements), for a total of 75 stimuli. With the inclusion of three non-data questions intended to acclimate subjects to the task, 78 trials were heard by each participant. 67 Following each trial, participants were given four seconds to rate how good the excerpt sounded, responding with a score from 1 (bad) to 6 (good). 68 After the experiment, participants answered a survey that addressed biographical information, time spent in university, musical training, primary instruments, and secondary instruments. The survey also asked participants to indicate their time spent listening to, performing, composing/arranging, and general interest in ten different musical genres. Results and Discussion Figure 5.3 shows that changes in harmony affected listener ratings (p <.001) as expected: the typical choice (IV) yielded a mean rating of 3.87, while the potentially acceptable substitute (bvii) and the unusual substitute (#IV) received substantially lower mean ratings of 3.32 and 2.60, respectively. A post-hoc Tukey analysis revealed that all three comparisons were significant (p <.001 in all cases). Overall, stimuli with normative timing were rated significantly higher than those with atypical timing (p =.003; see Figure 5.4). When the data were pooled by group, a series of one-way ANOVAs revealed that the graduate students were most responsible for the main effect of typical timing on rating. Ratings for typical timing were higher than atypical timing among the undergraduates, but the mean differences were insignificant 67 The music was played at 120 beats per minute, rendering each nine-measure excerpt (eight measures, plus a one-measure introduction) 18 seconds in length. Stimuli were presented in random order. Participants were given 4 seconds to respond to each stimulus. Including response time and 2 seconds for a recorded oration of the question number, each trial lasted 24 seocnds. There were seven groups of stimuli, each of which included separate stimuli for the three chords to be used in the experiment. Furthermore, groups B-G included 4 additional levels one for each quarter-note displacement. Thus, there were 75 ((3+(3*4*6)) trials to be completed in the experiment. At 24 seconds per trial, the experiment lasted 30 ((24*75)/60) minutes, plus an additional 10 minutes allotted for instructions and a survey. 68 A transcript of the instructions is provided in Appendix A. Following the hypotheses pertaining to Experiment 1 in Chapter 3, it is assumed that listeners qualitative ratings of stimuli are measures of expectation in accordance with the theory of misattribution. 60

79 (p =.240 and p =.143); only the graduate students produced a significant result in this regard (p =.008). 69 Unfortunately, because neither Group 1 nor 2 showed a significant overall preference for typical timing in this experiment, it was not possible to assess the effect of the drum track. Observing data subsets grouped by contrasting chord reveals that listeners preferred normative timing in successions that included IV or bvii (p=.050 and p=.006). There was also a less pronounced preference for normative timing in successions that included #IV, but the mean difference fell well short of statistical significance (p =.346). These results are illustrated in Figure 5.5. Contrary to my hypotheses, listeners showed no specific timing preferences among stimuli with atypical timing: neither the degree to which the non-tonic harmony was displaced nor the metrical strength of its onset had an effect on ratings. When grouping data subsets according to timing, one-way ANOVAs show that harmony significantly affected ratings in successions with normative and atypical timing (p <.001 in both cases). A post-hoc Tukey analysis of the data subset exclusively employing normative timing reveals that under these conditions, #IV was rated significantly lower than the other two chords, but the ratings for IV and bvii were not significantly different. As shown in Figure 5.6, #IV received a mean rating of 2.79, significantly lower than both bvii (3.85, p =.007) and IV (4.29, p <.001). While IV was rated higher than bvii, this difference was insignificant (p =.401). Within the atypical timing data subset, however, the Tukey analysis revealed that all mean differences were significant (p <.001 in all cases). IV once again received the highest rating (3.85), followed by bvii (3.29), and finally #IV (2.59). Contrary to my hypotheses, a univariate ANOVA showed no significant interaction between harmony and timing (p =.485), and so we cannot determine which parameter (harmony or timing) more strongly impacts listener preferences. The results suggest that a clearly atypical harmonic choice, such as #IV, will likely be rejected by listeners in all timing conditions. In other words, when #IV is involved, listeners show no preference for timing: all of the successions are equally unsatisfactory. In contrast, when the harmonic relationship was more idiomatic, such as in the successions that included IV and bvii, listener ratings were affected by timing. In 69 I speculate that the graduate music students may have stronger musical expectations, owing to their more substantial experience. It is also possible that these participants simply devoted more mental energy to the task at hand. 61

80 order to confirm that these findings may be generalized to a wider harmonic palette, a follow-up study using different chords was needed. EXPERIMENT 2B Task The task is identical to the one performed in Experiment 2A. Hypotheses Based on the results of Experiment 2A, I predict that stimuli using typical chord changes that occur with normative timing will be rated highest. Also in accordance with the results from Experiment 2A, an unusual substitute chord will receive low ratings regardless of its temporal placement. Participants Participants were enrolled in a second-semester music theory course at Florida State University. 70 The 8 participants (6 male, 2 female) ranged in age from 18 to 19 years (average age years). All participants were music majors. Stimuli The stimuli were identical to those used in Experiment 2A, except that different non-tonic chords were employed, as described below. Equipment This experiment utilized the same equipment enumerated for Experiment 2A. 70 The two courses were Music Theory 2 and Sight-Singing/Ear Training 2. Because Music Theory 2 is a co-requisite for Sight-Singing/Ear-Training 2, most participants were enrolled in both courses. 62

81 Design and Procedure With regard to the timing displacement, tempo, and number of harmonic changes, the design and procedure for this experiment were identical to those used for group 1 in Experiment 2A. In this experiment, V was chosen as the typical harmonic event, ii was chosen as the potential substitute, and vii was chosen as the unusual substitute. The primary reason these particular chords were chosen for this experiment is because V, ii, and vii received mean ratings in Experiment 1 (see Chapter 3) that were similar to the mean ratings received of IV, bvii, and #IV, respectively. Ratings were compared for successions in which these chords either followed or approached the tonic chord, so as to mimic the single departure from and return to tonic used in the stimuli in Experiment 2A. Additionally, each of these chords resembles those used in the previous experiment in one or more ways: V is a so-called primary triad (as is IV), ii is a whole step away from tonic (as is bvii), and vii (like #IV), is a highly atypical chord that contains #4. On the other hand, ii and IV are generally considered to have similar functions in common-practice music, and they share two common tones. Furthermore, like bvii, vii is a step below tonic (which is not to say that these chords are functionally equivalent). All of these stated similarities provide good reasons for comparing the results of this experiment to those of Experiment 2A. Results and Discussion Figure 5.7 illustrates that chord choice once again significantly affected rating (p <.001). V was given a mean rating of 3.87, which was significantly higher than either ii (2.94) or vii (3.21) (p <.001). Contrary to my hypotheses, the ii chord was rated lower than the vii chord (p =.039), suggesting that it may qualify as the less intuitive substitute chord in this situation I speculate that this inconsistency with the results of Experiment 1 has to do with the participants relatively narrow exposure to the diatonic collection upon which the stimuli were based. In total, participants heard four chords: V, I, ii, and vii. Given this context, it is possible that some participants heard these chords in the key of the dominant, as I, IV, v, and iii, respectively. Although tonic was constantly re-established through the resolution of a dominant turnaround resolving in m.1, an unfocused participant may have mistakenly interpreted the turnaround as tonic. If this was the case, v (or ii in the old key) would be the least common chord among the group; its low rating then would be more consistent with the findings of Experiment 1, which found non-diatonic chords to be rated lower than diatonic chords. Alternatively, participants may have more closely attended to the potential voice-leading between the tonic and non-tonic chords; I believe this is a distinct possibility, particularly given the small scope of the musical context. The succession vii-i can be achieved via a shorter path measured in semitone motion 63

82 Typical timing was rated higher than atypical timing, as Figure 5.8 illustrates, though not quite at the level of significance (p =.077). When the data are split according to harmony, as depicted in Figure 5.9, listener ratings indicate a consistent preference for typical timing; however, none of these preferences reached the standard level of statistical significance. Once again, the degree to which timing was altered in a stimulus had no effect upon participants ratings. 72 The effect of chord choice on rating again differed between datasets grouped by timing. In typical timing conditions, harmony had an insignificant effect (p =.102); however, the mean rating for V was substantially higher than ii or vii in this context. This difference approached significance (p =.148), while the difference between ratings for the remaining chords was much more likely due to random chance (p = 1.000). 73 Conversely, in atypical conditions listeners showed a distinct preference for V (mean rating 3.85), followed by vii (mean rating 3.20), and finally ii (mean rating 2.93), with ANOVA and post-hoc Tukey tests all at the level of significance. These findings are presented in Figure Finally, a univariate ANOVA on harmony and timing proved insignificant (p =.689), and so it is again impossible to assess whether timing or harmony more substantially impacted listener ratings. General Discussion The stimuli used in this pair of experiments were designed to elicit a blues/rock schema and its associated expectations through the presence of several stylistically appropriate features. These features included four-measure phrases, the presence of a blues/rock drum pattern, and a single harmonic event involving a departure from and return to tonic over the course of mm. 5-7 of an eight-measure excerpt. Listeners rated typical timing highest, suggesting that these features did indeed provide enough information to create schema-specific expectations. Listeners did not respond with high ratings for stimuli that included chord changes on strong beats or downbeats other than m. 5 and m.7, including stimuli that featured a dominant-tonic resolution on the downbeat of m.8. Events such as these would presumably be highly expected in than can ii-i (4 semitones vs. 5 semitones). Finally, it is possible that the presence of the leading tone in vii could have conveyed some sense of dominant-tonic functionality that led to higher ratings. 72 This is likely due to the small number of participants in this study. 73 Given that there were only 8 participants in this study, I speculate that the results would more closely resemble those found in Experiment 2A if a restudy was completed using a greater number of participants. 64

83 common-practice contexts. 74 Given that participants showed sensitivity toward the metrical placement of harmonic events in these stimuli, it is likely that they employed a schema specific to the twelve-bar blues form as opposed to one more generally applicable to the blues/rock idiom. Since comparing the twelve-bar blues context with another stylistic framework was not the aim of this study, further research would be needed to ascertain whether these expectations are twelve-bar blues specific. Given that the stimuli were intended to evoke a blues/rock schema, it is unsurprising that the stimuli bearing closest resemblance to twelve-bar blues received the highest ratings. However, it is remarkable that listeners showed no significant metrical preference among stimuli with atypical timing. One reason for this may be that atypical timings were always created at the beat level: the onset of the harmonic event always shifted by at least one quarter note. 75 If listeners were (consciously or unconsciously) keeping track of the meter, these shifts may have influenced, confused, or even clashed with their internalized metrical hierarchy. This metrical conflict may have been further emphasized for listeners who heard stimuli accompanied by drums. 76 As shown by Tillman and Lebrun-Guillaud, a lack of consistent, salient temporal periodicity can inhibit future-oriented attending (Tillman and Lebrun-Guillaud 2006, 355). If this was the case, participants hearing stimuli with atypical timing may have made less accurate predictions, and therefore (by misattribution) provided lower ratings. An interesting potential relationship between harmony and timing arose out of both experiments. In contexts with typical timing, listeners showed a less robust preference among chords that could be deemed acceptable. One interpretation of this aligns with theories implying that rock harmony operates in small four- or eight-measure units in which musicians use chords from a limited collection (such as those within a prevailing key or mode) freely with respect to order. 77 According to this view, listeners equally accept a variety of harmonies, provided that their timing strictly adheres to 74 In common-practice repertoire, one might expect cadences to occur on the downbeat of the fourth measure in a four-measure phrase. While twelve-bar blues forms are comprised of four-measure phrases, the fourth measure typically contains a reiteration of tonic harmony initiated on the third measure of that phrase. Important harmonic events in a twelve-bar blues occur in mm. 5, 7, 9, 10, and It may also be the case that displacements of this magnitude are simply uncommon in the repertoire. As David Temperley (2007) has pointed out, rhythmic displacements by eighth and sixteenth notes are common in both melodic and harmonic practice in rock music. A follow-up study of the effect of smaller onset displacements on harmonic expectation in twelve-bar blues phrases would undoubtedly be worthwhile. 76 As mentioned previously, it was not possible to assess the effect of the drum tracks since the undergraduate participants did not show a significant preference for typical timing. 77 See Bjornberg (1989/2001) and Moore (1992) as discussed in Chapter 2, for example. 65

84 formal schemata. Only truly unacceptable chords (such as #IV) breach the threshold of harmonic acceptance and are rejected regardless of their temporal placement within the schema. 78 The notion that taxonomically non-equivalent chords can be equally expected in specific musical schemata is supported by the findings of Schmuckler and Boltz (1994). In their studies, participants responded similarly to the present experiment when asked whether high-, medium-, and low-expectancy chords belonged or did not belong in a given musical context. Both high- and medium-expectancy chords were decidedly categorized as belonging to the context, and, more importantly, the results could not support the notion that one chord type conveyed more of a sense of belonging than the other (Schmuckler and Boltz 1994, 321). Schmuckler and Boltz also found a similar relationship between harmony and timing in which listeners ignored the temporal domain in the presence of specific harmonic events. Instead of listeners dismissing unexpected temporal events after rejecting a harmony, Schmuckler and Boltz found that listeners ignored the temporal domain when exposed to the harmonic strength of an authentic cadence (Schmuckler and Boltz 1994, 318). While the findings of the experiments presented in this chapter and those reported by Schmuckler and Boltz are not identical, their similarities lend support to results that might otherwise seem counterintuitive. It should be made clear that conclusions founded upon statistically insignificant results must be considered tenuous. The emergence of only a very few significant preferences among harmonies heard in normative temporal contexts does not mean that listeners have no preferences among chords in these situations. Since the experiment was designed to examine the effect of graded fluctuations in timing, it was necessary to have an equal number of stimuli in each timing category. This meant that there were only three stimuli that used normative timing one for each of the three chords used in the experiments. It is certainly possible that data pooled by typical/atypical timing did not show a significant effect of chord on rating simply because there were so few stimuli of this type. Participants heard far more successions with atypical timing, and therefore reached more favorable levels of significance for this stimulus class. The lack of interaction between timing and harmony shown in a univariate analysis of variance (a two-way ANOVA) can be also accounted for by the 78 It is possible that participants in this experiment employed a strategy that reflected this system. For instance, having decided that something sounded unsatisfactory, participants may have not further determined the degree to which they disliked the sound. With this in mind, it is possible that post-hoc judgments (such as those made on a rating scale) tend not to discriminate between the bad and the very bad. A follow-up study using a response mode that measures reaction time could allow for the confirmation or dismissal of this hypothesis. 66

85 fact that the two pools of data (typical and atypical timing) varied considerably in size. Further study strictly comparing successions with typical and atypical timing of events would be needed to verify a hypothesis concerning the relationship between harmony and timing. Although the results from these studies do not provide conclusive insight into the complex relationship between temporal and harmonic expectations in twelve-bar blues successions, they do help to dispel the notion that these expectations are generated exclusively in the temporal domain. The studies showed that certain harmonies better satisfy musical expectations regardless of the timing of their onset or duration. Moreover, despite the imbalances of the experimental design, these studies showed that listeners have a distinct preference for a harmonic/metrical framework that reflects the schematic features of the twelve-bar blues when the music is presented in the appropriate stylistic context. Summary The results of this experiment showed that the timing of harmonic events affects participants ratings of chord successions. Ratings were significantly lower when the location of the harmonic event shifted from its typical location in a twelve-bar blues (mm. 5-7). When atypical chords were used, metrical location did not significantly affect participants ratings. Overall, participants showed well-defined preferences for specific chords; however only the highest rated chords impacted listeners preference for typical timing. The results suggest two conclusions: listeners have very specific expectations of when harmonic events will occur in a twelve-bar blues, and highly unexpected chords can subvert or overshadow expectations of timing. 67

86 CHAPTER SIX HARMONIC EXPECTATION IN TWELVE-BAR BLUES PROGRESSIONS Harmonic expectations may derive from our understanding and activation of specific musical schemata, as explained in Chapter 3. Robert Gjerdingen notes that schemata are active processes that represent knowledge at all levels of abstraction. Schemata are embedded structures; low-level details called features are processed to form a schema, which in turn becomes a feature of a higher-level schema. When activated, a schema allows us to form expectations of future musical events. Numerous successive expectancy violations eventually cause us to choose and activate a new schema (Gjerdingen 1988, 5). The chord succession associated with the twelve-bar blues is undoubtedly a musical schema with which many North American listeners are familiar. This progression serves as a lower-level feature of the more general twelve-bar blues, which also includes features associated with text and rhyme scheme, blues scales, melodic idioms, and so on. One focus of this chapter is an investigation of the harmonic features that influence our perception of twelve-bar blues schema as it unfolds. The twelve-bar form consists of three phrases that can be identified by their unique chord successions. Each phrase serves as a feature, generating longer-range expectation of what will follow in order to fulfill the active twelve-bar blues schema. For instance, when we hear the chord succession IV-IV-I-I, it generates an expectation that the last phrase of the twelve-bar form will soon follow. 79 It should be noted that this type of expectation stems not specifically from harmonic function but instead more broadly from formal function, as described by William Caplin. In his book Classical Form, Caplin defines formal function as the role that a given section of music plays in the piece s larger organization (Caplin 1998, 9). For example, in a Classical-era two-phrase period, the antecedent phrase generates an expectation for the consequent phrase. Likewise, when a listener interprets the succession IV-IV-I-I as a middle phrase of a twelve-bar blues, it generates a formfunctional expectation for the last phrase of a twelve-bar blues. 79 This expectation would likely be greatly strengthened by the presence of the timbral and rhythmic features that would further entice listeners to invoke the blues schema. 68

87 Individual phrases of a twelve-bar blues serve as features of a larger schema, but they can also be considered lower-level schemata themselves. For the purposes of this study, I will consider the chords associated with each phrase of the twelve-bar blues to be the features that combine to activate appropriate phrase schemata. In addition to the investigation of harmonic expectation in twelve-bar blues successions, the experiment presented in this chapter also addresses the degree to which harmony affects the activation of phrase schemata and, by association, form-functional expectation. Finally, the study addresses the question of whether form-functional expectation, represented by our identification of phrases, interacts with moment-tomoment harmonic expectation, represented by listener ratings of the chord successions within those phrases. EXPERIMENT 3 PRE-TEST The experiment proper required participants to associate synthesized chord successions with twelve-bar blues phrases. The design of the experiment was founded upon two assumptions: 1) participants were able to identify phrases excerpted from a twelve-bar blues, and 2) the synthesized timbres used in the experiment proper did not impair listeners ability to perform this task. In order to validate these assumptions, participants completed a short pre-test. Pre-Test Task Participants listened to 14- to 18-second excerpts and categorized each excerpt as the beginning, middle, or end phrase of a standard twelve-bar blues. Pre-Test Hypotheses Participants success in identifying phrases will not be affected by the timbre of the stimuli or the type of phrase. Scores on the pre-test will correlate with participants ratings for questions pertaining to jazz, blues, and rock on the biographical survey following the experiment (i.e., participants who are especially familiar with jazz, blues, and rock will accurately distinguish the three phrases of the twelve-bar blues). 69

88 Pre-Test Participants Participants were enrolled in either a first-year music theory or a first-year sightsinging and ear-training course at Florida State University. This single group of 21 participants (12 male, 9 female) ranged in age from 18 to 21 years (average age years). All participants were music majors. Pre-Test Stimuli The pre-test stimuli consisted of ten four-measure progressions. Each trial represented one of the three phrases from a standard twelve-bar blues. Five of these trials were drawn from recordings of the Stevie Ray Vaughn songs Mary Had a Little Lamb, Scuttle Buttin, Gimme Back My Wig, and I m Cryin. Each excerpt began with a key-confirming lead-in and included several stylistic changes in texture and rhythmic accent that emphasized the beginning of the upcoming four-measure phrase. Of these stimuli, two were beginnings, two were middles, and one was an end. The five remaining stimuli consisted of phrases constructed with synthesized chords and accompanying drums (also synthesized). Chords were constructed with Shepard tones to eliminate any effect created by chord inversion or register. The synthesized trials featured a two-measure key-confirming introduction and ended with a stylistically appropriate drum-fill that emphasized the downbeat of the first measure of a four-measure phrase. Illustrations of the structure of the standard twelve-bar blues and the excerpts used for stimuli are provided in Figure 6.1. Of these five stimuli, one was a beginning, two were middles, and two were ends. Synthesized excerpts were played at a tempo of 160 BPM. Recorded excerpts ranged in tempo from 110 BPM to 159 BPM and had an average tempo of BPM. Along with question prompts and a 3-second response time, each synthesized trial was 14 seconds in length. Recorded trials ranged in duration from 14 to 18 seconds and had an average length of 15.6 seconds. All components of the pre-test stimuli were combined and normalized in a multi-track audio editing environment. Pre-Test Equipment Question prompts were synthesized using the MARY Text-to-Speech System. Recordings were transcoded from CD to.wav files with Exact Audio Copy and edited with Audacity. Shepard tones were synthesized with Csound and combined into chords 70

89 with Audacity. Each stimulus element was then combined, edited, and rendered in REAPER, a multi-track audio editing environment. All of these tasks were completed on a Lenovo R61i laptop computer. During the experiment proper, stimuli were played for participants over a high-quality stereo system in a quiet classroom. Pre-Test Design and Procedure Participants took part in a short training session prior to the pre-test. This training session allowed participants to become familiar with the standard three-phrase structure of the twelve-bar blues. The proctor played an excerpted verse from Chuck Berry s Sweet Little Rock N Roller that consisted of a single iteration of a standard twelve-bar blues. Included on the first page of the response sheet was a diagram that identified the three phrases of the twelve-bar blues as beginning, middle, and end. Following the training session, participants heard ten pre-test trials and were asked to identify each trial as beginning, middle, or end. Allowing two seconds for question prompts and three seconds for responses, the pre-test trials were all between 14 and 18 seconds in length. The proctor s script and response sheet are included in Appendix A. Pre-Test Results and Discussion On the pre-test there was a mean score of 7.05 out of 10, a median of 7, and an interquartile range of A chi-square test confirmed that question type (synthesized or recorded) did not significantly affect participants success on the pre-test (p =.545). A cross-tabulation of question type and accuracy is presented in Table 6.1. Another chisquare test revealed that phrase label (beginning, middle, or end) did not affect accuracy at the level of significance (p =.144). A cross-tabulation of phrase label and accuracy is presented in Table 5.2. Contrary to my hypotheses, participants selfreported ratings of musical interests did not correlate with pre-test scores. It is safe to assume that the synthesized stimuli conveyed enough schematic information to be considered stylistically appropriate excerpts from a twelve-bar blues, since the timbre of the excerpts did not affect participants ability to identify phrases. 80 The interquartile range refers to the difference between the third and first quartiles, representing the distribution of scores closest to the median. 71

90 EXPERIMENT 3 Task Participants listened to 16-second excerpts from twelve-bar blues progressions. Each synthesized excerpt represented a phrase from a traditional twelve-bar blues and included a single variable chord. For each trial, participants provided a goodness rating on a six-point scale and indicated whether they thought the excerpt came from the beginning (Phrase 1), middle (Phrase 2), or end (Phrase 3) of a twelve-bar blues. Hypotheses Stimuli that include phrase-defining chords will be categorized as phrases with which those chords are associated, regardless of chord substitution. Participants will most commonly identify phrases beginning on I as Phrase 1 Participants will most commonly identify phrases beginning on IV as Phrase 2 Participants will most commonly identify phrases beginning on V as Phrase 3 Stimuli that withhold tonic until measure 4 will be inconsistently categorized. Furthermore, progressions that include an ambiguous tonal center will receive inconsistent ratings and categorizations. 81 In accordance with the results from Chapter 4, root motion approaching and following the chord substitution will affect ratings, with progressions that feature typical root motion in these locations receiving the highest ratings. Stimuli The stimuli were intended to emulate possible variations of the three phrases of a twelve-bar blues. Stimuli included a single variable chord in one of measures 2, 5, 6, 7, 9, 10, or 11 in order to assess listeners' sensitivity to harmony in these locations In particular, progressions that include some combination of v, I, and IV might be heard as ii, V, and I in the key of the subdominant. 82 In the standard twelve-bar blues, important and predictable harmonic events occur in measures 5, 7, 9, 10, and 11, making these ideal locations for observing listeners' expectations. The identification of these measures as important harmonic events is also supported by the work of Lhost and Ashely (2006), who surveyed over 100 twelve-bar blues progressions. Although myriad variations occur in the context of twelve-bar blues, the harmonies initiating measures 5, 7, 9, 10, and 11 remain quite consistent. Substitutions were included in measure 2 to investigate the potential for listeners to hear any phrase that 72

91 Harmonic successions were accompanied by synthesized drums. Chords were constructed with Shepard tones to eliminate any effect created by chord inversion or register. Chords were articulated once and sustained for the duration of the measure. All trials held a tempo of 160 BPM and ended with a fade-out. All components of the stimuli were combined and normalized in a multi-track audio editing environment. Equipment The same equipment used to design and administer the pre-test was used for this experiment. Design and Procedure Table 6.3 outlines the design of this experiment, with stimulus groups defined by the chords that they hold in common. Each trial consisted of a two-measure key-confirming introduction followed by a four-measure harmonic succession. Together, these six-measure excerpts represented potential segments of the standard twelve-bar blues and included a single harmonic substitution. All twenty-four major and minor triads were used as harmonic substitutes in each group of stimuli, with the exception of those that created redundancies across the groups (indicated in parentheses in Table 6.3). In total, 160 trials were presented in random order. 83 Participants heard a two-second question prompt prior to each excerpt. Following the harmonic succession, participants were given five seconds to identify which phrase they heard (beginning, middle, or end) and rate how good the excerpt sounded. Including the question prompt and response time, each trial lasted 17 seconds. After the experiment, participants answered a survey that addressed biographical information, time spent in university, musical training, primary instruments, and secondary instruments. The survey also asked participants to indicate their time spent listening to, performing, composing/arranging, and general interest in ten different musical genres. starts with tonic as a beginning phrase. In addition, substitutions in measure 6 were included to test listeners' sensitivity to the typical lack of harmonic change in that measure. 83 There are 7 stimulus groups, each of which includes a single harmonic substitution. Group A does not include any redundancies and therefore has 24 variations. Groups B, C, F, and G avoid one redundancy, and therefore have 23 possible variations. Groups D and E avoid two redundancies. Thus, there are 160 (24+(23*4)+(22*2)) total stimuli to be used in this experiment. 73

92 Results and Discussion This experiment contains two independent variables, each with multiple levels: stimulus group (combinations of chords representing a potential phrase in the twelve-bar form) and variable chord (a single variable chord in a specific location within each stimulus group). The discussion below addresses these variables in isolation before investigating any potential interaction that occurred between them. Phrase labels A cross-tabulation of phrase label and stimulus group is presented in Table 6.4 and illustrated in Figure 6.2. Since the stimulus groups were designed to resemble the three phrases of the twelve-bar blues, 84 it is unsurprising that chi-square analyses revealed almost all label distributions between groups and within groups to be statistically significant 85 (Tables 6.5 and 6.6 illustrate where significant differences occurred between pairs of groups 86 and within groups 87 ). The consistent effect of stimulus group at all levels in the statistical analyses discussed above suggests that the chords common to each progression within a group have a strong influence on listeners decisions to assign phrase labels. For instance, stimuli from groups A-C were more frequently identified as Phrase 2. All of these stimuli prominently feature the IV chord: in Group A IV returns to I on the downbeat of measure 3, which, as discussed in Chapter 4, is a prominent harmonic event in this location within the twelve-bar form. Groups B and C begin with IV. Group C, which features two successive IV chords, 84 It is important to understand that some stimuli can be considered members of two groups; for instance, IV-IV-I-I might represent either *-IV-I-I or IV-*-I-I. However, it is only possible to code a stimulus as part of a single group when performing statistical analyses that compare groups. When analyzing data pertaining to a single group, though, all of its constituent successions can be included in the analysis. For instance, the succession IV-IV-I-I can be included in an analysis of the data subset that consists of all stimuli in the group *-IV-I-I. Likewise, it can be included in an analysis of the group IV-*-I-I. Analyses comparing groups exclude successions with multiple memberships. Analyses of single groups will be presented later in the chapter. 85 More pronounced differences (also p <.001) were found in an analysis examining only the participants with high pre-test scores (at least 8 out of 10 correct). Because the analysis of this data subset simply reinforced the significant findings drawn from the entire dataset, further analyses of the more selective data subset were not performed separate chi-square tests were completed, pairing each two-group combination stimulus groups: AB, AC, AD, AE, AF, AG, BC, BD, BE, BF, BG, CD, CE, CF, CG, DE, DF, DG, EF, EG, FG. 87 Upon examining the data subset for participants with high pre-test scores, the difference between observed categorizations of phrases 2 and 3 in Group E was also found to be significant at the p <.001 level. 74

93 received more Phrase 2 labels than did any other group. In contrast, the three stimulus groups that featured V (D, E, and F) were more likely than any of the other groups to be identified as Phrase Finally, Group G received more Phrase 1 labels than did the other groups. Participants likely identified Group G stimuli as Phrase 1 because of its three tonic chords. These results suggest that, overall, twelve-bar blues phrase schemata require more than a single harmonic substitution to provoke schemaswitching. The effect of the variable chord on phrase labels While the results discussed in the previous section suggest that the common chords within stimulus groups had a prominent effect on phrase labels, they do not mean that the variable chord was ineffectual: the variable chord did indeed affect phrase label at the level of significance (p <.001). Table 6.7 shows how frequently the three phrase labels were associated with each of the 24 major and minor triads (i.e., those represented by an asterisk in Table 6.3). In addition, Table 6.7 includes p-values corresponding to chi-square tests on phrase labels for each chord. Generally, these results suggest the presence of certain chords affects listeners applications of phrase labels. Of particular note are the distributions of labels for successions that include I, ii or V. I describe these chords as phrase-defining because of the significant and substantial listener preference for one particular phrase label. 89 Successions including the variable chord ii or V (regardless of location) were labeled as Phrase 3 by approximately 50% of participants an unsurprising result considering that both ii and V are found exclusively in Phrase 3 (and only Phrase 3) in two of the most standard manifestations of the twelve-bar blues. Similarly, successions containing the variable chord I were labeled as Phrase 1 by 46.4% of participants. Again, this result 88 Overall, there was no clear distinction between Phrase 2 and Phrase 3 among responses to Stimulus Group E. However, participants who scored 8 out of 10 on the pre-test more frequently interpreted Group E successions as Phrase 3 at the level of significance (p <.001). Incidentally, Phrase 2 was the most common label for Group E successions among participants who scored between 4 and 7 out of 10 on the pre-test (p <.001). This result might suggest the presence of competing signals: beginning on V signals Phrase 3, while non-functional motion to the tonic in m.3 indicates Phrase 2. If participants employed a listening strategy which determined all phrases beginning on V to be Phrase 3, the results may also suggest that those who scored higher on the pre-test were simply better at identifying phrases that began on the dominant. 89 I use the term phrase-defining when a chi-square analysis indicates the differences in label distribution is significant and also that the most popular phrase label is the source of this significant difference. 75

94 corresponds with a typical harmonic characteristic of the twelve-bar blues: Phrase 1 is more than half tonic. Interestingly, the presence of IV did not significantly influence phrase interpretation, most likely because IV is commonly found in all three phrases of the twelve-bar blues. Listeners appear to have evaluated most chords other than I, ii, and V as unsuitable for Phrase 1. Table 6.8 shows the statistical significance of the difference in distribution of labels for successions that were not identified as Phrase 1. Relatively few chords had a distribution that significantly differentiated Phrase 2 from Phrase 3 labels. As expected, both ii and V were more likely to be interpreted as components of Phrase 3. VI, vi, #iv, and vii, in contrast, were consistently ascribed to Phrase 2. VI, vi, and #iv are arguably similar to the IV chord: each shares one or two common tones with IV, and these four chords all contain the diatonic 6, which some theorists view as the quintessential subdominant scale degree (Harrison 1994, 51-53). Although it shares a note with #iv, the inclusion of vii among these seems somewhat anomalous, since it lacks any of the characteristics shared by the other three chords in this group. These results help explain the general impact of chord substitutions on formal function when placed within a common four-measure phrase from a twelve-bar blues. Chord location Another potential factor influencing phrase labeling may be chord placement within the four-bar phrase. To what extent does the first chord heard influence a listener s interpretation of the phrase within the twelve-bar form? A chi-square test on the cross-tabulation of Chord 1 and Phrase Label revealed that Chord 1 had a significant and substantial impact in this regard (p <.001). Table 6.9 presents the distribution of phrase labels for all possible initiating chords as well as the p-value for each possible comparison. 90 The next three tables illustrate how the location of the variable chord impacted listeners phrase interpretations. In many cases, the phrase-defining chords described previously are more identifiable due to clearer majorities in label distribution. While some chords generate a stronger consensus regarding phrase label than do others, the 90 It should be noted that the data for label-pair subsets are drawn from disproportionate sample sizes owing to the varying number of responses for any given phrase label as well as varying number of stimuli beginning on any given chord. Since stimulus groups were designed to emulate phrases from a twelvebar blues, stimuli begin far more often on I, IV, and V than on any other chord. When the data set is further reduced (only observing Phrase 2 and 3 responses, for instance), statistical analysis may become slightly less reliable. 76

95 prevalence of Phrase 3 labels among successions beginning on chords other than I or IV suggests that listeners perceptions of formal function may largely depend on whether phrases begin with I (Phrase 1), IV (Phrase 2), or any other chord (Phrase 3). Chord 2 also significantly affected Phrase Label (p <.001). Table 6.10 shows the distribution of phrase labels organized according to the second chord used in each succession and the associated p-values for each comparison. However, Chord 2 had a much less consistent impact on participants phrase labels than did Chord 1. While the overall effect of Chord 2 on Phrase Label was significant (p <.001), the data show that this result is largely due to only a few individual chords. IV and V were again associated with Phrase 2 and Phrase 3, respectively, and #iv and vii, along with VII, were labeled consistently as Phrase 2. VI and vi were identified both as Phrase 1 and as Phrase 2, perhaps because of the similarities (such as common tones) between these chords and phrase-defining chords I and IV. More important is the lack of significant differentiation among the remaining Chord 2s, suggesting that, with the exceptions listed above, Chord 2 has very little influence on listeners perceptions of formal function. An initial chi-square analysis of the cross-tabulation of Chord 3 and Phrase Label seems to demonstrate that Chord 3 had a substantial and significant (p <.001) impact on the perception of formal function. While chi-square analyses of data subsets grouped by Chord 3 indicate a large number of significant results (shown in Table 6.11), closer inspection of the Phrase 2 and Phrase 3 responses reveals that the large majority these results can likely be attributed to listeners apparent reluctance to apply a Phrase 1 label. Only #iv and V prompted single definitive labels of Phrase 2 and Phrase 3, respectively. While the data above suggest that all chord locations affected phrase label to some degree, a greater number of definitive labels emerge when the data are grouped by chords heard earlier in the phrase. I will describe labels as definitive when one phrase label is applied significantly more often than either of the two remaining phrase labels (as determined by a series of chi-square tests on label pairs). For example, when Chord 1 was I, 55.8% of participants identified the succession as Phrase 1 (refer to Table 6.9). Listeners were more likely to label a tonic-initiated phrase as Phrase 1 than as Phrase 2 or Phrase 3, and both of these differences were statistically significant. We can therefore say that successions beginning with I were definitively labeled as Phrase 1 by participants. When the data are grouped by Chord 1, eight chords yield definitive phrase labels: I, II, IV, #IV, V, bvi, bvii, and bvii. 77

96 Exclusionary labels emerge when one phrase label is applied significantly less often than either of the remaining two labels (again determined by a series of chi-square tests on label pairs). For example, when Chord 1 is ii, 11.9% of participants applied a Phrase 1 label. Listeners were less likely to label a supertonic-initiated phrase as Phrase 1 than as Phrase 2 or Phrase 3, and both of these differences were statistically significant (p =.039 and p =.003, respectively); however, the Phrase 2 and Phrase 3 responses were not significantly different from each other (p =.139). We can therefore say that participants will exclude the Phrase 1 label when interpreting successions beginning with ii. When the data are grouped by Chord 1, five chords yield the exclusionary label not Phrase 1 : ii, iii, v, vi, and vii. The number of definitive labels decreases when the data are grouped by Chord 2 (four definitive labels) and further still when the data are grouped by Chord 3 (only #iv and V yield definitive labels). Generally, these results suggest that chords heard earlier in a phrase have the greatest impact on listeners interpretations of formal function. A few specific chords heard in measure 2 of a four-bar phrase will inform labeling decisions; however, aside from these chords, harmony heard in this location has very little impact on listeners interpretations. Twelve exclusionary labels emerge when the data are grouped by Chord 3, all of which indicate that the successions are not Phrase 1. This could be attributed to the fact that Phrase 1 typically contains the fewest chord changes in a twelve-bar blues. 91 Which chords prompt listeners to abandon a schema? The analyses above present two interpretations of how stimuli affected listeners interpretations of formal function. The first, which examined the effect of stimulus group, suggested that the chords held in common within a group (the non-variable chords) had a great impact on phrase labels, regardless of the variable chord. The second analysis revealed that individual chords, independent of stimulus groups, still affected phrase labels, especially when they occurred early in the phrase. Since these analyses were (necessarily) done separately, it was impossible to gauge whether one factor had a stronger impact than the other. To do so requires individual analyses of the effect of the variable chord within each stimulus group. 91 One might also posit that any near-definitive labels could instead be attributed to the influence of other factors, such as Stimulus group, since most Stimulus groups were labeled as either Phrase 2 or Phrase 3 (as discussed earlier). This possibility will be discussed shortly. 78

97 As noted earlier, certain successions can be considered members of more than one stimulus group. For example, groups A, B, and C all include the succession IV-IV-I-I. When comparing groups, it is impossible to account for this multiple categorization; however, when examining groups individually, the data may be coded to reflect multiple group memberships. What follows is a discussion of the impact of variable chords within data subsets divided by stimulus group. We will be particularly interested in harmonic substitutions that led listeners to choose a phrase label that was not typically associated with the stimulus group as a whole. Our assumption is that significant deviations from the prevailing trend may be attributed to the variable chord. Tables show the proportions with which the three phrase labels were assigned to each member of each stimulus group. The average for each stimulus group is presented in the last row of its table. The last column of the table provides p-values for individual chi-square tests on Phrase Label for each level of the variable chord, determining whether the differences in label distribution for a specific succession are significant. 92 Rows have been shaded to reflect whether the succession s label distribution favors Phrase 1 (blue), Phrase 2 (green), or Phrase 3 (beige). I will now briefly discuss the trends and identify the exceptions in label distributions for each individual stimulus group. Following this, I will discuss the exceptions in more detail and attempt to summarize some commonalities among them. Stimulus Group A (*-IV-I-I). The label distribution for Stimulus Group A (shown in Table 6.12) illustrates the overall tendency for listeners to interpret these successions as Phrase 2. The difference between the tallies of responses for each phrase label was significant (p <.001). The distributions for ten successions differed from the prevailing trend; this result can be attributed to the significant overall impact of the variable chord 92 These p-values should be viewed with some caution. When the data are grouped in this way, only 21 responses are observed for each succession, making the sample size quite small, especially when testing for significant differences between label pairs. Furthermore, these chi-square tests were performed with a null hypothesis that assumes an equal distribution of labels for each chord. This assumption does not take into account the potential effect of the remaining chords in the succession. For example, if Chord 1 from Group A had no effect on phrase labels, we should expect a label distribution that reflects the effect of the three remaining chords in the succession. This distribution may be best represented by the total distribution for the group. Alternatively, a chi-square test could be performed using an expected distribution that reflects the total group distribution, which would result in a different set of p-values. While these values may more accurately reflect the true significance of the distribution, a problem emerges when we consider the successions that belong to more than one group. For example, an expected distribution of <23.4%, 43.1%, 33.5%> could be used for a chi-square test on label distribution for the succession IV-IV-I-I, based on the overall distribution for successions in Stimulus Group A. By the same logic, an expected distribution of <20.2%, 50.4%, 29.4%> would be used for testing the same succession, based on the overall distribution for successions in Stimulus Group B. The logic is also flawed, as it applies two expected distributions to the same succession based on grouping contexts that are generated solely outside of the experiment. 79

98 (Chord 1, located in m. 1) on listeners interpretations of the phrase (p <.001). Of these ten, one was most commonly interpreted as Phrase 1 (initiated by I), seven were most commonly labeled Phrase 3 (initiated by ii, #IV/bV, #iv/bv, V, bvii, bvii, and vii), and two did not have a single preferred phrase label (initiated by II and VI). Stimulus Group B (IV-*-I-I). As indicated by the label distribution in Table 6.13, listeners most commonly associated successions from Stimulus Group B with Phrase 2 (p =.005). The variable chord, however, significantly impacted listeners interpretation of the phrase (p =.005). Of the six successions with distributions that differed from the prevailing trend, three were most commonly labeled Phrase 3 (initiated by IV-iii, IV-iv, and IV-V), two were most commonly labeled Phrase 1 (initiated by IV-II and IV-v), and one received an equal number of Phrase 2 and Phrase 3 labels (initiated by IV-III). Of all the variable chords, only V broke the trends of both Stimulus Group A and Stimulus Group B. The succession IV-V-I-I produced the most dramatic change in label distribution, with 71.4% of participants applying the Phrase 3 label. Stimulus Group C (IV-IV-*-I). The label distribution shown in Table 6.14 illustrates that listeners are most likely to interpret successions in Stimulus Group C as Phrase 2 (p <.001). While the variable chord significantly impacted listeners interpretation of the phrase (p <.001), only two chords yielded label distributions that favored anything but Phrase 2. V again had a notable impact, with IV-IV-V-I successions labeled as Phrase 3 by 61.9% of participants. Beyond this, the variable chord did not sway the majority listeners from identifying these successions as Phrase 2. Stimulus Group D (*-V-I-I). Overall, Stimulus Group D received Phrase 3 labels from 62.7% of participants (p <.001). The variable chord significantly impacted participants responses (p <.001); however, the responses to two specific successions were entirely responsible for this result: I-V-I-I was interpreted as Phrase 1 by 66.7% of participants and V-V-I-I was interpreted as Phrase 2 by 42.9% of participants. These results are illustrated in Table Stimulus Group E (V-*-I-I). As shown in Table 6.16, Stimulus Group E received a label distribution that slightly favored Phrase 3; however, the significance of this result (p <.001) is largely due to the low number of Phrase 1 responses (recall that the chisquare test for the subset of Phrase 2 and 3 responses in Group E revealed that the difference between the number of labels for these two responses was insignificant). The variable chord significantly impacted participants responses, resulting in twelve label distributions that differed from the prevailing trend. Ten of these successions (which included biii, biii, #iv/bv, V, v, bvi, VI, vi, VII, and vii) were most commonly 80

99 identified as Phrase 2. The succession V-bVII-I-I was most commonly identified as Phrase 1, while the label distribution for the succession V-II-I-I favored Phrase 2 and Phrase 3 equally. Stimulus Group F (V-IV-*-I). Participants most frequently interpreted successions from Stimulus Group F as Phrase 3 (p <.001; see Table 6.17). The variable chord did not significantly impact participants responses (p = 0.536), which suggests that the variable chord was virtually irrelevant when interpreting Group F successions. 93 Stimulus Group G (I-*-I-I). Harmonic successions from Stimulus Group G were overwhelmingly interpreted as Phrase 1. In fact, 20 of the 24 members of Stimulus Group G were most often identified by listeners as Phrase 1. For the four outlying members, the Phrase 1 label was still chosen frequently always within 5% of the leading phrase label. Even IV and V, which overall were definitively associated with Phrases 2 and 3 respectively, evidently did not lead listeners to activate different schemata in this particular context. These results are shown in Table Phrases that begin on the tonic are associated with Phrase 1. Since almost all successions initiated by tonic (Stimulus Group G) were interpreted as Phrase 1, we can easily conclude that the I chord carries substantial form-functional weight. As the data indicate, when listeners heard I in m.1, the form-functional strength of the remaining chords was severely reduced. While the mere presence of V may be a strong indication of Phrase 3 in most successions, when it follows I in m.1, listeners are likely to interpret the phrase as Phrase 1. Similarly, although the use of IV may be a strong marker for Phrase 2, this strength is nullified when IV follows I in m.1. The tonic chord must initiate the phrase for the effect to occur: this effect was not observed when a non-tonic chord began the phrase, nor was it observed when the tonic chord occurred only later in the phrase. Thus, while I has a considerable effect on the activation of phrase schemata, its form-functional strength is location-specific. V is strongly associated with Phrase 3. One feature found in numerous twelvebar blues songs is the descending step succession V-IV at the beginning of the third phrase. It is therefore unsurprising that a 52.4% majority of listeners labeled V-IV-I-I as Phrase 3. Consider, however, that overall Stimulus Group A (*-IV-I-I) was typically interpreted as Phrase 2; clearly the V-IV pattern significantly influences listeners. Given 93 There were four substitutions in Group F that received phrase labels other than Phrase 3. In two of the four cases, the difference in distribution between two labels was small enough that the overall chi-square test for the entire group still produced an insignificant result. 81

100 that the succession V-IV-I-I received Phrase 3 labels from a majority of participants, we might wonder whether the results can be attributed to its descending step root progression, to the statistical frequency with which V-IV appears in the repertoire, or to the association of V (as an independent harmonic feature) with Phrase 3. The responses to Group B successions including V indicate that the last is at least a partial factor contributing to the perception of a phrase s formal function. Among Group B successions with label distributions that differed from the overall Phrase 2 trend, IV-V-I-I produced the most dramatic result, with 71.4% of participants applying the Phrase 3 label. 94 Even among Group C successions, of which only two chords received label distributions that favored anything but Phrase 2, V again had a notable impact, with IV-IV-V-I successions labeled as Phrase 3 by 61.9% of participants. All members of Stimulus Groups D, E, and F prominently featured V. As expected, the presence of V corresponded with an overall association of each of these groups with Phrase 3. Successions from groups D and F were usually identified as Phrase 3 (62.7% and 53.0% of stimuli, respectively). Group E successions were typically identified as Phrase 3 (40.9% of stimuli) or as Phrase 2 (40.7% of stimuli), but only rarely as Phrase 1 (18.5% of stimuli). When the variable chord preceded V (as in Group D, *-V-I-I), very few chords impacted participants interpretations of the phrase. When the variable chord followed V (as in Group E, V-*-I-I), a substantial number of successions were perceived as phrases other than Phrase 3. I speculate that V more strongly supports Phrase 3 s formal function when it directly resolves to tonic, as it does in the successions IV-V-I-I, IV-IV-V-I, and all of the Group D successions (*-V-I-I). When the resolution of dominant to tonic is displaced by an intervening chord (as it is in Group E successions), V s impact on the formal function of the phrase is weakened. The exception to this trend is, of course, Stimulus Group F successions (V-IV-*-I), which were identified as Phrase 3 by 53.0% of participants. Among these, all but the successions V-IV-I-I and V-IV-V-I displaced the resolution of the dominant by two measures. If the displacement of resolution leads to a lack of agreement regarding phrase labels, then the distributions for these successions should reflect this disparity. Nevertheless, the majority of participants interpreted these successions as Phrase 3. Moreover, the variable chord did not significantly affect participants interpretations. These results suggest that the two-chord succession V-IV conveys enough 94 It is also possible that the combination of V and IV in either order is associated with Phrase 3. Because many other V-* and *-V progressions were associated with Phrase 3, though, I believe V should be viewed as the primary factor. 82

101 form-functional information about the phrase that the remaining two chords have very little impact on participants interpretations of the phrase. Indeed, it is even possible that listeners responded to these chords in succession without waiting to hear the remaining two chords. Root motion affects the interpretation of phrases. Since V-IV was revealed to be such a strong independent marker for Phrase 3, it is worth investigating whether or not this feature can be generalized to include other instances of descending stepwise root motion. Indeed, across many of the stimulus groups, descending stepwise root motion heard at the beginning of a succession led to its classification as Phrase 3. Conversely, when this feature was not present in the succession, listeners tended not to label it as Phrase Successions beginning with #IV-IV and #iv-iv (Stimulus Group A) were most frequently identified as Phrase 3. Participants also most commonly labeled successions beginning with IV-III and IV-iii (Stimulus Group B) as Phrase 3. Since successions in Stimulus Group D were almost uniformly labeled Phrase 3, it is difficult to discern whether descending root motion had any impact on participants responses, or if the result was simply due to the direct resolution of dominant to tonic. Of the fourteen successions beginning with descending root motion in Stimulus Group E, eleven were most frequently labeled Phrase 3. Like Stimulus Group D, the constant presence of V in Group E successions may account for the Phrase 3 responses. Alternatively, we may choose to observe the responses to the successions that were not initiated by descending root motion. Of these, only V-bVI-I-I and V-bvii-I-I were most commonly interpreted as Phrase 3; the rest received labels contrary to the overall Phrase 3 trend. The overall results of this experiment suggest that generic root motion may have a strong impact on listeners orientation within the twelve-bar form. This trend reflects a general characteristic of twelve-bar blues songs: Phrase 3 typically begins with a descending root progression. 96. Further investigation is warranted, however, because the descending successions IV-bIII, IV-biii, V-bIII, V-biii, and V-#iv were most frequently interpreted as belonging to Phrase 2. Chords built upon 2 or b7 have a location-specific association with Phrase 3. The label distributions for successions beginning with II or ii strongly favor Phrase 3. I 95 Since these chords were constructed with Shepard tones, stepwise root motion is likely to be interpreted as stepwise motion in all voices. 96 Similarly, Phrase 2 most typically includes chords with the same root in its first two measures. Unfortunately, the design of the experiment did not allow for thorough testing of this particular feature, since only eight successions used in the experiment exhibited this characteristic (IV-IV-I-I, iv-iv-i-i, IV-iv- I-I, V-V-I-I, V-v-I-I, v-v-i-i, I-I-I-I, and I-i-I-I). 83

102 believe that successions beginning with ii or II may generate an expectation that V will follow; this assumption is supported both by the frequency of ii-v successions appearing in the last phrase of twelve-bar blues songs and by the strong general expectation for chord roots to move by perfect fifth (as discussed in Chapter 3 and in countless other studies). Because V has such a strong association with Phrase 3, it follows that ii and II may also have an association with Phrase 3, owing to their tendency to precede V. Indeed, when ii or II was followed by V, a stronger majority of participants labeled the succession as Phrase 3. These results may more generally indicate that, in addition to associating harmonies with specific phrases in a twelve-bar blues, listeners also associate their expectations for those harmonies with the appropriate phrases. 97 We might more simply posit that these label distributions favor Phrase 3 because when twelve-bar blues progressions contain ii and II, these chords are statistically most often heard in Phrase 3. However, this interpretation is not well supported by the data. Group B and C successions in which ii and II were not the initiating chord were not interpreted by the plurality of listeners as Phrase 3. The form-functional strength of these chords appears to be location-specific: in order to signify Phrase 3, ii or II must initiate the phrase. Successions beginning with either bvii or bvii were also most often identified as Phrase 3. If chords built on b7 share V s character as a harmonic marker that orients the listener to Phrase 3 of a twelve-bar blues, we might speculate whether they could be said to have dominant function; certainly many music theorists that bvii in rock music is analogous to V in common-practice music. However, like triads built on 2, bvii and bvii only appear to convey Phrase 3 formal function when initiating a phrase and this is quite unlike V. When heard as the variable chord in Group B (IV-*-I-I), Group G (I-*-I-I) or Group C (IV-IV-*-I), the triads built on b7 did not prompt interpretations that differed from the prevailing trends of the groups. Thus, like ii, the b7 triads have a locationspecific influence on our interpretation of a phrase. The b7 triads do not seem to be equivalent to V: V has a more location-independent effect on formal function. Harmonic rhythm affects the interpretation of phrases. We ve seen how an initial tonic negates the usual effect of IV and V. Duration and timing also impact the interpretation of phrases. Group D successions (*-V-I-I) were most commonly interpreted as Phrase 3. However, when V was used, the resulting V-V-I-I succession 97 As with successions initiated by V-IV, these successions could have been identified as Phrase 3 before the stimulus was heard in its entirety. 84

103 presented a generic feature common in Phrase 2 of the twelve-bar blues: a twomeasure departure from and subsequent return to tonic. This harmonic rhythm (*-*-I-I) seems to be a strong indicator of Phrase 2; so strong that it overrides a harmonic feature (V) that is otherwise statistically likely to lead to a Phrase 3 identification. Ratings This discussion has thus far focused on the relationship between harmony and musical form, but it has not directly addressed harmonic expectation. Participants in Experiment 3 were asked to rate the goodness of each succession on a six-point scale. As in Experiments 1 and 2, ratings are assumed to correlate with predictability, following the theory of misattribution (discussed more fully in Chapter 2): in short, a phrase that sounds good receives a high rating presumably because it is predictable. My analysis and interpretation of the effect of chord succession on ratings is followed by a discussion on the potential relationships between ratings and phrase labels. Did variable chord affect rating? A series of one-way ANOVAs revealed that variable chords (those represented by asterisks in Table 6.3) significantly affected participant ratings. Several trends emerged from the data. Variable chords were categorized as diatonic (within key), mixture (borrowed from the parallel mode), or chromatic (all remaining major and minor triads). As shown in Figure 6.3, listeners preferred diatonic chords, followed by mixture chords; they rated chromatic chords lowest. A one-way ANOVA and post-hoc Tukey analysis revealed that the overall result and the mean differences for each category pair were significant at the p <.001 level. Ordered pitch-class intervals (OPCI) between chord roots were measured both approaching and departing from the variable chord (hereafter abbreviated as OPCI-to and OPCI-from ). Both OPCI-to and OPCI-from significantly (p <.001) affected listening ratings, as shown in Figures 6.4 and 6.5, respectively. When observing the mean ratings for the data grouped by OPCI-to, common-practice root motion clearly emerges as most desirable to participants. Successions in which the variable chord is approached by root motion of a unison (or common tone), perfect fourth or fifth, ascending step, or descending third are rated highest. Ascending minor thirds are also highly rated an interesting result considering 85

104 that these successions necessitate the use of a non-diatonic chord built upon a scale degree borrowed from the minor mode (e.g. 1-b3, 4-b6, and 5-b7). A slightly different trend is seen when the data are grouped by OPCI-from. Not surprisingly, unisons, perfect fourths, and perfect fifths are rated highest; however, the descending major second is also highly rated. This root motion described by Ken Stephenson as pivotal to rock s harmonic language (Stephenson 2002, ) did not appear to be an expected succession in Experiment 1. Since the results from the current experiment lack a common-practice comparison (which was provided in Experiment 1), a future study examining these types of successions in context is warranted. Variable chord location Because variable chord location was shown to have a significant impact on phrase labels, it is worth investigating whether it similarly affected ratings. A one-way ANOVA on variable chord location revealed that the mean differences in ratings for all locations were significant (p <.001 for all combinations). To better understand these results, a one-way ANOVA focused on the impact of Stimulus Group, revealing that participants rated some groups significantly higher than others (p <.001). The post-hoc Tukey analysis showed that ratings for Stimulus Groups fell into three distinct categories. These results are illustrated in Figure 6.6 and Table Groups A (*-IV- I-I) and D (*-V-I-I) received the highest ratings; followed by B (IV-*-I-I), C (IV-IV-*-I), F (V-IV-*-I), and G (I-*-I-I); and finally Group E (V-*-I-I). Thus, the effect of variable chord location on ratings can be considered largely due to the chords surrounding the variable chord. Groups A and D received the highest ratings and both featured a highly expected chord succession elapsing from weak to strong measures (IV-I and V-I mm. 2-3). These two groups also featured label distributions in which a clear overall label emerged. Groups A and D also consistently featured three consecutive measures (mm. 2-4) in which a typical harmonic succession transpired (IV-I-I and V-I-I, respectively). Groups B, C, D, and F all have especially strong phrase associations. Stimulus Group E was the most formally ambiguous of all the stimulus groups: it was the only group for which the label distribution did not significantly reveal a single, definitive label. Group E successions were rated lowest and likewise were the least consistently labeled successions in the experiment. The results reveal two subtle details about expectation in twelve-bar blues successions. First, listeners expect idiomatic chord successions (such as IV-I and V-I, represented by Groups A and D) to 86

105 resolve in hypermetrically strong locations. Second, listeners expect chord successions that create easily identifiable phrases within the twelve-bar form. Although it might be interesting to focus on situations in which specific OPCIs receive high ratings within an overall low-rated context, examining interactions with location across all stimulus groups is problematic. This would equate levels of variables that would otherwise be considered vastly different, and compare levels of variables that have unbalanced representation. Because these inconsistencies preclude reliable statistical analysis, such comparisons have been excluded from this discussion. The relationship between Experiment 1 and Experiment 3 The results of this experiment (most notably the significant effect of the context provided by the stimulus group and also the significant effect of temporal location) raise the question of whether or not the variable chord produces a truly independent effect on listener ratings. One means of investigating this is to compare the results with those found in Experiment 1 (discussed in Chapter 3). Recall that Experiment 1 required participants to rate two-chord successions that included I, IV, or V on a six-point scale. Although each stimulus was preceded by a style prime, the succession itself was otherwise void of a specific musical context. Comparing the results from Experiments 1 and 3 will provide some insight into the question of whether additional musical context interacts with harmonic variables. If the ratings for successions used in Experiment 1 differ significantly from those used in Experiment 3, we can consider the context-related interactions discussed in this chapter to be much more meaningful. The simplest way to achieve this comparison is through tests of correlation. The stimuli used in Experiment 1 can be organized into six categories: I-*, IV-*, V-*, *-I, *-IV, and *-V. The variable chord, represented here by asterisks, consists of every non-redundant major and minor triad. Each of these categories is also present in the stimuli used in Experiment 3. In some cases, categories are represented multiple times in the Experiment 3 stimuli, differentiated only by the surrounding musical context. For example, the succession IV-* is present in Stimulus Group B (mm. 1-2), Stimulus Group C (mm. 2-3), and Stimulus Group F (mm. 2-3). In these three cases, the succession IV-* is surrounded by a slightly different musical context. If this context truly affected participants ratings in Experiment 3, the ratings for IV-* successions should be different between different stimulus groups and between the stimulus groups and the ratings provided in Experiment 1. Conversely, if the context did not matter, then the ratings for 87

106 IV-* successions in all four contexts should strongly and significantly correlate. 98 Table 6.20 shows where each of the six stimulus categories from Experiment 1 can be found among the stimulus groups used in Experiment 3. In this table, m.0 refers to the last measure of the tonic lead-in. Each of the six stimulus categories used in Experiment 1 has a corresponding set of 23 mean ratings: one for each two-chord succession in the category (recall that Experiment 1 excluded the direct repetition of a chord). Similar sets of mean ratings exist for successions found in Experiment 3. For example, there are 23 mean ratings for the succession IV-* found in the data from Experiment 1. There are three corresponding sets of 23 mean ratings found in the data from Experiment 3: one for Group B successions, one for Group C successions, and one for Group F successions. Correlations were run for each stimulus category from Experiment 1 and the corresponding sets of ratings from Experiment 3. Tables provide correlation tables for the ratings for all stimulus categories from Experiment 1 and the corresponding sets of ratings for the stimuli that contained that succession in Experiment 3. As these tables indicate, there are strong and significant correlations between ratings for successions in Experiment 3 and the ratings of two-chord successions from Experiment 1. Moreover, these tables also show strong correlations among pairs of stimulus groups from Experiment 3. To summarize, two variables producing main effects on listener ratings occurred in this experiment: variable chord (and its various subsets such as substitution type, OPCI-to, OPCI-from, etc.) and stimulus group (which also involves variable chord location). While interaction did occur between these two variables, the correlation found between mean ratings for stimulus groups and the equivalent context-free two-chord successions from Experiment 1, along with the correlation among stimulus groups suggests that the variable chord had an independent influence on listeners expectations. Phrase labels and ratings Figures and Tables present summaries of information pertaining to each stimulus group. Summaries contain overall mean ratings for each succession in the group, sorted by its variable chord. These results are presented in 98 Alternatively, context may not affect how the variable chord is rated, but rather the context itself receives a rating. Admittedly, these two situations are quite difficult to differentiate. 88

107 both graphic and tabular form. A one-way ANOVA confirmed that, overall, the variable chord in each stimulus group affected rating at the level of significance (p <.001 for each group). In addition, the tables include tallies of phrase labels assigned to each succession, along with the mean ratings provided by the participants who applied that particular label. For example, Table 6.27 shows that 17 (out of 21) participants labeled the succession I-IV-I-I as Phrase 1, 2 participants labeled the succession Phrase 2, and 2 labeled it Phrase 3. The mean rating of the 17 responses labeled Phrase 1 was 4.71 (found in the Phrase 1 mean column). Likewise, the mean rating of the two responses labeled Phrase 2 was 5.0, and the mean rating of the two responses labeled Phrase 3 was 4.0. The right-most column of the table, labeled p, indicates the significance of the differences between the three mean ratings for a given succession. A single one-way ANOVA for each succession was used to calculate these values. A quick glance at the means plots for each stimulus group confirms many of the results gathered from previous analyses of the effects of variable chord on rating. Again, diatonic chords were rated highest, followed by mixture chords, and finally chromatic chords. Likewise, common-practice root motion received high ratings. Since many of these results have already been discussed (and since the effect of substitution has been shown to be largely independent), they will not be further analyzed here. Instead, the remainder of this chapter will be spent discussing the relationship between the phrase labels and ratings assigned to specific successions. At the forefront of investigating the relationship between form orientation (phrase labels) and harmonic expectation (ratings) is the question of whether a given chord succession can both represent a highly expected instance of one phrase and an unexpected instance of another phrase. For instance, can a single succession represent both a suitable Phrase 3 and an unsuitable Phrase 1? These situations occur when the differences in mean ratings provided by respondents who interpret the phrases differently prove to be statistically significant. In some situations, the highest rating is associated with the most popular phrase label for that succession, implying strong expectations for both harmonic and formal function. For example, the succession ii-iv-i-i (Stimulus Group A) was most frequently identified as Phrase 3. Among those who indicated that they heard Phrase 3, the mean rating assigned to this succession was 5.22 significantly higher (p =.001) than the mean rating of responses labeled as Phrase 2 (M = 3.88) or Phrase 1 (M = 3.00). This distribution of phrase labels and ratings for ii-iv-i-i might reflect the fact that ii would be more expected by listeners in the third phrase of a twelve-bar blues than in the first or second phrase. Several other successions received significantly higher ratings from participants who 89

108 identified them as Phrase 3 (the most common interpretation): V-IV-I-I (Stimulus groups A, E, and F), ii-v-i-i (Stimulus Group D), biii-v-i-i (Group D), V-bII-I-I (Group E), and V- IV-biii-I (Group F). The first two of these represent progressions idiomatic to the twelvebar blues. The remaining three successions are interesting, however, since some music theorists have attributed dominant function their variable chords (biii and bii). 99 When the frequency of phrase label designation does not correlate with participant ratings, it may indicate varying listening strategies. Respondents who apply the most consistently used phrase label to a succession and also give it a low rating are likely making their phrase label judgment based on the chords surrounding the substitution. For example, imagine a participant who, upon hearing the succession IV-bVI-I-I, remarks, That sounds awful, but it s definitely Phrase 2. Such a response would indicate that bvi is highly unexpected, yet enough information was present in the succession for that participant to apply the same label as the majority. Successions such as these present conflicting harmonic and formal functions. For listeners who focus on the formal role evoked by this phrase, the succession may sound harmonically ungrammatical. Conversely, listeners who think the harmonic succession sounds good may have difficulty placing it within the context of the larger form. We might attribute the contradiction of rating and label distribution to the conflicting phrase associations presented by the variable chord and the stimulus group. For example, as discussed earlier, ii is strongly associated with Phrase 3. The successions included in Stimulus Group C (IV-IV-*-I) are strongly associated with Phrase 2. Thus, when ii is heard in the context of Group C (IV-IV-ii-I), those focused on the variable chord may assign it to Phrase 3 and award it a high rating (because it is a highly expected Phrase 3 chord), while those focused on the surrounding chords may assign it to Phrase 2 and give it a low rating (because it is an unexpected chord in Phrase 2); see Table Similarly ambiguous successions heard in this experiment include IV-bvii-I-I (the variable chord bvii is associated with Phrase 3, but the surrounding framework of Stimulus Group B is associated with Phrase 2; see Table 6.28), biii-iv-i-i (Phrase 3/Phrase 2; Table 6.27), IV-iv-I-I (Phrase 3/Phrase 2; Table 6.28), I-iii-I-I (Phrase 3/Phrase 1; Table 6.33), and I-VII-I-I (Phrase 2/Phrase 1; Table 6.33). 99 The bii triad is closely related to the dominant seventh chord built upon b2, which among jazz-influenced musicians has long been used as a replacement for V via tritone substitution. Incidentally, in his 2007 dissertation, Christopher Doll suggests that chords built upon b3 (biii and biii) have dominant function. (Doll 2007, 204-5). 90

109 A few noteworthy successions were given the same phrase label by a majority of listeners and yet received similar ratings regardless of the phrase label assigned; for example, ratings from participants who applied Phrase 1 labels were not significantly different from those who applied Phrase 2 labels or Phrase 3 labels, and so on. Unlike the examples discussed previously, we cannot fully assess the impact of harmony on formal function, because the mean ratings were consistently high across regardless of phrase categorization. For example, the succession I-IV-I-I (Groups A and G) received high ratings from most participants, regardless of the phrase label that was applied. 100 There is no evidence to indicate whether harmony or formal function had a stronger influence on the perception of this phrase. Nevertheless, the high mean rating and near-unanimous labeling indicate that this is undoubtedly a highly expected Phrase 1. Successions involving V produced even greater degrees of harmonic and formfunctional expectation. Both IV-V-I-I and IV-IV-V-I received unanimously high ratings across all labels and were consistently given Phrase 3 labels, despite the fact that most successions in their constituent stimulus groups were identified by participants as Phrase 2. Thus, we can say that these successions, and indeed any other that includes V, might be highly expected in Phrase 3 of a twelve-bar blues. Similarly, the succession bvii-iv-i-i received high ratings for all labels and was identified as Phrase 3 by the majority of participants Conclusions Phrase schemata clearly exist in twelve-bar blues successions. These schemata are defined both by their harmonic content and by the order in which that content is presented. Single chords can affect the strength of an active schema and can suppress the activation of other viable schemata. Some chords, such as V, have especially pervasive influence in this regard. While other chords (such as I, ii, IV, and bvii) also strongly impact schema choice, their influence is weakened when those chords are heard later in the phrase. In general, a chord heard earlier in the phrase has a greater impact on the formal function projected by that phrase. 100 It is also possible that high ratings given to successions that were also mislabelled (such as a highly rated I-IV-I-I that was also called Phrase 2) could be accounted for by random error, participants lack of focus, or simply the fact that some participants possess atypical expectations due to a weak sense of style. 91

110 The exception to this trend occurs when V initiates the phrase. While still most often associated with Phrase 3, the form-functional strength of V is severely weakened when its resolution to I is displaced or its harmonic rhythm is made to reflect Phrase 2 (V-V-I-I). This suggests that listeners may be influenced by competing blues and common-practice form-functional expectations. Formal function projected by other chords is enhanced by their earlier occurrence within a phrase, perhaps owing to the fact that phrases in twelve-bar blues songs can typically be identified by their starting chords. Alternatively, the V chord s projection of formal function may be facilitated by an immediate resolution to the tonic a prominent feature of common-practice tonality. Twelve-bar blues phrase schemata are also affected by more general characteristics, such as root motion contour and harmonic rhythm. The data from this experiment suggest that descending-step root motion is understood as characterizing Phrase 3, and that a two-measure departure from and return to tonic is a general characteristic of Phrase 2. Both bvii and bvii disrupted the overall label distribution for a stimulus group. Similarly, bii and biii received significantly higher ratings among those who assigned them a Phrase 3 label. The results from this experiment suggest that several chords may be acceptable substitutes for V in certain circumstances, and perhaps should be further evaluated as potential dominants in blues and blues-influenced rock music. Finally, the results of this experiment suggest that phrase schemata and harmonic expectations can often influence one another. Generally, when a phrase schema has a particularly strong presence, listeners have heightened expectations for harmony. Evidence for this can be found in the overall high ratings for stimulus groups that also received a clear and consistent bias for one particular phrase label. Conversely, when phrase identification is particularly difficult (indicated by inconsistent labeling), overall ratings generally suffer as well. These findings lend support to Gjerdingen s speculation that when a schema is strongly engaged, we are more easily able to fill in the blanks by predicting future events (Gjerdingen 1988, 7). When hearing twelve-bar blues music, listeners have strong expectations for diatonic substitutions and typical root motion characteristics also commonly associated with common-practice music. Nevertheless, the results of this experiment show that root motion by ascending minor third and descending major second are also highly expected in the twelve-bar blues. Thus, while our expectations of harmony in blues and common-practice music overlap, when we listen to blues our expectations for its idiomatic chord successions appear to be heightened. 92

111 Summary Stimulus group had a significant effect on the application of phrase labels. The variable chord also significantly affected phrase labeling across all stimulus groups; however, the magnitude of this effect depended on the location of the variable chord and the specific stimulus group in which it occurred. Ratings were affected by chord type (diatonic, mixture, or chromatic) and root motion, with diatonic chords and common-practice root motion receiving the highest ratings. Two instances of root motion idiosyncratic to blues/rock also received high ratings, suggesting that harmonic expectation in blues/rock music includes a wider range of acceptable root motion (instead of simply a different range). Ratings for chord substitutions correlated across stimulus groups, suggesting that the effect of chord substitution on rating was independent. Ratings were also affected by stimulus group. Phrase defining successions also received higher overall ratings. The opposite was also true: groups in which a clear-cut phrase label did not emerge received lower overall ratings. Finally, in some cases ratings and phrase labels combined to reveal that specific chord successions can invoke different expectations depending on the presently active phrase schema. 93

112 CHAPTER SEVEN CONCLUSIONS The three experiments in this dissertation provide evidence that trained musicians possess specific graded expectations of harmony when engaged with musical stimuli representative of the blues/rock genre. Although many of these expectations align with those already known for common-practice music, each experiment revealed subtle but significant discrepancies between expectations for these two genres. Experiment 1 showed that listeners are less accepting of out-of-key successions when they are primed by classical style cues than when they are primed by blues/rock cues. When primed by blues/rock cues, listeners rated primary triads equally when initiating or terminating a succession; however, in identical situations primed with classical cues, listeners showed a preference for tonic and dominant over subdominant harmony. Experiments 2 and 3 showed that listeners have strong and specific expectations of musical phrases within the context of twelve-bar blues schemata. Participants displayed sensitivity to the normative harmonic rhythm and timing in the twelve-bar blues phrase structure (Experiment 2) and largely depended on the normative events of these schemata to orient their listening within the overall twelve-bar form (Experiment 3). Experiment 3 also provided evidence that listeners prefer (presumably because they have stronger expectations for) a four-measure phrase when that phrase conveys a clear orientation within the larger twelve-bar form. Comparison of experimental results with previous research As discussed in Chapter 1, several divergent claims in the music-theoretical literature motivated the empirical investigation central to this dissertation. The first premise was that rock s harmonic syntax is governed by common intervals formed by successive chord roots (Stephenson 2002, Carter 2005). This theory, dependent upon the notion of scale-degree symmetry, was not well supported by the data from my experiments: in both experiments 1 and 3, participants displayed significant graded preferences among instances of the same root motion. In other words, listeners did not expect all chords to participate equally in the same set of allowable root progressions. Moreover, these preferences reflected the tonal hierarchy, with diatonic successions receiving higher ratings than non-diatonic successions. Both experiments 1 and 3 showed that participants react differently to diatonic and non-diatonic chords with the 94

113 same root, indicating that we attend to more than just the root of the chord when making judgments about harmony. These findings again contradict the claims of Stephenson (2002), whose work implies that our preference for hearing chord roots outweighs even the strongest tendency tones, such as secondary leading tones. The findings of this dissertation do, however, support the claims posed by Walter Everett (2004) and Christopher Doll (2007), both of whose research largely depends upon the importance of voice leading and therefore necessarily privileges attending to non-root chord members such as tendency tones. However, the connection between the empirical results of this dissertation and the work of Everett and Doll must be considered preliminary, since the stimuli used in my experiments were constructed with Shepard tones, which create inherently ambiguous voice-leading strands because each pitch class is heard in all registers simultaneously. Further research will be necessary to assess more thoroughly the impact of voice leading and specific chord members more thoroughly in these successions. The primary point of departure for this study was the question of whether musical style influences our expectations of harmony. Are our harmonic expectations different when listening to blues/rock music than when listening to classical music? In one camp are scholars such as Moore (1992), Stephenson (2002), and Tagg (2003), all of whom claim to some extent that rock music uses a unique harmonic language. Opposing arguments are presented by Everett (2004) and Doll (2007), who view rock harmony as an extension of common-practice tonality. As discussed previously, the results of my experiments show that, generally, harmonic expectations in blues/rock music are similar to those held for common-practice music. This conclusion is further solidified by the strong correlation of the results from Experiment 1 (Chapter 4) with the table of chord progressions in Walter Piston s textbook, the numerical scores provided by Fred Lerdahl s tonal pitch space model (Lerdahl 2001), and the empirical data reported by Carol Krumhansl (1990) and Bigand et al (1996). In addition, my results contribute more evidence in support of Lhost and Ashley s (2006) claim that listeners possess graded expectations of harmony in twelve-bar blues settings. While my results are by no means comprehensive, they do suggest that the harmonic language of rock is not drastically different from common-practice tonality, and thus my conclusions align more closely with the work of Everett and Doll than with that of Stephenson, Tagg, or Moore. Nevertheless, some subtle differences between rock and common-practice harmonic expectations were revealed. Notably, the difference in ratings between diatonic and non-diatonic successions was significantly less pronounced when heard in a blues context. As proposed in Chapter 4, this difference 95

114 may stem from the frequency and treatment of non-diatonic chords in rock music. Moore (1992), Tagg (2003), and Everett (2004) all point out that harmony in rock music is often established through metrical, durational, and periodic emphasis. Both syntactical and non-syntactical chord progressions are frequently forced into regular repeated phrases with a harmonic rhythm that does not privilege one chord over another (i.e., one chord per measure in a repeated four-measure unit). If a songwriter chooses to use a particularly strange chord, that strange (i.e., generally rare) chord will be emphasized through repetition. Given that pop and rock songs typically use relatively few chords, the strange chord will likely be emphasized purely because it is one of only a few chords used in the song. If these assumptions are true, experienced listeners may have stronger expectations for non-diatonic successions when these successions are heard in rock rather than classical contexts. Another significant finding in this study seemingly unique to rock music was participants equal preference among primary triads in Experiment 1. Although participants significantly preferred tonic and dominant to subdominant when beginning or ending two-chord successions, ratings among the three primary triads were not significantly different in the same situations when preceded by a blues/rock prime. I speculated that these results were likely due to the statistical frequency in which these chords are used as phrase openings or endings in the common practice and blues/rock repertoire. It is rare for a chord other than tonic or dominant to begin or end a commonpractice phrase, whereas phrases in blues/rock and popular music frequently begin with chords other than tonic or dominant. Likewise, the four- and eight-measure repeated harmonic patterns routinely used in this repertoire may end with any of a variety of chords. In a query of his database of formal attributes of Billboard Top 40 songs from , Jay Summach (2010) found that the majority of bridge sections begin on chords other than tonic or dominant, positing that IV was commonly used in this location. David Temperley s recent work (Temperley 2011; Temperley and De Clercq 2011) confirms IV s statistical prominence in a wide-ranging corpus of rock music. According to his analyses, IV is the second-most frequent chord in the repertoire Temperley studied and is routinely used in structurally important locations in songs. Several theorists (Moore 1992; Tagg 2003; Everett 2004) have speculated that harmonic successions in rock music are made to sound acceptable through rhythmic, metrical, and/or durational emphasis. Some (Björnberg 1989/2001) have gone so far as to suggest that chords are interchangeable within these periodic harmonic patterns. Experiment 2 therefore addressed a fundamental question: Do the chords matter at all when placed in a normative rhythmic and metrical framework? My results showed that 96

115 participants had a threshold at which harmony and timing formed an interactive relationship. When a chord was highly unexpected (reflected by low ratings), the timing of its onset or terminus did not impact participants ratings: these successions were rated low in both normative and atypical temporal contexts. In atypical temporal contexts participants rated chords that are idiomatic in the genre significantly higher than chords we might consider to be acceptable substitutions. In normative temporal contexts, there was no such significant differentiation. In other words, when heard in a typical location within a phrase, chords from a select group (acceptable and typical) may be freely substituted for one another. This result somewhat reflects the speculations of Björnberg (1989/2001) and Everett (2004), who suggested that such interchangeability takes place in rock music written exclusively in the minor pentatonic harmonic system. However, as noted in Chapter 4, relatively few instances of normative timing were used as stimuli in this experiment. In order to support this claim fully, an additional study investigating a greater number of successions with normative timing is needed. The relationship between my results and previous experimental research on harmony and timing was slightly inconsistent. Overall, participants in my study showed a preference for normative timing, supporting the findings of Schmuckler and Boltz (1994) and Tillman and Lebrun-Guillaud (2006), all of whom found that disrupted or absent periodicity negated expectations for all but the most salient harmonic events. However, contrary to these studies, participants in my experiment appeared rigid in their expectations of timing. Listeners did not differentiate between metrically strong and metrically weak harmonic events that occurred in atypical locations. This suggests that the established schema (the first two phrases of a twelve-bar blues progression) had a particularly strong impact on participants ratings. It is possible that once they inferred the presence of the blues schema, participants employed a listening and rating strategy that cast aside successions that did not align with their projected metrical framework. Additional experiments employing a non-post-hoc response mode (such as a forced choice judgment in which reaction time is measured) would be useful for comparison with the findings of this experiment, since participants would not be able to employ subjective listening strategies as easily. The final experiment in this dissertation addressed the relationship between harmony and form in the twelve-bar blues progression. Participants were asked to provide two responses for each four-measure succession that they heard: a rating (representing expectation) and a phrase label (representing the phrase s location within the larger twelve-bar structure). Overall, the ratings in this experiment correlated significantly with those from Experiment 1, suggesting that, with a few notable 97

116 exceptions, expectations for local harmonic events are generally independent of the surrounding musical events. My results differ from the findings of Lhost and Ashley (2006), who found that expectations were context-dependent in twelve-bar blues progressions. Although the difference in response mode and number of harmonic variables (Lhost and Ashley used 3 chords in each location while I used 24) makes it difficult to compare the results of these two experiments, it may be that these studies simply investigated expectation from different perspectives. The accuracy and response time in Lhost and Ashley s experiment may reflect listeners expectations for the harmonic succession at that given moment; alternatively, they could indicate a more general sense of fulfilled or unfulfilled expectations within the overall twelve-bar form. Given that their participants were listening to stimuli that consisted of entire twelve-bar progressions, it is difficult to interpret exactly what kind of expectation Lhost and Ashley s results represent. In my experiment, harmony significantly impacted participants orientation within the implicit twelve-bar form. Moreover, participants ratings were significantly higher for successions that were more consistently labeled that is, expectations were stronger for phrases that were more clearly defined in the twelve-bar form. Successions that were quickly and accurately identified in Lhost and Ashley s experiment may have been consistently labeled in my experiment. The twelve-bar blues represents a schema for which listeners possess expectations with both short and long time courses (to use Elizabeth Margulis terms). Both Lhost and Ashley s experiment and my own experiment attempt to address each of these types of expectation in this musical context, and it is certainly possible that shortand long-term expectations could have been conflated by the constraints of the response modes or the durations of stimuli. It is clear that both of these studies leave open the possibility for substantial research further investigating harmony in twelve-bar blues music (and more generally, popular music), as well as the relationship between harmony and form in this literature. Opportunities for further research For many listeners, it is difficult perhaps even impossible to process harmony without considering voice leading. Voice leading for a single two-chord succession can be composed in numerous ways, some of which are likely more expected than others. Nevertheless, even in a study investigating two-chord successions there exists an unwieldy number of voice leading possibilities. This issue was central in the design of 98

117 all three experiments in this dissertation. To eliminate this potential problem, stimuli were constructed with Shepard tones, which greatly interfere with a listener s ability to attend to specific voice-leading strands. Also, unfortunately, Shepard tones produce an unfamiliar and arguably unmusical timbre. Although my stimuli adequately conveyed the features necessary to evoke blues/rock schemata (as confirmed in the pre-test in Experiment 3), it is possible that stimuli with timbres more representative of rock and classical music might have produced more robust results. Moreover, the voice leading of chord successions in most guitar-oriented rock music differs greatly from that found in common-practice successions. It would undoubtedly be interesting to investigate the impact of timbre and voice leading on harmonic expectations in rock and commonpractice music, even if the scope of the experiment was restricted to relatively few voice-leading and timbre combinations. Experiment 2 produced curious results and would likely benefit from a restudy that used more stimuli with normative timing. In addition, it would be useful to include a greater number of chords in order to gain further insight into the possibility that listeners possess a harmonic expectancy threshold beyond which timing becomes irrelevant to their musical experience. Since participants did not differentiate between the degrees of metrical shift in Experiment 2, one possibility for further study would be to include only two levels of the timing variable: normative and random. This would allow for a greater number of chords to be used as stimuli without substantially impacting the length of the experiment. As the results from experiments 2 and 3 indicate, listeners are keenly aware of the different phrase schemata in a twelve-bar blues progression, and this awareness is significantly affected by harmony. In his recent work, Jay Summach (2010) has demonstrated the close relationship between pop music and common-practice formal units (specifically the sentence structure). An empirical investigation of harmonic and form-functional expectation in these contrasting styles would also likely be greatly beneficial to this growing body of research. Empirical research has demonstrated that expectations for musical events are shaped by the statistical frequency in which those events occur within the repertoire. Several scholars have shown this to be true for common-practice music (Krumhansl 1990 and Aarden 2003, among many others), non-western music (Castellanto et al 1984; Von Hippel, Huron, and Harnish 2006; Krumhansl et al 2000), and even novel musical systems (Jonaitis and Saffran 2009). Throughout this dissertation, perhaps the least supported speculations made pertained to the statistical frequency with which particular events occur in the blues/rock repertoire. The results from my studies provide 99

118 some evidence that the distributional hierarchy of harmonic events in rock may be somewhat idiom-specific, but the evidence is bound by the relatively narrow scope of the experiments. The recent study by Temperley and De Clercq (2011) provides a point of departure for future comparisons of the statistics of rock harmony with the evidence presented in this dissertation. Lerdahl and Jackendoff claimed that our understanding of musical grammar is gained through exposure to the music of our culture (Lerdahl and Jackendoff 1983, 3-4). The participants in my studies have most certainly received substantial exposure to rock music. On the surveys following each experiment, the mean ratings for questions pertaining to rock music were never below 3 out of 5. Nevertheless, for reasons of practicality, the demographic range of participants in my experiments was rather narrow: all participants were music majors at Florida State University between the ages of 18 and 30, and most played orchestral instruments. Unsurprisingly, survey responses to questions pertaining to classical music were significantly higher than those pertaining to rock music in all of the experiments. Including listeners from different demographics and with different levels of musical training would likely provide an opportunity for a fruitful comparison with the experimental results presented in this dissertation. Summary This dissertation aimed to investigate empirically the assumptions behind some of the prominent theories of rock harmony from contemporary music-theoretical discourse. When we cast the notion of harmonic function as harmonic expectation, the experimental results of this study show that we have similar graded expectancies when listening either to blues/rock or to common-practice music. However, as discussed in Chapter 1, our concept of function may be defined in many different ways. While the overall results suggest that the tonal hierarchy pervades expectations for both genres of music, several details of the experiments reveal subtleties that make rock s harmonic usage stand out. Moreover, these experiments confirm that listeners possess specific expectations of phrase schemata idiomatic to blues/rock music. The experimental results suggest that listeners use harmony as a means of forming longer range formal expectations; put differently, they use harmony as a means of ascribing formal function. Expressed this way, we can begin to separate the function of harmony in rock music from our notions of function in other genres. 100

119 This dissertation represents a small step toward a general understanding of harmony in popular music. I hope that the results discussed in earlier chapters and the further studies proposed in this chapter will serve as a point of departure for further interdisciplinary work in music theory, music cognition, and popular music scholarship. Finally, I hope that this dissertation will inspire music scholars to continue to investigate and criticize the things that we take for granted in our understanding of music. Such inquiries are what enrich and advance our field and our discourse. 101

120 ILLUSTRATIONS Figure 1.1. Howlin Wolf/Willie Dixon, Little Red Rooster, first verse. 102

121 I V/vi IV V/V I V/vi IV V/V I V/ii I V/ii I V/V I V/ii Figure 2.1. Chord progression for (Sittin On) The Dock of the Bay, by Otis Redding 103

122 Table 4.1. A summary of trials used in Experiment 1. All successions contain at least one primary triad. Chord combinations are heard only once in each context. 101 Group Question # Question prompt Style Cue Length Silence Chord 1 (750ms) Silence Chord 2 (750ms) Response 1 3s Blues 1A 24s 1s Major or minor triad 500ms Major or minor triad 4s s Blues 1B 2s 1s 70 3s Blues 2A 24s 1s Major or minor triad Major or minor triad 500ms 500ms Major or minor triad Major or minor triad 4s 4s s Blues 2B 2s 1s Major or minor triad 500ms Major or minor triad 4s 1 3s Classical 2A 24s 1s Major or minor triad 500ms Major or minor triad 4s s Classical 2B 2s 1s 70 3s Classical 1A 24s 1s Major or minor triad Major or minor triad 500ms 500ms Major or minor triad Major or minor triad 4s 4s s Classical 1B 2s 1s Major or minor triad 500ms Major or minor triad 4s 101 If Chord 1 is not I, IV, or V, then Chord 2 must be I, IV, or V. 104

123 Table 4.2. Main effect of ordered pitch-class intervals (OPCIs) between chord roots on rating (p < 0.001) in Experiment 1. Ordered Pitch-Class Interval N Rating (Mean) Unis Asc. Min. 2nd/Desc. Maj. 7th Asc. Maj. 2nd/Desc. Min. 7th Asc. Min. 3rd/Desc. Maj. 6th Asc. Maj. 3rd/Desc. Min. 6th Asc. Perf. 4th/Desc. Perf. 5th Asc. Tritone/Desc. Tritone Asc. Perf. 5th/Desc. Perf. 4th Asc. Min. 6th/Desc. Maj. 3rd Asc. Maj. 6th/Desc. Min. 3rd Asc. Min. 7th/Desc. Maj. 2nd Asc. Maj. 7th/Desc. Min. 2nd Total

124 Figure 4.1. Plot of mean ratings for data grouped by ordered pitch-class interval in Experiment

125 Table 4.3. Mean ratings for data grouped by primary triads used in each succession in Experiment 1. A one-way ANOVA revealed a significant difference between mean ratings for successions containing multiple primary triads and those containing only a single primary triad (p <.001). Primary Chord(s) Used N Rating I IV V Multiple Total

126 Figure 4.2. Plot of mean ratings for chord successions in Experiment 1 grouped according to the number and type of primary triads used. 108

127 Table 4.4. Main effect of primary chord(s) used on rating in Experiment 1 for data subsets grouped by ordered pitch-class interval. Participants rated successions that included multiple primary triads significantly higher than those that included only a single primary triad (p <.001 in all cases). Ordered Pitch-Class Interval Primary Chord(s) Used N Mean Asc. Maj. 2nd/Desc. Min. 7th I IV V Multiple Total Asc. Perf. 4th/Desc. Perf. 5th I IV V Multiple Total Asc. Perf. 5th/Desc. Perf. 4th I IV V Multiple Total Asc. Min. 7th/Desc. Maj. 2nd I IV V Multiple Total

128 Figure 4.3. Plot of mean ratings for data grouped by root motion by ascending major second/descending minor seventh. 110

129 Figure 4.4. Plot of mean ratings for data grouped by root motion by ascending perfect fourth/descending perfect fifth. 111

130 Figure 4.5. Plot of mean ratings for data grouped by root motion by ascending perfect fifth/descending perfect fourth. 112

131 Figure 4.6. Plot of mean ratings for data grouped by root motion by ascending minor seventh/descending major second. 113

132 Table 4.5. Main effect (p <.001) of OPCI on rating for successions that did not include multiple primary triads or multiple primary triad roots (such as i-iv or v-i). Ordered Pitch-Class Interval N Mean Asc. Min. 2nd/Desc. Maj. 7th Asc. Maj. 2nd/Desc. Min 7th Asc. Min. 3rd/Desc. Maj. 6th Asc. Maj. 3rd/Desc. Min 6th Asc. Perf. 4th/Desc. Perf. 5th Asc. Tritone/Desc. Tritone Asc. Perf. 5th/Desc. Perf. 4th Asc. Min. 6th/Desc. Maj. 3rd Asc. Major Sixth/Desc. Minor Third Asc. Min. 7th/Desc. Maj. 2nd Asc. Maj. 7th/Desc. Min. 2nd Total

133 Figure 4.7. Plot of mean ratings for successions that did not include multiple primary triads or multiple primary triad roots (such as i-iv or v-i), grouped by OPCI. 115

134 Table 4.6. Statistical significance of mean differences between ratings for instances of the same OPCI. OPCI p Unison.000 Asc. Minor Second/Desc. Major Seventh.000 Asc. Major Second/Desc. Minor Seventh.000 Asc. Minor Third/Desc. Major Sixth.000 Asc. Major Third/Desc. Minor Sixth.000 Asc. Perfect Fourth/Desc. Perfect Fifth.015 Asc. Tritone/Desc. Tritone.001 Asc. Perfect Fifth/Desc. Perfect Fourth.000 Asc. Minor Sixth/Desc. Major Third.000 Asc. Major Sixth/Desc. Minor Third.000 Asc. Minor Seventh/Desc. Major Second.000 Asc. Major Seventh/Desc. Minor Second

135 Table 4.7. Mean ratings for chords following the tonic (p <.001), subdominant (p <.001), and dominant (p <.001). Chord #1 Chord #2 I IV V I N/A i bii bii II ii biii biii III iii IV 4.79 N/A 4.02 iv #IV/bV #iv/bv V N/A v bvi bvi VI vi bvii bvii VII vii Total

136 Figure 4.8. Plots of ratings for chords following the tonic, subdominant, and dominant. 118

137 Table 4.8. Mean ratings for chords approaching tonic (p <.001), subdominant (p <.001), and dominant (p <.001). Chord #2 Chord #1 I IV V I N/A i bii bii II ii biii biii III iii IV 4.82 N/A 4.52 iv #IV/bV #iv/bv V N/A v bvi bvi VI vi bvii bvii VII vii Total

138 Figure 4.9. Plots of ratings for chords approaching tonic, subdominant, and dominant. 120

139 Table 4.9. A comparison of ratings for diatonic successions used both in Experiment 1 and Krumhansl Krumhansl s ratings range from 1 to 7; mine range from 1 to 6. Also included are Krumhansl s ad-hoc ratings (195) of successions found in Piston s table of root progressions (Piston 1941/1978), which range from 0 to 3. Succession Krumhansl Piston Hughes (overall) Hughes (blues) Hughes (classical) I-ii I-iii I-IV I-V I-vi ii-i ii-iv ii-v iii-i iii-iv iii-v IV-I IV-ii IV-iii IV-V IV-vi V-I V-ii V-iii V-IV V-vi vi-i vi-iv vi-v

140 Table Correlations between the different ratings of two-chord successions listed in Table 4.9. Krumhansl Piston Hughes (overall) Hughes (blues) Hughes (classical) Krumhansl **.876 **.829 **.816 ** Piston.722 ** **.662 **.521 ** Hughes (overall).876 **.686 ** **.820 ** Hughes (blues).829 **.662 **.973 ** ** Hughes (classical).816 **.521 **.820 **.693 ** 1 **. Correlation is significant at the 0.01 level (2-tailed). 122

141 Table Correlations between Lerdahl's chord distance measurement and the mean ratings for all 132 successions used in Experiment 1. Lerdahl Hughes (overall) Hughes (blues) Hughes (classical) Lerdahl ** ** ** Hughes (overall) ** **.877 ** Hughes (blues) **.991 ** ** Hughes (classical) **.877 **.806 ** 1 Total half steps * Largest leap Common tones ** **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed). 123

142 Table A comparison of mean ratings for diatonic and non-diatonic successions (p <.001). Type of Succession N Mean Diatonic Non-Diatonic Total

143 Figure Plot of mean ratings for diatonic and non-diatonic successions. 125

144 Table A comparison of mean ratings for diatonic, mixture, and chromatic successions (p <.001). Type of Succession N Mean Diatonic Mixture Chromatic Total

145 Figure Plot of mean ratings for diatonic, mixture, and chromatic successions. 127

146 Table A comparison of mean ratings for successions grouped by style and type of succession (diatonic, non-diatonic). The difference between mean ratings for nondiatonic successions in blues and classical contexts is significant (p =.001). Style Type of Succession Mean N Blues Diatonic Non-Diatonic Total Classical Diatonic Non-Diatonic Total Total Diatonic Non-Diatonic Total

147 Figure Plot of mean ratings for diatonic and non-diatonic successions in both blues and classical contexts. 129

148 Table A comparison of mean ratings for successions grouped by style and type of succession (diatonic, mixture, other chromatic). The difference between mean ratings for mixture and other chromatic successions in blues and classical contexts is significant (p =.001). Style Type of Succession Mean N Blues Diatonic Mixture Chromatic Total Classical Diatonic Mixture Chromatic Total Total Diatonic Mixture Chromatic Total

149 Figure A plot of mean ratings for diatonic, mixture, and other chromatic successions in both blues and classical contexts. 131

150 Table The effect of the type of succession (diatonic vs. non-diatonic) on ratings among successions with diatonic chord roots (p <.001). Style Type of Succession Mean Rating N Blues Diatonic Non-Diatonic Total Classical Diatonic Non-Diatonic Total

151 Figure Plot of mean ratings for successions with diatonic chord roots. 133

152 Table A comparison of mean ratings for successions grouped by first chord. The higher ratings for non-primary first chords are significant (p <.001), but there are no significant differences between primary triad openings. First Chord N Mean I IV V Other Total

153 Figure Plot of mean ratings for successions grouped by opening chord. 135

154 Table Comparison of means for successions beginning with primary triads. The difference in mean ratings between styles was significant (p =.014). Style Opening Chord Mean N Blues I IV V Total Classical I IV V Total Total I IV V Total

155 Figure Plot of mean ratings for successions beginning with primary triads in both blues and classical contexts. 137

156 Table A comparison of means for successions grouped by closing chord. At the level of significance, tonic endings were rated highest and non-primary endings were rated lowest. The mean difference between dominant and subdominant endings was not significant. Closing Chord N Mean I IV V Other Total

157 Figure Plot of mean ratings grouped by closing chord. 139

158 Table A comparison of mean ratings for successions that close with primary triads. The difference between mean ratings between styles was significant (p =.019). Closing Chord Style Mean N I Blues Classical Total IV Blues Classical Total V Blues Classical Total Total Blues Classical Total

159 Figure Plot of mean ratings for successions ending with primary triads in both blues and classical contexts. 141

160 Figure 5.1. Score of the accompanying drum track used in Experiments 2A and 2B. 142

161 Figure 5.2. A summary of stimuli used in Experiment 2A and Experiment 2B. Illustrated here are stimulus groups A, B, and C. The non-tonic chord is indicated by brackets and asterisks. Trials also used bvii, #IV (Experiment 2A), V, ii, and vii (Experiment 2B) in these locations. 143

162 Figure 5.2 (continued). Illustrated here are stimulus groups D and E. The non-tonic chord is indicated by brackets and asterisks. Trials also used bvii and #IV in these locations. 144

163 Figure 5.2 (continued). Illustrated here are stimulus groups F and G. The non-tonic chord is indicated by brackets and asterisks. Trials also used bvii and #IV in these locations. 145

164 Figure 5.3. A plot of mean ratings for IV (M = 3.87), bvii (M = 3.32), and #IV (M = 2.60) in all timing conditions. All mean differences were significant (p <.001). 146

165 Figure 5.4. A plot of mean ratings for typical (M = 3.65) and atypical (M = 3.25) timing in all harmonic conditions. The mean difference was significant (p =.003). 147

166 Figure 5.5. A plot of mean ratings for typical and atypical timing conditions when the data are grouped by contrasting chord shows a significant effect of timing when progressions include IV (p =.050) and bvii (p =.006) but not for progressions that include #IV (p =.347). 148

167 Figure 5.6. A plot of mean ratings for non-tonic chords when the data are grouped by timing. In typical timing conditions, only ratings for #IV were significantly distinct (p <.001, p =.007). In atypical timing conditions, all mean ratings were significantly different (p <.001 in all cases). 149

168 Figure 5.7. A plot of mean ratings for non-tonic chords in all timing conditions in Experiment 2B (p <.001). 150

169 Figure 5.8. A plot of means for ratings of typical and atypical timing conditions in Experiment 2B. The difference between means approached, but did not achieve, the level of statistical significance (p =.077). 151

170 Figure 5.9. A plot of mean ratings for typical and atypical timing when the data are grouped by non-tonic chord. Only successions that included V approached the level of statistical significance (p =.070). 152

171 Figure A plot of mean ratings for non-tonic chords when the data are grouped by timing. In typical timing conditions, none of the ratings was statistically distinct, although the separation of V from the remaining chords approached the level of significance (p =.148). In atypical timing conditions, all mean differences were significant. 153

172 Figure 6.1. The structure of the standard twelve-bar blues and the excerpts from which stimuli were constructed. 154

173 Table 6.1. Cross-tabulation of question type (recorded or synthesized) and accuracy (correct or incorrect) for the pre-test. A chi-square test revealed that there was no significant effect of question type on accuracy (p = 0.545). Incorrect Correct Total Question Type Recorded Count % within Question Type 27.6% 72.4% 100.0% Synthesized Count % within Question Type 31.4% 68.6% 100.0% Total Count % 29.5% 70.5% 100.0% 155

174 Table 6.2. A cross-tabulation of phrase (beginning, middle, or end) and accuracy (correct or incorrect) for the pre-test. A chi-square test revealed that there was no significant effect of phrase on accuracy (p = 0.144). Incorrect Correct Total Phrase Phrase 1 Count % within Phrase 38.1% 61.9% 100.0% Phrase 2 Count % within Phrase 28.6% 71.4% 100.0% Phrase 3 Count % within Phrase 22.2% 77.8% 100.0% Total Count % 29.5% 70.5% 100.0% 156

175 Table 6.3. A summary of the Stimulus Groups for the trials used in Experiment 3. Asterisks indicate the measures in which a variable chord occurs. Timing: 2s 9s 5s Introduction (fade-in) (fade-out) Group A I I * IV I I Group B I I IV * (not IV) I I Group C I I IV IV * (not I) I Group D I I * (not IV, I) V I I Group E I I V * (not IV, V) I I Group F I I V IV * (not I) I Prompt Group G I I I * (not IV) I I Response 157

176 Table 6.4. A cross-tabulation of Stimulus Group and phrase label. A chi-square test showed that the observed differences in distribution of phrase labels between groups were significant at the p <.001 level. Phrase 1 Phrase 2 Phrase 3 Stimulus Group (A): *-IV-I-I 20.0% 45.4% 34.7% (B): IV-*-I-I 19.9% 51.9% 28.1% (C): IV-IV-*-I 17.8% 61.9% 20.3% (D): *-V-I-I 11.3% 22.7% 66.0% (E): V-*-I-I 17.3% 41.3% 41.3% (F): V-IV-*-I 11.8% 35.2% 53.0% (G): I-*-I-I 54.1% 26.6% 19.3% Total 22.5% 21.7% 40.9% 158

177 Figure 6.2. A representation of phrase label distribution for each stimulus group. A chisquare test showed that the observed differences in distribution of phrase types between groups were significant at the p <.001 level. 159

178 Table 6.5. The p-values of chi-square tests for all pairs of Stimulus Groups (labeled A through G). Stimulus Group A B C D E F G A <.001 < <.001 <.001 B < <.001 <.001 C < <.001 <.001 <.001 <.001 D <.001 <.001 <.001 <.001 <.001 <.001 E <.001 < <.001 F <.001 <.001 <.001 < <.001 G <.001 <.001 <.001 <.001 <.001 <

179 Table 6.6. The p-values of chi-square tests for all pairs of listener-assigned phrase labels (Phrases 1-3) within Stimulus Groups (A-G). Stimulus Group Phrases 1 & 2 Phrases 2 & 3 Phrases 1 & 3 A < B <.001 < C <.001 < D <.001 <.001 <.001 E < <.001 F <.001 <.001 <.001 G < <

180 Table 6.7. Overall frequency distribution of phrase labels for all variable chords. Variable Chord Phrase 1 Phrase 2 Phrase 3 p I 46.4% 23.8% 29.8%.031 i 21.1% 43.5% 35.4%.003 bii 21.1% 44.2% 34.7%.003 bii 19.0% 39.5% 41.5%.001 II 29.3% 34.0% 36.7%.531 ii 20.4% 32.0% 47.6%.000 biii 20.4% 44.2% 35.4%.002 biii 22.4% 40.1% 37.4%.018 III 23.1% 40.1% 36.7%.028 iii 20.4% 40.1% 39.5%.004 IV 25.4% 41.3% 33.3%.304 iv 18.4% 38.1% 43.5%.000 #IV/bV 15.6% 41.5% 42.9%.000 #iv/bv 19.0% 51.0% 29.9%.000 V 25.4% 23.8% 50.8%.000 v 21.8% 41.5% 36.7%.009 bvi 19.7% 37.4% 42.9%.002 bvi 25.2% 40.8% 34.0%.066 VI 32.7% 40.8% 26.5%.104 vi 29.3% 46.9% 23.8%.002 bvii 26.5% 32.0% 41.5%.080 bvii 17.0% 44.2% 38.8%.000 VII 18.4% 46.9% 34.7%.000 vii 15.0% 50.3% 34.7%.000 Total 22.5% 40.3% 37.2%

181 Table 6.8. The p-values of chi-square tests for all variable chords in stimuli interpreted as either Phrase 2 or Phrase 3. Variable chord p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii

182 Table 6.9. Distribution of phrase labels organized by Chord 1; p-values provided for all three phrase designations as well as for each of the three possible pairs of phrase designations. Chord 1 Phrase 1 Phrase 2 Phrase 3 p (all Ps) p (P1 & P2) p (P1 & P3) p (P2 & P3) I 55.8% 25.0% 19.2% i 23.8% 38.1% 38.1% bii 19.0% 45.2% 35.7% bii 19.0% 31.0% 50.0% II 19.0% 21.4% 59.5% ii 11.9% 33.3% 54.8% biii 9.5% 38.1% 52.4% biii 14.3% 31.0% 54.8% III 21.4% 33.3% 45.2% iii 14.3% 47.6% 38.1% IV 19.0% 56.0% 24.9% iv 19.0% 38.1% 42.9% #IV/bV 7.1% 31.0% 61.9% #iv/bv 19.0% 35.7% 45.2% V 15.2% 38.0% 46.8% v 11.9% 33.3% 54.8% bvi 16.7% 21.4% 61.9% bvi 16.7% 38.1% 45.2% VI 21.4% 28.6% 50.0% vi 7.1% 40.5% 52.4% bvii 11.9% 23.8% 64.3% bvii 11.9% 23.8% 64.3% VII 19.0% 45.2% 35.7% vii 14.3% 35.7% 50.0%

183 Table Distribution of phrase labels organized by Chord 2; p-values provided for all three phrase designations as well as each of the three possible pairs of phrase designations. Chord 2 Phrase 1 Phrase 2 Phrase 3 p (all Ps) p (P1 & P2) p (P1 & P3) p (P2 & P3) I 34.9% 28.6% 36.5% i 28.6% 36.5% 34.9% bii 31.7% 33.3% 34.9% bii 22.2% 44.4% 33.3% II 44.4% 31.7% 23.8% ii 28.6% 31.7% 39.7% biii 31.7% 41.3% 27.0% biii 28.6% 44.4% 27.0% III 28.6% 36.5% 34.9% iii 28.6% 28.6% 42.9% IV 17.8% 46.7% 35.6% iv 23.8% 36.5% 39.7% #IV/bV 25.4% 41.3% 33.3% #iv/bv 22.2% 54.0% 23.8% V 14.7% 22.6% 62.7% v 33.3% 39.7% 27.0% bvi 25.4% 41.3% 33.3% bvi 36.5% 38.1% 25.4% VI 41.3% 44.4% 14.3% vi 42.9% 46.0% 11.1% bvii 46.0% 27.0% 27.0% bvii 23.8% 44.4% 31.7% VII 22.2% 49.2% 28.6% vii 19.0% 60.3% 20.6%

184 Table Distribution of phrase labels organized by Chord 3; p-values provided for all three phrase designations as well as for each of the three possible pairs of phrase designations. Chord 3 Phrase 1 Phrase 2 Phrase 3 p (all Ps) p (P1 & P2) p (P1 & P3) p (P2 & P3) I 25.6% 37.0% 37.4% i 7.1% 59.5% 33.3% bii 7.1% 59.5% 33.3% bii 14.3% 40.5% 45.2% II 16.7% 50.0% 33.3% ii 16.7% 31.0% 52.4% biii 14.3% 54.8% 31.0% biii 21.4% 42.9% 35.7% III 16.7% 52.4% 31.0% iii 14.3% 50.0% 35.7% IV 19.0% 38.1% 42.9% iv 9.5% 40.5% 50.0% #IV/bV 9.5% 52.4% 38.1% #iv/bv 14.3% 61.9% 23.8% V 7.1% 26.2% 66.7% v 14.3% 52.4% 33.3% bvi 14.3% 47.6% 38.1% bvi 16.7% 47.6% 35.7% VI 31.0% 47.6% 21.4% vi 31.0% 54.8% 14.3% bvii 11.9% 47.6% 40.5% bvii 11.9% 64.3% 23.8% VII 11.9% 45.2% 42.9% vii 9.5% 50.0% 40.5%

185 Table Cross-tabulation of Chord 1 and Phrase Label (p <.001) for Stimulus Group A (*-IV-I-I). Overall, these successions were identified as Phrase 2. Individual successions, identified by Chord 1, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 1 Phrase 1 Phrase 2 Phrase 3 p I 81.0% 9.5% 9.5%.000 i 28.6% 52.4% 19.0%.156 bii 23.8% 66.7% 9.5%.004 bii 23.8% 42.9% 33.3%.565 II 33.3% 33.3% 33.3% ii 19.0% 38.1% 42.9%.368 biii 9.5% 61.9% 28.6%.012 biii 19.0% 42.9% 38.1%.368 III 33.3% 38.1% 28.6%.867 iii 19.0% 61.9% 19.0%.021 IV 38.1% 47.6% 14.3%.156 iv 28.6% 42.9% 28.6%.651 #IV/bV 9.5% 42.9% 47.6%.066 #iv/bv 28.6% 28.6% 42.9%.651 V 23.8% 23.8% 52.4%.180 v 14.3% 47.6% 38.1%.156 bvi 28.6% 38.1% 33.3%.867 bvi 4.8% 52.4% 42.9%.018 VI 23.8% 38.1% 38.1%.651 vi 9.5% 61.9% 28.6%.012 bvii 14.3% 38.1% 47.6%.156 bvii 14.3% 23.8% 61.9%.018 VII 23.8% 57.1% 19.0%.066 vii 9.5% 42.9% 47.6%.066 Total 23.4% 43.1% 33.5%

186 Table Cross-tabulation of Chord 2 and Phrase Label (p =.005) for Stimulus Group B (IV-*-I-I). Overall, these successions were identified as Phrase 2. Individual successions, identified by Chord 2, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 2 Phrase 1 Phrase 2 Phrase 3 p I 23.8% 47.6% 28.6%.368 i 28.6% 42.9% 28.6%.651 bii 19.0% 47.6% 33.3%.276 bii 9.5% 66.7% 23.8%.004 II 42.9% 33.3% 23.8%.565 ii 4.8% 52.4% 42.9%.018 biii 19.0% 52.4% 28.6%.156 biii 23.8% 47.6% 28.6%.368 III 14.3% 42.9% 42.9%.180 iii 14.3% 33.3% 52.4%.102 IV 38.1% 47.6% 14.3%.156 iv 19.0% 38.1% 42.9%.368 #IV/bV 19.0% 52.4% 28.6%.156 #iv/bv 9.5% 71.4% 19.0%.001 V 9.5% 19.0% 71.4%.001 v 38.1% 33.3% 28.6%.867 bvi 19.0% 57.1% 23.8%.066 bvi 23.8% 42.9% 33.3%.565 VI 14.3% 66.7% 19.0%.005 vi 19.0% 76.2% 4.8%.000 bvii 28.6% 47.6% 23.8%.368 bvii 23.8% 47.6% 28.6%.368 VII 14.3% 66.7% 19.0%.005 vii 9.5% 76.2% 14.3%.000 Total 20.2% 50.4% 29.4%

187 Table Cross-tabulation of Chord 3 and Phrase Label (p <.001) for Stimulus Group C (IV-IV-*-I). Overall, these successions were identified as Phrase 2. Individual successions, identified by Chord 3, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 3 Phrase 1 Phrase 2 Phrase 3 p I 38.1% 47.6% 14.3%.156 i 4.8% 85.7% 9.5%.000 bii 4.8% 81.0% 14.3%.000 bii 19.0% 38.1% 42.9%.368 II 23.8% 66.7% 9.5%.004 ii 19.0% 57.1% 23.8%.066 biii 14.3% 71.4% 14.3%.001 biii 19.0% 61.9% 19.0%.021 III 19.0% 71.4% 9.5%.001 iii 23.8% 61.9% 14.3%.018 IV 19.0% 57.1% 23.8%.066 iv 14.3% 47.6% 38.1%.156 #IV/bV 14.3% 71.4% 14.3%.001 #iv/bv 23.8% 76.2%.016 V 9.5% 28.6% 61.9%.012 v 19.0% 66.7% 14.3%.005 bvi 19.0% 61.9% 19.0%.021 bvi 14.3% 61.9% 23.8%.018 VI 42.9% 52.4% 4.8%.018 vi 38.1% 61.9%.275 bvii 9.5% 61.9% 28.6%.012 bvii 14.3% 66.7% 19.0%.005 VII 14.3% 47.6% 38.1%.156 vii 9.5% 66.7% 23.8%.004 Total 18.7% 61.3% 20.0%

188 Table Cross-tabulation of Chord 1 and Phrase Label (p <.001) for Stimulus Group D (*-V-I-I). Overall, these successions were identified as Phrase 3. Individual successions, identified by Chord 1, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 1 Phrase 1 Phrase 2 Phrase 3 p I 66.7% 4.8% 28.6%.002 i 19.0% 23.8% 57.1%.066 bii 14.3% 23.8% 61.9%.018 bii 14.3% 19.0% 66.7%.005 II 4.8% 9.5% 85.7%.000 ii 4.8% 28.6% 66.7%.002 biii 9.5% 14.3% 76.2%.000 biii 9.5% 19.0% 71.4%.001 III 9.5% 28.6% 61.9%.012 iii 9.5% 33.3% 57.1%.028 IV 9.5% 19.0% 71.4%.001 iv 9.5% 33.3% 57.1%.028 #IV/bV 4.8% 19.0% 76.2%.000 #iv/bv 9.5% 42.9% 47.6%.066 V 38.1% 42.9% 19.0%.368 v 9.5% 19.0% 71.4%.001 bvi 4.8% 4.8% 90.5%.000 bvi 28.6% 23.8% 47.6%.368 VI 19.0% 19.0% 61.9%.021 vi 4.8% 19.0% 76.2%.000 bvii 9.5% 9.5% 81.0%.000 bvii 9.5% 23.8% 66.7%.004 VII 14.3% 33.3% 52.4%.102 vii 19.0% 28.6% 52.4%.156 Total 14.7% 22.6% 62.7%

189 Table Cross-tabulation of Chord 2 and Phrase Label (p <. 001) for Stimulus Group E (V-*-I-I). Overall, these successions were identified as Phrase 3 (though just barely). Individual successions, identified by Chord 1, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 2 Phrase 1 Phrase 2 Phrase 3 p I 33.3% 23.8% 42.9%.565 i 14.3% 33.3% 52.4%.102 bii 14.3% 33.3% 52.4%.102 bii 9.5% 38.1% 52.4%.050 II 14.3% 42.9% 42.9%.180 ii 19.0% 19.0% 61.9%.021 biii 9.5% 47.6% 42.9%.066 biii 14.3% 47.6% 38.1%.156 III 23.8% 19.0% 57.1%.066 iii 19.0% 33.3% 47.6%.276 IV 23.8% 23.8% 52.4%.180 iv 14.3% 28.6% 57.1%.050 #IV/bV 9.5% 38.1% 52.4%.050 #iv/bv 4.8% 61.9% 33.3%.006 V 38.1% 42.9% 19.0%.368 v 9.5% 52.4% 38.1%.050 bvi 4.8% 38.1% 57.1%.012 bvi 23.8% 47.6% 28.6%.368 VI 38.1% 47.6% 14.3%.156 vi 23.8% 61.9% 14.3%.018 bvii 52.4% 19.0% 28.6%.156 bvii 9.5% 42.9% 47.6%.066 VII 14.3% 57.1% 28.6%.050 vii 4.8% 76.2% 19.0%.000 Total 18.5% 40.7% 40.9%

190 Table Cross-tabulation of Chord 3 and Phrase Label (p = 0.536) for the Stimulus Group F (V-IV-*-I). Overall, these successions were identified as Phrase 3. Individual succession, identified by Chord 1, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 3 Phrase 1 Phrase 2 Phrase 3 p I 23.8% 23.8% 52.4%.180 i 9.5% 33.3% 57.1%.028 bii 9.5% 38.1% 52.4%.050 bii 9.5% 42.9% 47.6%.066 II 9.5% 33.3% 57.1%.028 ii 14.3% 4.8% 81.0%.000 biii 14.3% 38.1% 47.6%.156 biii 23.8% 23.8% 52.4%.180 III 14.3% 33.3% 52.4%.102 iii 4.8% 38.1% 57.1%.012 IV 19.0% 19.0% 61.9%.021 iv 4.8% 33.3% 61.9%.006 #IV/bV 4.8% 33.3% 61.9%.006 #iv/bv 4.8% 47.6% 47.6%.021 V 4.8% 23.8% 71.4%.001 v 9.5% 38.1% 52.4%.050 bvi 9.5% 33.3% 57.1%.028 bvi 19.0% 33.3% 47.6%.276 VI 19.0% 42.9% 38.1%.368 vi 23.8% 47.6% 28.6%.368 bvii 14.3% 33.3% 52.4%.102 bvii 9.5% 61.9% 28.6%.012 VII 9.5% 42.9% 47.6%.066 vii 9.5% 33.3% 57.1%.028 Total 12.3% 34.7% 53.0%

191 Table Cross-tabulation of Chord 2 and Phrase Label (p =.041) for the Stimulus Group G (I-*-I-I). Overall, these successions were identified as Phrase 1. Individual successions, identified by Chord 2, are highlighted with colors corresponding with the most frequently assigned phrase label: Blue (Phrase 1), Green (Phrase 2), or Beige (Phrase 3). Chord 1 Phrase 1 Phrase 2 Phrase 3 p I 47.6% 14.3% 38.1%.156 i 42.9% 33.3% 23.8%.565 bii 61.9% 19.0% 19.0%.021 bii 47.6% 28.6% 23.8%.368 II 76.2% 19.0% 4.8%.000 ii 61.9% 23.8% 14.3%.018 biii 66.7% 23.8% 9.5%.004 biii 47.6% 38.1% 14.3%.156 III 47.6% 47.6% 4.8%.021 iii 52.4% 19.0% 28.6%.156 IV 81.0% 9.5% 9.5%.000 iv 38.1% 42.9% 19.0%.368 #IV/bV 47.6% 33.3% 19.0%.276 #iv/bv 52.4% 28.6% 19.0%.156 V 66.7% 4.8% 28.6%.002 v 52.4% 33.3% 14.3%.102 bvi 52.4% 28.6% 19.0%.156 bvi 61.9% 23.8% 14.3%.018 VI 71.4% 19.0% 9.5%.001 vi 85.7% 14.3%.001 bvii 57.1% 14.3% 28.6%.050 bvii 38.1% 42.9% 19.0%.368 VII 38.1% 23.8% 38.1%.651 vii 42.9% 28.6% 28.6%.651 Total 55.8% 25.0% 19.2%

192 Figure 6.3. Mean ratings for variable chords categorized by type: diatonic, mixture, and other chromatic. A one-way ANOVA revealed that the differences between these ratings were significant (p <.001). 174

193 Figure 6.4. Mean ratings for variable chords grouped by the ordered pitch-class interval leading into the variable chord (OPCI-to). A one-way ANOVA revealed that these ratings were significantly different (p <.001). 175

194 Figure 6.5. Mean ratings for variable chords grouped by the ordered pitch-class interval leading out of the variable chord (OPCI-from). A one-way ANOVA revealed that these ratings were significantly different (p <.001). 176

195 Figure 6.6. Mean ratings grouped by Stimulus Group (p <. 001). 177

196 Table Ratings for stimulus groups, categorized by significant mean differences. The differences between categories were significant; the differences within categories were insignificant. For example, Groups A and D were rated significantly higher than any of B, C, F, and G, but were not significantly different from one another. Stimulus Group Category 1 Category 2 Category 3 A (*-IV-I-I) 3.80 D (*-V-I-I) 3.99 G (I-*-I-I) 3.39 B (IV-*-I-I) 3.46 C (IV-IV-*-I) 3.54 F (V-IV-*-I) 3.59 E (V-*-I-I)

197 Table Chord successions from Experiment 1 and where they appear in Experiment 3 (located by Stimulus Group). I-* IV-* V-* *-I *-IV *-V A (mm. 0-1) B (mm. 1-2) E (mm. 1-2) B (mm. 2-3) A (mm. 1-2) D (mm. 1-2) D (mm. 0-1) C (mm. 2-3) C (mm. 3-4) G (mm. 0-1) F (mm. 2-3) E (mm. 2-3) F (mm. 3-4) G (mm. 2-3) 179

198 Table Correlations between mean ratings for the I-* succession heard in Stimulus Groups from Experiment 3 and the ratings for the succession I-* from Experiment 1. In Group A successions, the I-* succession occurs in the introduction and m.1 (tonic introduction-*-iv-i-i). In Group D successions, the I-* succession occurs in the introduction and m.1 (tonic introduction-*-v-i-i). In Group G successions, the I-* succession occurs in mm. 1-2 (I-*-I-I). Correlations followed by two asterisks indicate that the correlation is significant. The level of significance is indicated in the cell directly below the correlation. Group A Group D Group G Expt.3 (average) Expt. 1 I-* Group A Group D Group G Expt.3 (average) Expt. 1 Pearson Correlation **.710 **.895 **.723 ** Sig. (2-tailed) Pearson Correlation.726 ** **.901 **.700 ** Sig. (2-tailed) Pearson Correlation.710 **.687 ** **.757 ** Sig. (2-tailed) Pearson Correlation.895 **.901 **.896 ** ** Sig. (2-tailed) Pearson Correlation.723 **.700 **.757 **.812 ** 1 Sig. (2-tailed)

199 Table Correlations between mean ratings for the IV-* succession heard in Stimulus Groups from Experiment 3 and the ratings for the succession IV-* from Experiment 1. In Group B successions, the IV-* succession occurs in mm. 1-2 (IV-*-I- I). In Group C successions, the IV-* succession occurs in mm. 2-3 (IV-IV-*-I). In Group F successions, the IV-* succession occurs in mm. 2-3 (V-IV-*-I). Correlations followed by two asterisks indicate that the correlation is significant. The level of significance is indicated in the cell directly below the correlation. Group B Group C Group F Expt. 3 (average) Expt. 1 IV-* Group B Group C Group F Expt. 3 (average) Expt. 1 Pearson Correlation **.764 **.948 **.661 ** Sig. (2-tailed) Pearson Correlation.900 ** **.964 **.725 ** Sig. (2-tailed) Pearson Correlation.764 **.824 ** **.831 ** Sig. (2-tailed) Pearson Correlation.948 **.964 **.912 ** ** Sig. (2-tailed) Pearson Correlation.661 **.725 **.831 **.788 ** 1 Sig. (2-tailed)

200 Table Correlations between mean ratings for the V-* succession heard in Stimulus Groups from Experiment 3 and the ratings for the succession V-* from Experiment 1. In Group E successions, the V-* succession occurs in mm. 1-2 (V-*-I-I). Correlations followed by two asterisks indicate that the correlation is significant. The level of significance is indicated in the cell directly below the correlation. Group E Expt. 1 V-* Group E Expt. 1 Pearson Correlation ** Sig. (2-tailed).004 Pearson Correlation.578 ** 1 Sig. (2-tailed)

201 Table Correlations between mean ratings for the *-I succession heard in Stimulus Groups from Experiment 3 and the ratings for the succession *-I from Experiment 1. In Group B successions, the *-I succession occurs in mm. 2-3 (IV-*-I-I). In Group C successions, the *-I succession occurs in mm. 3-4 (IV-IV-*-I). In Group E successions, the *-I succession occurs in mm. 2-3 (V-*-I-I). In Group F successions, the *-I succession occurs in mm.3-4 (V-IV-*-I). In Group G successions, the *-I succession occurs in mm. 2-3 (I-*-I-I). Correlations followed by two asterisks indicate that the correlation is significant. The level of significance is indicated in the cell directly below the correlation. Group B Group C Group E Group F Group G Expt. 3 (average) Expt. 1 *-I Group B Group C Group E Group F Group G Expt. 3 (average) Expt. 1 Pearson Correlation **.779 **.764 **.650 **.928 **.840 ** Sig. (2-tailed) Pearson Correlation.900 ** **.824 **.638 **.939 **.906 ** Sig. (2-tailed) Pearson Correlation.779 **.794 ** **.701 **.903 **.764 ** Sig. (2-tailed) Pearson Correlation.764 **.824 **.755 ** **.873 **.741 ** Sig. (2-tailed) Pearson Correlation.650 **.638 **.701 **.531 ** **.725 ** Sig. (2-tailed) Pearson Correlation.928 **.939 **.903 **.873 **.792 ** ** Sig. (2-tailed) Pearson Correlation.840 **.906 **.764 **.741 **.725 **.903 ** 1 Sig. (2-tailed)

202 Table Correlations between mean ratings for the *-IV succession heard in Stimulus Groups from Experiment 3 and the ratings for the succession *-IV from Experiment 1. In Group A successions, the *-IV succession occurs in mm. 1-2 (*-IV-I- I). Correlations followed by two asterisks indicate that the correlation is significant. The level of significance is indicated in the cell directly below the correlation. Group A Expt. 1 *-IV Group A Expt. 1 Pearson Correlation 1.789** Sig. (2-tailed).000 Pearson Correlation.789** 1 Sig. (2-tailed)

203 Table Correlations between mean ratings for the *-V succession heard in Stimulus Groups from Experiment 3 and the ratings for the succession *-V from Experiment 1. In Group D successions, the *-V succession occurs in mm.1-2 (*-V-I-I). Correlations followed by two asterisks indicate that the correlation is significant. The level of significance is indicated in the cell directly below the correlation. Group D Expt. 1 *-V Group D Expt. 1 Pearson Correlation ** Sig. (2-tailed).001 Pearson Correlation.656 ** 1 Sig. (2-tailed)

204 Figure 6.7. Means plot for Stimulus Group A (*-IV-I-I) grouped by variable chord. A one-way ANOVA on the variable chord (Chord 1) was significant (p <.001). 186

205 Table Mean ratings for all variable chords in Stimulus Group A (*-IV-I-I), grouped by phrase label response. The significance of these differences is indicated in the rightmost column. Chord 1 Phrase 1 (mean) # Phrase 1 Phrase 2 (mean) # Phrase 2 Phrase 3 (mean) # Phrase 3 Overall (mean) p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii Total

206 Figure 6.8. Means plot for Stimulus Group B (IV-*-I-I) grouped by variable chord. A one-way ANOVA on the variable chord (Chord 2) was significant (p <.001). 188

207 Table Mean ratings for all variable chords in Stimulus Group B (IV-*-I-I), grouped by phrase label response. The significance of these differences is indicated in the rightmost column. Chord 2 Phrase 1 (mean) # Phrase 1 Phrase 2 (mean) # Phrase 2 Phrase 3 (mean) # Phrase 3 Overall (mean) p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii Total

208 Figure 6.9. Means plot for Stimulus Group C (IV-IV-*-I) grouped by variable chord. A one-way ANOVA on the variable chord (Chord #3) was significant (p <.001). 190

209 Table Mean ratings for all variable chords in Stimulus Group C (IV-IV-*-I), grouped by phrase label response. The significance of these differences is indicated in the rightmost column. Chord 3 Phrase 1 (mean) # Phrase 1 Phrase 2 (mean) # Phrase 2 Phrase 3 (mean) # Phrase 3 Overall (mean) p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii Total

210 Figure Means plot for Stimulus Group D (*-V-I-I) grouped by variable chord. A one-way ANOVA on the variable chord (Chord 1) was significant (p <.001). 192

211 Table Mean ratings for all variable chords in Stimulus Group D (*-V-I-I), grouped by phrase label response. The significance of these differences is indicated in the rightmost column. Chord 1 Phrase 1 (mean) # Phrase 1 Phrase 2 (mean) # Phrase 2 Phrase 3 (mean) # Phrase 3 Overall (mean) p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii Total

212 Figure Means plot for Stimulus Group E (V-*-I-I) grouped by variable chord. A one-way ANOVA on variable chord (Chord #2) was significant (p <.001). 194

213 Table Mean ratings for all variable chords in Stimulus Group E (V-*-I-I), grouped by phrase label response. The significance of these differences is indicated in the rightmost column. Chord 2 Phrase 1 (mean) # Phrase 1 Phrase 2 (mean) # Phrase 2 Phrase 3 (mean) # Phrase 3 Overall (mean) p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii Total

214 Figure Means plot for Stimulus Group F (V-IV-*-I) grouped by variable chord. A one-way ANOVA on the variable chord (Chord 3) was significant (p <.001). 196

215 Table Mean ratings for all variable chords in Stimulus Group F (V-IV-*-I), grouped by phrase label response. The significance of these differences is indicated in the rightmost column. Chord 3 Phrase 1 (mean) # Phrase 1 Phrase 2 (mean) # Phrase 2 Phrase 3 (mean) # Phrase 3 Overall (mean) p I i bii bii II ii biii biii III iii IV iv #IV/bV #iv/bv V v bvi bvi VI vi bvii bvii VII vii Total

216 Figure Means plot for Stimulus Group G (I-*-I-I) grouped by variable chord. A one-way ANOVA on the variable chord (Chord #2) was significant (p <.001). 198