Contemporary Microtonal Music

Transcription

1 1 Contemporary Microtonal Music To what extent does the use of microtonality in contemporary American music affect traditional Western notions of intervallic ratios and chordal structuring? Subject: Music Connor Towns Lubbock High School Word Count: 3930

2 C o n n o r T o w n s 2 Abstract As the evolution of music has progressed, musical concepts like harmony, rhythm, structure, and sound have developed into such fluid systematic ideas within Western music theory that the need for more creative musical outlets has allowed composers and theorists to create abstract landscapes of sound with various techniques and practices. One of these practices is the utilization of microtones in music. My research question is, To what extent does the use of microtonality in contemporary American music affect traditional Western notions of intervallic ratios and chordal structuring? Because Western music theory operates within the boundaries of a 12 tone octave, certain aspects like perfect temperament and interval accuracy are difficult to achieve. By splitting up the octave into microtones however, a composer is given a broader array of tools with which to build chords and create new sounds. However, I have found that microtonal studies are only a few decades old in regard to serious study, and this leaves theorists with the challenge of needing intense musical experimentation, like in Ferneyhough s Exordium and Kessner s Micro-images, two of the three pieces I analyzed as part of my research. However, I also found Chiaroscuro by Corigliano while I conducted my research, and this piece uses a blend of traditional harmonics and microtonal concepts, and for these all of these reasons I came to the conclusion that microtonality is a tool for expanding and building upon traditional musical concepts rather than replacing them. Two studies were carried out that explored both Western music theory and microtonal theory as to have a substantiated basis for comparison between the two. Then three pieces were selected that displayed different aspects of microtonality for which I would analyze and compare to conventional musical ideologies. Relevant articles, books, and personal writings were referenced for evidence. [297 Words]

3 C o n n o r T o w n s 3 Table of Contents Introduction Equal Temperament and Western Music Theory.5 2. Microtonality and Contemporary Theory Melodic Interval Construction in Micro-images by Kessner On the Greek Chromatic and Enharmonic Genera.13 Scherzando.14 Nanologue Harmonic Rhythm in Exordium by Ferneyhough Semitonal Intervals and Homophonic Movement..17 Polyphonic Microtonal Movement Microtonal Expressionism in Corigliano s Chiaroscuro Alternating Tonics by a Quarter-tone..23 Microtonal Continuity.26 Conclusion 27 Bibliography 28

4 C o n n o r T o w n s 4 Introduction Research Question: To what extent does the use of microtonality in contemporary American music affect traditional Western notions of intervallic ratios and chordal structuring? Beginning with the Greek use of 4ths and 5ths, and gradually moving from monophonic chants to polyphonic symphonies, current day western music theory has developed methods of taking apart musical aspects down to the individual vibrations that generate sound at all. One branch of this evolution is microtonality, which is becoming increasingly present despite the strong dissonances that it is attributed with in regard to traditional western theory. In addition to a comparative analysis of traditional western theory and microtonal theory, I have selected three works that provide a substantial amount of microtonal material: Micro-images by Daniel Kessner, Exordium: Elliotti Carteri in honorem centenarii by Brian Ferneyhough, and Chiaroscuro by John Corigliano. I have decided to study this topic because of the prevalence microtonality has gained over the past half century, and also because it examines a much more calculable part of music, and music theory in particular. If this is to be the future evolution of music, it is imperative that comprehension of these concepts is as cohesive as possible. To accurately assess my research question, I will investigate the mechanics of both traditional western theory and microtonal theory so that I have a strong foundation for the progressive evolution of western music theory, and so that I can justify traditional expectations in relation to microtonal works. Then I will analyze each of the three works with specific emphasis on the effects of microtonality on the sound and harmony of each piece. Based on these findings I will determine the degree of influence of microtones in relation to traditionally established western musical concepts.

5 C o n n o r T o w n s 5 1. Equal Temperament and Western Music Theory While popular western music is written for an audience that is familiar with diatonic progressions and theory based around the 12 tone system, the evolution of musical concepts like harmony and tonality has exceeded the constraints of such a limited musical base and has further split the 12 tone scale into scales with as many as 53 tones within an octave. 1 Intervallic relationships between pitches provide an infinite number of ways to create chords and intervals, however only a few create overtones and perfectly consonant harmony. These pitches are part of the harmonic series (Figure 1.1), an acoustical phenomenon that is based off the wavelength ratios of tones. In regard to the frequency of each rising interval in the harmonic series, the ratio of wavelengths come out to very clean numbers: an octave being a 2:1 ratio; a fifth 3:2; a fourth 4:3; major third 5:4, minor third 6:5, repeating throughout the harmonic series in this pattern, with the size of the intervals decreasing upwards. 2 The elegance of these ratios is not echoed in their cent format, which is converted using the logarithmic equation 1200 log ( ). 3 Figure 1.1: The Harmonic Series (arrows indicate a pitch flatter or sharper than notated) 4 1 Johnston, Ben. "Maximum Clarity" and other writings on music. 1st ed. Chicago, IL: University of Illinois Press, Print. 2 Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print. 3 Benson, David J. Music: A Mathematical Offering. 1st ed. New York, NY: Cambridge University Press, Print. 4 Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print.

6 C o n n o r T o w n s 6 The pure intervals and their natural relationships to one another, based on their wavelengths, are varied so that one interval is not the equal amount of cents as any other. Beginning with the fundamental of a 12 tone scale, distance in cents from one pitch to the next is extremely particular (Figure 1.2). The purity of the intervals is not dependent upon the chromatic note itself, but the key and placement of the interval within a scale. The problem that arises then is that with every change of key the intervals and chords within the new key are not pure. The most prevalent compromise has been the development of equal temperament (ET), in which each of the twelve tones is an equal number of cents apart from one another (Figure 1.3). Figure 1.2: Pure Intervals in Cents 5 Figure 1.3: Equal Temperament Intervals in Cents 6 ET is the standard for tuning in the modern world, and while the system does not keep each note in its pure enharmonic state, ET has been used long enough consistently that most human ears are trained to tune to ET, regardless of the impure intervals and the lack of overtones. 7 While the system is practical for practicality s sake, the harmonies that are lost using ET mean that qualities such as resonance, tonality, 5 Barbour, J. Murray. Tuning and Temperament. 1st ed. East Lansing, MI: Michigan State College Press, Print. 6 Ibid, pg Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print.

7 C o n n o r T o w n s 7 and texture are impaired. It is necessary to mention that no standard system has been invented that consistently allows for only pure intervals and chords. The main obstacle that prevents such an arrangement is the presence of commas, small overlaps within a system that create a gap between octaves (Figure 1.4). If tuning only applied to one octave, it is possible that one comma would only create a negligible variance in the octave. However, when repeated over and over, like on a piano, multiple commas would accumulate (Figure 1.5) and octaves far away from each other would be distorted to different notes entirely, hence the need for a system that eliminates the comma without narrowing or broadening intervals too much. Figure 1.4: Single Octave Comma Difference 8 Figure 1.5: Double Octave Comma Difference 9 The question stands, Is one composing with a collection of individual tones or with a set of relationships between tones? 10 In ET, or any 12 tone system, it is assumed that composition deals with a collection of individual tones, because the purity of intervals is subject to a particular key within a 8 Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print. 9 Ibid, pg Fox, Christopher. "Hybrid Temperaments and Structural Harmony: A Personal History." Contemporary Music Review. 22.1/2 (2003): 124. Web. 21 Oct

8 C o n n o r T o w n s 8 particular temperament. This mistakenly conveys enharmonic notes as equal in pitch, which they are not (Figure 1.6). Ross Duffin explains the discrepancy between enharmonic notes using major thirds. 11 Figure 1.6: Enharmonic Differentiation between G# and Ab 12 A pure major third is narrower than an equal major third. So if in a scale D and Bb are definitely pure, then in the pure major third D F#, F# will be lower in relation to the D, and in the pure major third Gb Bb, the Gb will be higher in relation to the Bb. The result is that there is a comma between F# and Gb, making them different notes harmonically. 13 Of course many players, even today, can hear a chord and temper a note by ear without any particular notation. 11 Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print. 12 Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print. 13 Ibid, pg. 48

9 C o n n o r T o w n s 9 2. Microtonality and Contemporary Theory Enter microtonal theory, in which semitones in a scale are divided even further to make intervallic measurements more precise (Figure 2.1). The first difference between traditional theory and microtonal theory is that with more pitches within an octave, composers can specify more precisely where they want a specific pitch to be. New notational techniques are required, but most instrumentalists can learn to read and hear microtonal changes with substantial training. Microtonal theory has also introduced a new concept of pitch determinacy, and it has only been studied for the past half century. Figure 2.1: 31-tone F scale 14 Harmonic Space, the term defining multidimensional acoustic space between pitches, outlines the way a pitch is perceived in regards to other pitches, using intervallic ratios as a unit. It is necessary to know that every interval within a collection has a range of relative frequencies within which some slight mistuning is possible without altering the harmonic identity of an interval, 15 or a tolerance range. Microtonal music usually has a low tolerance range if the music is specifically dictating with precision what each pitch/interval is, as a slight variation in the frequency of a pitch could change its identity 16 entirely. 14 Read, Gardner. 20th-Century Microtonal Notation. 1st ed. Westport,CT: Greenwood Press, Print. 15 Tenney, James. John Cage and the Theory of Harmony. 2nd ed. Sante Fe, NM: SOUNDINGS Press, Web. < 16 Wolf, Daniel James. "Alternative Tunings, Alternative Tonalities." Contemporary Music Review. 22.1/2 (2003): 7. Web. 21 Oct

10 C o n n o r T o w n s 10 However, it is exceedingly common that the written music only asks for a general movement or area of pitch. Pitch is only one dimension of Harmonic Space though, as things like intervallic relationships and octave equivalence (the phenomenon of pitches eight diatonic degrees apart from each other sounding similar) 17 create multiple dimensions of harmony. Contemporary theorists have created a basic model for visualizing harmonic space. Sometimes referred to as the Tonality Diamond (also called the pitch-class projection axis), in which tones and ratios are arranged in a matrix displaying the amount of harmonic space between intervals and pitches (Figure 2.2 and 2.3). Overall, Harmonic Space is a concept used to explain why equivalent ratios of pitches and intervals do not always sound the same, and to visualize distance between ratios of various pitches and intervals. Figure 2.2: Two Dimensional Tonality Diamond Tenney, James. John Cage and the Theory of Harmony. 2nd ed. Sante Fe, NM: SOUNDINGS Press, Web. < 18 Ibid, pg. 26

11 C o n n o r T o w n s 11 Figure 2.3: Three Dimensional Tonality Diamond 19 Outside of the realm of precisely tuned and out of tune intervals, microtonal theory does not yield limited chordal structures, but often encourages the combination of dissonant intervals and pitches that have an uncomfortably close tolerance range (or, are aesthetically displeasing to the ear). Before moving on, it should be noted that various ideas have been proposed arguing against the notion that adjacent pitches and very small intervals are inherently unpleasing to the human ear. In western music, whether from art music or popular music traditions, we are used to hearing pitch deviations within a bandwidth of at least a quarter-tone as being expressive, 20 and it is this established deviation repeated throughout history (with diatonic scalar theory dating back to the 16 th century) that has made the human ear despondent when presented with an interval smaller than about half a semitone (quarter-tone). 19 Tenney, James. John Cage and the Theory of Harmony. 2nd ed. Sante Fe, NM: SOUNDINGS Press, Web. < 20 Fox, Christopher. "Hybrid Temperaments and Structural Harmony: A Personal History." Contemporary Music Review (2003): 127. Web. 15 Sep

12 C o n n o r T o w n s 12 So, if our ears can be tuned themselves to a particular system of music, it should stand that with enough repetition of microtonal systems in wide-spread music, our ears could find current unpleasant intervals to be simply of a different characteristic or color. It is virtually impossible to pinpoint an intervallic ratio within a collection of pitches though, with most instruments being only a relative tool for the human ear, which is not perfect. Electronic frequency generators can accurately create exact ratios, but this is not practical for live performance and removes one of the most important aspects of music: the musician. However it is safe to say that because of the existence of an aural tolerance range, players can make very close approximations. The complexity is in the almost negligible differences between smaller intervals, and players learning how to hear these intervals as they would semitones. Given a set of pitches, we will interpret them in the simplest way possible 21 says Robert Hasegawa in reference to human interpretation of interval relationships. 21 Hasegawa, Robert. Tone Representation and Just Intervals in Contemporary Music Contemporary Music Review (2006): 267. Web. 21 Oct

13 C o n n o r T o w n s Melodic Interval Construction in Micro-images by Kessner To analyze monophonic interval changes, I have chosen Kessner s Micro-images for solo flute. The piece is split into three distinct areas: Greek genera, a scherzando movement, and the nanologue, with a refrain in between each section. Each focuses on a particular aspect of quarter-tonal changes, the majority of which contains a heavy use of conjunct melody. On the Greek chromatic and enharmonic genera Emphasis is placed on two distinct Greek genera, the chromatic genus, consisting of a minor third with two semitones, and the enharmonic genus, consisting of a major third with two quartertones. 22 The first three measures (Figure 3.1) are derived from the chromatic genus, with a minor third descent from a Bb to a G, followed by a semitone change to a Gb and again to an F, thus completing the chromatic genus. The fourth measure (Figure 3.2)however begins with a three-quarter-tone flat B, making a whole step descent to a three-quarter-tone flat G, and then proceeds to drop one quarter tone to an F and then another to a quarter-tone flat F. Figure 3.1: m. 1-3 Micro-images, the Chromatic Genus 22 Barbour, J. Murray. Tuning and Temperament. 1st ed. East Lansing, MI: Michigan State College Press, Print.

14 C o n n o r T o w n s 14 Figure 3.2: m. 4-8 Micro-images, the Enharmonic Genus With the chromatic genus using intervals that are common and easily recognizable in a diatonic context, and the enharmonic genus utilizing subtler yet more dramatic use of quarter-tones, the movement allows for a direct comparison between the two, giving listeners the opportunity to aurally learn the differences in tonality and color associated with these small changes. Scherzando The premise of the scherzando section is the repetition of a series of notes all within a semitone of a given fundamental. The opening line of this section is five measures of a slightly altered Bb 16 th note series (Figure 3.3), with every other note alternating between a pure Bb and a slightly flat Bb. Without the intentional repetition, the line could be perceived as a severely out of tune unison. Figure 3.3: m. 1-5 Scherzando Again revolving around a Bb, the piece progresses the same but with a three quarter-tone flat Bb added to the collection (Figure 3.4), stretching the fundamental lower in regards to definite pitch

15 C o n n o r T o w n s 15 placement. This reference pitch is continually present throughout the first half of the movement, but the fundamental reference pitch gradually shifts lower and lower until the end of the movement. Figure 3.4: m Schezando Upon isolation of any measure within the movement, a common fundamental reference pitch can be derived upon analysis of the average tone. For example, even with the use of a multiphonic, measure 42 (Figure 3.5) can be categorized as a variation on a C fundamental reference pitch. Figure 3.5: m Scherzando The slight but prevalent changes made to reference pitches throughout the scherzando add color to what is close to unison intervals, creating a flexible continuity around set of specific pitches. Such specificity is foreign to the diatonically tuned ear, and the piece can possibly be perceived as an out-oftune, inaccurately played etude when only analyzed aurally. Nanologue While the rest of Micro-images is split into quartertones, the nanologue section of the work is split even further, creating between a little more than three semitones, fifteen individual pitches. This

16 C o n n o r T o w n s 16 means that not only must special fingerings be utilized, but the flutist must also raise or lower the pitch slightly by adjusting his/her own airflow accordingly. The melodic line is conjunct and contains many repeated series of notes, suggesting motifs and repetitive choruses alike, giving the monophonic line a traditional structure. The probability of these traits reveal that, when compared using intervallic ratios, this movement is constructed to parallel a traditional melody, with the presence of building phrases, a climax, and a descent to resolution (Figure 3.6). The problem that occurs when trying to aurally recognize these traits is that the intervals are compressed probably beyond the point of recognition. 23 Figure 3.6: m nanologue, circled section indicates theoretical climax. Bottom staff is only a reference for alternate fingerings. The compression of harmonically stable intervals into equivalent microtones makes the melody unrecognizable to the diatonically tuned ear, thereby affecting the music as to disguise the melody beyond natural distinguishment. 23 Kessner, Daniel. Micro-images for solo flute New York: BMI, Print.

17 C o n n o r T o w n s Harmonic Rhythm in Exordium: Elliotti Carteri in honorem centenarii by Ferneyhough With regards to polyphonic microtonal harmonies, Exordium is a prime example of exact pitch placement. Not because of its use of sub-accidentals, but because Ferneyhough includes notation that dictates distortion and sub-accidental modifications. The piece is composed of forty-three short sections that are played continuously by a string quartet. The instrumentation is an intentional and crucial part of the piece, as string instruments are the only kind that can easily play any pitch without extensive tuning, meaning that the string family is the most efficient means of quickly and accurately playing pitches and intervals that are not diatonically (or even modally) defined. Semitonal Intervals and Homophonic Movement The beginning sections in Exordium are written so that each of the four parts plays within a particular collection of pitches and intervals when moving simultaneously. These collections can also be found and organized within a diatonic context, making the actual pitches dissonant in regard to any sense of tonality, but consonant when compared to the individual phrase or section. During the II section, measure 3 (Figure 4.1), the rhythmic pattern of the strings is the same, and even the actual pitches carry the same movement, with three descents more than an octave lower from various upper register pitches before all four strings end the measure with a step from an E to a Perfect 5 th (D in the three upper strings, and a G below the staff in the fourth string).

18 C o n n o r T o w n s 18 Figure 4.1: m. 3 Exordium The first descent contains only semitonal notation, with the next descent employing accidental modifications, and the third descent employing the first quarter tonal notes in the entire piece. Until the last four notes of measure 3, all string parts use the same kinds of accidentals (Figure 4.2).

19 C o n n o r T o w n s 19 Figure 4.2: m. 1-2 Exordium, there are no microtonal notes within the introduction, only traditional accidentals While this subtle quality does not make the incredibly large jumps between notes easier to identify and analyze aurally, it introduces the piece in a kind of tonal unison, in which the listener can hear a harmonic similarity between the parts. This occurs because western music is written in the context of semitones, and even while intervals that include two adjacent semitones is considered dissonant rather than consonant, diatonically tuned ears accept this dissonance as uncomfortable and harsh rather than incorrect or out of tune (as quarter-tones are perceived). The introduction of Exordium quickly establishes this perception of the pitches, and almost immediately disturbs the semitonal balance in the last four notes of measure 3, which are essentially the same notes as the previous four notes, but modified on a microtonal level, giving the last four pitches (and the rest of the piece) a chaotic and intensely dense texture.

20 C o n n o r T o w n s 20 Polyphonic Microtonal Movement The abstraction and complexity of Ferneyhough s writing makes traditional chordal analysis near incomprehensible without a fluid mathematical understanding of intervallic ratios (technically speaking microtonal intervals can be found by calculating the exact wavelength of pitches within a chord and comparing their lengths, but often times these measurements do not fit into any musical nomenclature) 24. However, qualities like tonality, contrast, color, growth, and trends in harmonic rhythm are observable, and often are even easier to observe as a result of such explicit complexity. Atonality is established distinctively as in measure 46 (Figure 4.3) of section XXVIII, in which Ferneyhough does not repeat a single note not only in each instruments tessitura, but in the entire range of the ensemble. This variation creates unpredictability in regard to the harmonic rhythm and flow of the piece because each new chord created does not bear a resolvable tension. The impact on the Western ear is a lack of flow in the composition, as most western cadences provide a commonly used means of tension and resolution, such as the I-IV-V-I or the I-vi-IV-vii -I progression. These progressions are based on triads, and the chords in Exordium are much more complex than even the most intricate diatonic chords. Although that does not mean that color is not present within the piece. The five measures following measure 46 employ a variety of intervals and techniques (including double octave intervals, placement of harmonies that contain adjacent quarter-tones, and ascending climactic phrases) that simultaneously add a distinctive color and show growth both in vertically ascending lines and sharp dynamic contrasts. These qualities are not, however, structured into such a way that patterns or motifs would be present, adding to the chaotic texture and sound of the piece. 24 Benson, David J. Music: A Mathematical Offering. 1st ed. New York, NY: Cambridge University Press, Print.

21 C o n n o r T o w n s 21 Figure 4.3: m. 46 Exordium, gradual stacking of notes builds chords, but they do not carry harmonic dissonance or consonance. In the final three sections of Exordium (XLI, XLII, XLIII) (Figure 4.4), in the fourth string part, a series of microtonal ascending arpeggios, followed by the entire ensemble playing gradually descending notes, communicates a basic structure of building tension to a climax before a downward slope towards resolution (in regard to the structure of these phrases, not the harmonics), conveying a familiar sense of resolve in the midst of such complex and abstract tonal progressions. Figure 4.4: m Exordium, horizontal circle highlights arpeggios, vertical circle highlights descending trend in all parts

22 C o n n o r T o w n s 22

23 C o n n o r T o w n s Microtonal Expressionism in Corigliano s Chiaroscuro Being a relatively recent serious development in Western Music Theory, microtonality is a natural experimentation ground for theorists and composers, and because the majority of the western globe population is so used to diatonic, pentatonic, and other traditional tonalities, there is no need for experimenters to try and make their work aesthetically pleasing, as this would take gradual integration of microtones into popular music, and the reception associated with this evolution would most likely take a large quantity of time (it should be noted that music is constantly evolving, and the use of microtones in popular music is not non-existent, but it is rare). However, John Corigliano s Chiaroscuro, written for two pianos tuned a quarter-tone apart, makes use of microtones in an expressionistic light. I wanted to use quarter-tone music expressively, writes Corigliano, I was looking for the expressive power between two notes, like a blues singer does. 25 Alternating Tonics by a Quarter-tone Throughout the first movement of Chiaroscuro: Light, both pianos alternate playing antiphonally, with their phrases closely resembling each other, if not being the exact same. The third movement, Strobe combines both fast paced antiphony and continuum playing (in the case of each piano picking up where the other left off). In measures 1-5 of Light, the first piano plays a series of arpeggiated chords rooted in C that are sounded until a final compound chord on the first beat of measure 4 (Figure 5.1) is mimicked by the second quarter-tone flat piano, whose answer is a slow, soft, and fluid descent, which directly contrasts the first piano s grandiose chords, which resume at the beginning of measure Corigliano, John. Chiaroscuro New York: G. Schirmer Inc., Print.

24 C o n n o r T o w n s 24 Figure 5.1: m. 4 Chiaroscuro Light, ending of the first piano s first phrase simultaneously occurs with the second piano s opening chord, which is the same except tuned a quarter-tone flat. Playing alternately again in measures (Figure 5.2), the frequency and speed of the alternating pianos creates a tension for only one piano to establish a definite tonic. This effect can be seen again in measures (Figure 5.3) of the Strobe movement. Thick, rich chords are played alternatively, as only a quarter-tone dramatically sets the two apart, even though both pianos are not far from being in unison tuning.

25 C o n n o r T o w n s 25 Figure 5.2: m Chiaroscuro Light Figure 5.3: m Chiaroscuro Strobe The close dissonance between the two pianos pitches does not make the resulting sound harsh or uncomfortable, but adds a slight thickness to the texture and color that would not be present had the chords been purely consonant, bringing an aesthetically pleasing quality to this section.

26 C o n n o r T o w n s 26 Microtonal Continuity The second movement, Shadow, focuses on blending both of the pianos lines, to create a continuous and eerie progression from chord to chord. Corigliano demonstrates both semitonal and quarter-tonal distinction in measures (Figure 5.4) of this movement by writing several gradual descents, used to convey a darkening of mood. Figure 5.4: m Chiaroscuro Shadow, circles denote first the chromatic descent, and then the quartertonal descent between the pianos With only the first piano playing a descending chromatic scale in measure 11, a standard is established for what semitonal changes sound like, and these should register comfortably with the diatonically tuned ear. This establishment is imperative, as the next chromatic descent includes both pianos, and steps are now quarter-tonal rather than semitonal. The first exposure to such minute changes can seem out of tune to listeners, which is why Corigliano repeats this quarter-tonal process twice in Shadows. Because each note is equally distanced from the previous one, continuity of a gradually descending line is perceived rather than a chromatic scale filled with out-of-tune notes. The addition of this feature reorients the listeners perception of two different pianos into one continuous instrument, further defining the structure of the piece and blending microtones into two semitonal instruments.

27 C o n n o r T o w n s 27 Conclusion: Research Question: To what extent does the use of microtonality in contemporary American music affect traditional Western notions of intervallic ratios and chordal structuring? With regard to both Micro-images and Exordium, microtones were so prevalent throughout each piece, harmonic concepts like color, texture, structure, and tonality became chaotic and dysfunctional, even though certain traditional ideas remained, like standard rhythmic features, and melodic presence. Although the piece was in a constant state of quarter-tone dissonance, Chiaroscuro integrated microtonality into common traditional harmonic concepts, adding distinctive color, tonic tension and variation, and slightly dissonant texturing, moving beyond old tonal restrictions into a world of far richer expression. 26 Chiaroscuro was not written as an experimental piece either, unlike the other two pieces. Because of this, the techniques and style of Corigliano s writing are justified by his direction and intentionality in the use of microtones. In conclusion, microtonality affects expressionistic American contemporary music by reinforcing western concepts of music theory, while extending music beyond the degree by which inexpressive music already functions. 26 Read, Gardner. 20th-Century Microtonal Notation. 1st ed. Westport,CT: Greenwood Press, Print.

28 C o n n o r T o w n s 28 Bibliography Barbour, J. Murray. Tuning and Temperament. 1st ed. East Lansing, MI: Michigan State College Press, Print. Benson, David J. Music: A Mathematical Offering. 1st ed. New York, NY: Cambridge University Press, Print. Corigliano, John. Chiaroscuro New York: G. Schirmer Inc., Print. Duffin, Ross W. How Equal Temperament Ruined Harmony (and why you should care). 1st. ed. New York, NY: W. W. Norton & Company, Print. Ferneyhough, Brian. Exordium: Elliotti Carteri in honorem centenarii London: Edition Peters, Print. Fox, Christopher. "Hybrid Temperaments and Structural Harmony: A Personal History." Contemporary Music Review. 22.1/2 (2003): 0-0. Web. 21 Oct Hasegawa, Robert. "Tone Representation and Just Intervals in Contemporary Music." Contemporary Music Review (2006): 0-0. Web. 21 Oct Johnston, Ben. "Maximum Clarity" and other writings on music. 1st ed. Chicago, IL: University of Illinois Press, Print. Kessner, Daniel. Micro-images for solo flute New York: BMI, Print. Read, Gardner. 20th-Century Microtonal Notation. 1st ed. Westport,CT: Greenwood Press, Print. Tenney, James. John Cage and the Theory of Harmony. 2nd ed. Sante Fe, NM: SOUNDINGS Press, Web. < Wolf, Daniel James. "Alternative Tunings, Alternative Tonalities." Contemporary Music Review. 22.1/2 (2003): 0-0. Web. 21 Oct