The Convergence of Schenkerian Music Theory and Generative Linguistics: An Analysis and Composition

Transcription

1 College o the Holy Cross CrossWorks Honors Theses Honors Projects The Convergence o Schenkerian Music Theory and Generative Linguistics: An Analysis and Composition Michael A. Ciaramella College o the Holy Cross, maciar17@g.holycross.edu Follow this and additional works at: Part o the Composition Commons, Linguistics Commons, and the Music Theory Commons Recommended Citation Ciaramella, Michael A., ": An Analysis and Composition" (2017). Honors Theses This Thesis is brought to you or ree and open access by the Honors Projects at CrossWorks. It has been accepted or inclusion in Honors Theses by an authorized administrator o CrossWorks.

2 The Convergence o Schenkerian Music Theory and Generative Linguistics: An Analysis and Composition College Honors Senior Thesis Spring, 2017 Advisor: Proessor Shirish Korde Reader: Proessor Chris Arrell

3 Table o Contents Abstract... 3 Forward... 4 Chapter 1: Linking Music and Language... 6 Section A: Situating the Minimalist Program within Music Theory... 7 Formalist vs. Functionalist... 7 Generation vs. Perception Section B: An Overview o the Minimalist Program within Generative Linguistics Section C: Schenkerian Music Theory and the Minimalist Program Conclusion Chapter 2: Case Studies rom Western Idioms Section A: Mozart Piano Sonata K. 332 Mvt Section B: Georgia on My Mind Section C: Blue Bossa and Cyclic Forms Conclusion Chapter 3: An Exploration o Musical Syntax Program Note Bibliography Ciaramella 2

4 Abstract This thesis engages a purported connection between Schenkerian music theory and the Minimalist Program within generative linguistics both scientiically and creatively. The irst chapter expounds the link between Schenkerian theory and the Minimalist Program which has been recently substantiated in a doctoral dissertation by Somangshu Mukherji at Princeton University and details the methodological ramework or investigating musical structures within this paradigm. Chapter two presents three case studies including the opening phrase o Mozart s K. 332 Mvt. 1 piano sonata, and the tunes Georgia on My Mind and Blue Bossa in order to exempliy the aorementioned methodology and provide scientiic evidence airming this generative ramework. Chapter three concludes with a creative investigation o the theoretical ideas which this thesis engages and consists o a string quart that draws upon the notions o music and language, and music as derived rom a computational system. Ciaramella 3

5 Forward The questions o the processes and orms that underlie musical structure which this thesis engages are a maniestation o a deeper question: What is the basis o human creativity? Scholars o all times, geographies and disciplines have debated this question and yet, it persists unanswered. Further, though the phenomenon o creativity seems almost impenetrable to inquiry, scholars have never tired o addressing it in novel ways. This thesis enters into this rich scholarly space by asking the question: How might the human mind generate an ininitely many unique and expressive musical structures rom a inite set o musical inputs? By no means do I purport that I will arrive at a deinitive answer or this question. Rather, it is my hope that journeying through this intellectual space will orce me to think critically about the basis o music within the human mind, what makes it so meaningul to us, and what it means to be musical. Indeed, this inquiry marks my entrance into a lie s worth o questions. I was irst exposed to the ideas in this thesis while a high school student taking music theory classes at Princeton University. Somangshu Mukherji was a graduate student at Princeton during my time there and an assistant or both o the classes I was enrolled in. Over several lunch conversations, Dr. Mukherji discussed his doctoral dissertation entitled, Generative Musical Grammar- A Minimalist Approach with me and opened my eyes to rich questions o how music and language interact with the human mind and what makes them so uniquely special to humanity. These questions stuck with me as I began my time at the College o the Holy Cross and grew in my mind under the supportive mentorship o many great proessors, perhaps most notably my advisor, Shirish Korde, and reader, Chris Arrell, or this Ciaramella 4

6 thesis. Proessor Korde has instilled within me an interest in world music and cross- cultural musical compositions and has always lent a patient ear or my explorations in this regard. Additionally, it was in Proessor Arrell s music theory course that I was irst exposed to the ideas o Heinrich Schenker and developed an interest in analysis. All the while, the questions raised to me while still a high schooler suraced and resuraced throughout these ormative experiences at Holy Cross and have motivated me to pursue a thesis integrating my loves or composition, world music, and analysis to engage the questions Dr. Mukherji had presented me with. This thesis is thereore indebted to the work o Dr. Mukherji and engages speciically with the ideas put orth in his Princeton doctoral dissertation. The irst chapter expounds Dr. Mukherji s approach to generative musical grammar by engaging both his theoretical and methodological ramework. Chapter two then presents three original case studies which investigate generative basis or three compositions rom a diverse set o idioms. The chosen pieces not only maniest rom dierent cultures, but also cover a timespan o almost two centuries. The goal o these case studies is to provide support or situating Dr. Mukherji s generative approach as an accurate relection o an aspect o the human mind and o human nature. Finally, in Chapter three, I write a string quart inspired by the ideas o music s generative structure that were encountered previously in the thesis. By concluding in this way, I look to counterbalance my scientiic and theoretical investigation o music with an artistic and creative encounter o the same ideas. Ciaramella 5

7 Chapter 1: Linking Music and Language The irst substantial attempt to link Schenkerian music theory to the Minimalist Program in generative linguistics was done by Somangshu Mukherji in his Princeton University dissertation entitled Generative Musical Grammar- A Minimalist Approach. This thesis will draw upon Mukherji s work or its theoretical ramework and methodology, which will be detailed in this chapter. To illuminate this theoretical ramework and situate it within contemporary music theoretic discourse, Section A will develop two key distinctions that separate the application o the Minimalist Program rom other research methodologies within the ield o music theory. These distinctions are: ormalist vs. unctionalist, and generation vs. perception. The ormer in each are speciic claims by Mukherji toward the application o the Minimalist Program to music. Exploring these claims will also problematize some o the other approaches to understanding musical structure and present application o the Minimalist Program as a potential avenue toward resolving some o these issues. Sections B and C o this chapter provide the substantive basis or the connection between Schenkerian music theory and the Minimalist Program rom generative linguistics, which was also put orth by Dr. Mukherji. The advances in generative linguistics through the Minimalist Program that make it suitable or connection to Schenkerian music theory are briely reviewed, in order to then demonstrate the striking similarities between them and thereby substantiate the link between the two paradigms. The emerging program works within a ormalist ramework and seeks understand the psychological activity requisite to musical Ciaramella 6

8 activity and to characterize the basic mental processes by which humans generate musical orms with ininite capacity or creativity and expression. 1 Section A: Situating the Minimalist Program within Music Theory Formalist vs. Functionalist Music is an undeniable cultural artiact, since it is practiced in all known cultures throughout the world. Thereore, any scientiic investigation o music must acknowledge the diverse kinds o musics ound in cultures throughout the world and present an argument which is able to account cohesively or their many dierences and similarities. John Blacking, in his book How Musical is Man?, arguably one o the most oundational texts o ethnomusicology and certainly one o the most impactul, deined music as humanly organized sound. Through his emersion into the culture o the Venda, a tribal group in Western Arica, Blacking came to observe that all people and cultures are capable o being musical, not just the select ew who have been ortunate enough to have had ormal music training. Further, he recognized that dierent musics maniest uniquely around the world and argued that cultural orces shape these unique maniestations. On this basis, he advocates or the study o music by its unction in each society. He acknowledges that music seems to be a unique characteristic o human behavior, but claims that to truly understand music, one must look at the culture rom which it was generated. 2 1 Mukherji, Somangshu. "Generative Musical Grammar- - - a Minimalist Approach." (PhD Diss. Princeton University 2014). 2 Blacking, John. How Musical Is Man? Seattle: University o Washington Press, Ch. 1. Ciaramella 7

9 Blacking is arguing or a unctionalist view o music. 3 This perspective has become ubiquitous among ethnomusicological literature and poses an obstacle to the study o music as something universal and uniquely human. I music is a uniquely cultural artiact, then it should not be subject to any natural law or scientiic principle. For a unctionalist, any attempt to map the origins o music, answer the question o why humans are musical, or explain what the capacity or music is, will inevitably end in the study o culture. This is an obstacle or any scientiic study o music, because culture is known not to adhere to any natural laws, such as those ound in evolutionary theory. This also poses a more direct obstacle or the connection between music and language. Music and language maniest in very distinct ways rom a cultural perspective and serve very dierent unctions in a sociocultural context. Thus, an entirely unctionalist investigation o music will render it a completely separate phenomenon rom language. Dr. Mukherji, in his dissertation entitled Generative Musical Grammar- A Minimalist Approach addresses the issue o deining music in unctional terms as Blacking does, rather than ormal terms. Mukherji begins this discussion by acknowledging that while one o Blacking s goals in How Musical is Man? was to advocate or a unctionalist perspective o music and claim that music is unique in each society, he was also speaking out against many ethnocentric and potentially racist conceptions o music commonly held in the Western tradition. Blacking recognizes that where in Western European culture is there a separation between perormer and audience, in many other places around the world there is no such 3 Proceeding discussion rom Mukherji, Somangshu Generative Musical Grammar- A Minimalist Approach p Ciaramella 8

10 distinction. In other cultures, such as the Venda studied in How Musical is Man?, music is an inherently participatory practice among all members o a society, rather than just a perormance practice. 4 In recognizing this contrast, Blacking also calls into question the distinction between art music, and cultural or ethnic music. The ormer, he argues, has an association with high society and intellectual elitist culture. The latter, is associated with low society and the lower class. Intrinsic to this distinction is also the value judgement that art music is a superior practice to ethnic music by its association with high society. By extension, this oten leads to the ethnocentric perception o Western art music as superior to other musical orms, on the basis o its complexity and association with high society. Blacking clearly intended to topple this ethnocentric conception, in preerence or equality and inclusion. This is known in anthropology literature, and by extension in ethnomusicology, as an emic bias, which overemphasizes certain aspects o a phenomenon to topple such prejudices. 5 Blacking is not wrong in the assertion that all musics are equal and that value judgements based on perceived superiority o certain societies is condemnable. On the contrary, this is an admirable pursuit. However, this motive poses a problem or any claims about the universal, and uniquely human aculty o music as a psychological phenomenon. By overemphasizing the unctional aspect o music, Mukherji claims that this approach becomes a study o dierences. 6 This inherently poses a problem or a psychological theory o music, which must look or what is shared throughout all humans, rather than the characteristics that distinguish them. By painting each culture as entirely unique, and by extension, each kind o 4 Blacking, How Musical is Man? Ch. 2 5 Mukherji, Generative Musical Grammar- A Minimalist Approach p Ibid. 17 Ciaramella 9

11 music as unique as well, all we are let to do is discuss what dierences there are between cultures and musics, without any standard or comparison. Mukherji thereore claims that such pursuit misses the opportunity to characterize perhaps the most powerul aspect o music: that it is a shared practice or all o humanity with some commonly held eatures. 7 For Mukherji, one commonality o all musics is that they give humans the ability to express themselves and understand one another. This essential trait o music is also shared with language, as a uniquely human practice which allows or expression and understanding. The universal communicative aspect o music and language and their centrality to human expression led Mukherji to deine these phenomena as undamental aspects o human nature. 8 Thereore, music is irreducible to simply an artiact o culture, though he will argue culture is one actor that shapes it, and he argues or its study as part o human nature, as well as o human biology. Where Blacking acknowledges the unique human maniestation o music and goes on to explain its dierent realizations through culture, Mukherji ocuses on what exactly the uniquely human characteristics o music are, hence ocusing on its natural orm, rather than its cultural unction as Blacking does. 9 Additionally, he argues that understanding what music is in a human species- speciic sense would beneit the study o music as a cultural artiact by creating a set o commonalities upon which the anthropological study o music might be based. Thereore, such study ceases to become simply a study o dierences, but rather a more ruitul cross- cultural investigation Ibid Ibid Ibid Ibid. 17 Ciaramella 10

12 Thereore, the application o the Minimalist Program to music is a ormalist argument, rather than a unctionalist one. Speciically, it treats music as an object o human biology, with a natural and universal structure underlying its seemingly unique maniestations across culture. It will claim that music, is based on an inner model, that governs its external, individual characteristics, taking the internal orm o a inite hierarchical and recursive computational system embedded within the human mind, maniesting externally as the ininitely unique array o sounds which we hear as music. 11 Such a claim makes music a human psychological reality, and an indispensable aspect o human nature. The Minimalist Program in generative linguistics likewise treats language as an aspect o human biology with a singular internal orm, which maniests in the same ways that Mukherji, proposes music does. 12 On these grounds, he connects the well- deined research program known as the Minimalist Program to music to generate a psychological theory o music. There is one inal point relevant to the ormalist vs. unctionalist argument. This is the dierence between musical (and linguistic) competence versus perormance. In suggesting musical and linguistic behaviors to be aspects o human biology, with which all humans are naturally endowed at birth, the Minimalist Program is claiming that all humans are born with musical and linguistic competence. This means that all humans minds are encoded with the speciic inite computational system which allows the hierarchical and recursive operations necessary to produce and comprehend music or language. This says nothing, however, about how music and language maniest externally in terms o sounds, word order, and other 11 Ibid Ibid Ciaramella 11

13 characteristics, other than that they maniest rom the internal computational system that deines music and language. These external characteristics are deined as musical and linguistic perormance. 13 Thus, someone working within the Minimalist paradigm, as Mukherji does, would respond to Blacking s observation that the music o each culture is unique by saying that musical perormance allows or its unique characteristics. The unique ways these sounds come together, however, is governed by the hierarchical and recursive computational system that maniests internally within the human mind. 14 It is this aspect o musical and linguistic competence which the Minimalist Program claims is a universal human trait and attempts to characterize. This distinction between perormance and competence will also be relevant to the other three distinctions which this chapter makes. Generation vs. Perception Given its ocus on linguistic competence, rather than perormance, the Minimalist Program is speciically ocused on the mental process by which linguistic structures are generated with ininite creativity rom the inite material o the mind s computational system. As such, the Minimalist Program resists the notion that the perceived sounds that make up language (or by extension, music) may be reduced to some abstract orm, but rather begins with the undamental abstract units o language (or music) and describes the mechanism by which such material is ormed into a recognizable language, allowing or the ininite creativity seen in language and by extension, music. To be described more in Section B, the mechanism by which the Minimalist Program claims language is constructed is called Merge, in which 13 ibid Personal communication with Dr. Mukherji. Ciaramella 12

14 lexical linguistic units are combined into larger units called phrases. These phrases may then be combined into larger units, orming language we hear, read, or see. Two constraints, however, are applied to the products o Merge beore language is realized. These are that they conorm to a phonetic orm, which entails that the product is able to be articulated via our sensorimotor system; and logical orm, which requires that the product passes some conceptual- intentional system within the brain so that it has a meaning that is intelligible. The Minimalist Program is speciically generative in orientation, as opposed to reductive, since it works rom the bottom up, showing how our minds create language rom the natural biological linguistic system which we are endowed with. 15 An extension o the work done by the music theorist Henrich Schenker will provide a oundational link between the Minimalist Program or language and or music. The most important basis o this connection is the claim that Schenker s music theory, like Chomsky s linguistics, is generative in nature, rather than reductive. Beore this claim is deended, it must be noted that any literature which uses Schenker in a scientiic context, or seeks to apply his theory to anything outside o common practice Western tonal music must acknowledge a sort o neo- Schenkerian approach as opposed to a strict and traditional sense o Schenkerian theory. Schenker was an Austrian music theorist living rom 1868 to 1935 who ocused exclusively on the works o the Germanic master composers, which limited his scope to the analysis o essentially the Germanic composers rom Bach to Brahms chronologically. His analytical approach was aimed at highlighting the mastery o certain group o composers within 15 Berwick, Robert C., and Noam Chomsky. Why Only Us: Language and Evolution. Cambridge, MA: MIT Press, Pg Ciaramella 13

15 the Western tonal tradition. Additionally, Schenker claimed that these so called master composers were the only ones capable o creating music o such skill. Inherent to his work, thereore, was an elitist and nationalist bias which limited both the scope o his analyses and theory, as well as his reception in the music community. Thus, Schenker was blinded by his biases to the true power o his theory. This is a stance adopted by all o his students who came to the United States in the post- war era and vehemently condemned his biases and politics, but advocated or and taught his technical theories in the country. Nevertheless, it may be argued that the process that Schenker set out to depict through his analyses can be viewed as the basis o a generative theory o music. In essence, he desired to characterize the process by which master composers intuitively built upon a single orm and generated unique and genius musical creations with seemingly ininite creativity. 16 I we strip away Schenker s reservation that only a select ew were capable o such a process, what remains is the claim that musical structures are generated with ininite creativity upon a single rame. This idea is also shared with generative linguistics and provides the most undamental connection between the two disciplines. Even removing the nationalist and elitist restrictions rom Schenker s theories and allowing them to be applied to other cultures and time periods, it is a urther extension to make any psychological claims about music rom Schenkerian theory. Schenker s theories were meant to showcase natural the genius o the ew master composers, as well as provide musical perormers with an analytical tool to aid their perormance. By perorming a Schenkerian 16 The above discussion rom many personal communications with Proessor Shirish Korde and Dr. Mukherji as well as Proessor Chris Arrell s Music Theory 3 course. Ciaramella 14

16 analysis o a piece o music, one o Schenker s intentions was or a perormer to be clued into the genius o the composer s work, in the hopes that this knowledge would allow or a more virtuous perormance o the piece. 17 This interpretation o his theory is known to some as the conservatory Schenker, which unctions as an analytical poetic device or perormance. 18 Regardless, it is apparent that Schenker did not mean or his work to hold any psychological implications. The psychological extension o Schenker s work emerged much later in the 20 th century, almost concurrently with advancement in the ield o Generative Linguistics, because o the many similarities between the two. The most amous attempt is Lerdahl and Jackendo s amous A Generative Theory o Tonal Music, which seemed to be the peak o interest in the connection between Schenkerian music theory and generative linguistics. Mukherji engages this text in detail in his dissertation, since it purports to address the same issue o generative musical grammar. He ultimately concludes that their attempt ailed. This will be discussed at greater length to ollow. Returning to Schenker, it is speciically the generative conception o his analytical paradigm that has drawn interest or a connection to linguistics. In Schenkerian theory, one analyzes a piece o music by breaking it down into three layers, the oreground, middleground, and background, to reveal the undamental abstract structure upon which the composition is constructed. This most oundational layer within a Schenkerian analysis is the background, which reveals what Schenker called the Ursatz, or undamental structure. The Ursatz is the undamental harmonic structure upon which the entire composition is built, in the orm o a I- 17 This stance is taken by other advocates o analysis as well, such as Koi Agawu. See Agawu, Koi How We Got Out o Analysis, and How to Get Back In Music Analysis, 2004: Mukherji, Generative Musical Grammar- A Minimalist Approach pg. 159 Ciaramella 15

17 V- I progression. Accompanying the Ursatz at the background level is the oundational voice leading structure o the piece, known as the Urlinie, or undamental line. The Urlinie can take three separate orms at the background level, each a descending line, which include scale degrees (3-2- 1), ( ), or ( ). Upon the oundation o the Ursatz and through the Urlinie, the master composer builds a composition by employing voice leading principles originating in species counterpoint. Each harmonic area o the Ursatz is composed out, which Schenker termed Auskomponierung, which adds layers upon the background in a hierarchical and recursive manner, eventually leading to the surace music heard by the listener. 19 Mukherji believes that Schenker speciically intended this process o composing out the Ursatz to be generative in nature and uses this as the basis or the connection o Schenkerian music theory to the Minimalist Program. Schenker claimed that the Ursatz arises rom the Der Naturklang, or chord o nature, which is the harmonic sequence that arises above any undamental pitch. The basic triadic Ursatz o Schenkerian theory is thereore based more undamentally on natural acoustic laws, to which the human mind is attuned. 20 Thus, the distinctive ability o the master composers was their ability to connect with the natural orm o the Ursatz, and build a composition upon these roots. This will provide the basis or a psychological extension o Schenker since or him, music is undamentally dependent on the ability o the human mind to connect with the most basic material or music (the harmonic tones which orm the Ursatz) and build ininitely many unique structures upon this inite 19 Ibid Ibid. 142 Ciaramella 16

18 undamental orm. A psychological extension o Schenkerian theory within the paradigm o the Minimalist Program, however, will modiy Schenker s conception o the most basic musical material slightly. Instead o claiming that the Ursatz is the most undamental characteristic o music, arising rom the chord o nature (the harmonic series), this approach will take the Ursatz as a cultural artiact within the Western Classical idiom that arises rom a more basic set o universal musical material. To be discussed more in Sections B and C, this approach will claim that a inite set o chord- like atoms within a universal musical lexicon is the most undamental musical material and innate within the human mind. A process called Merge, in which lexical items are combined in binary arrangements results in structures like the Ursatz. The idea o the Ursatz also renders Schenker s theory distinctively generative. Rather than beginning with the surace, a composer connects unconsciously with the most undamental abstract structure o music (or Schenker, the Ursatz, and or this approach, the combination o the musical lexicon and Merge), realizing the surace in ininitely creative ways based on a inite abstract structure through the principles o voice leading and counterpoint. It was the ability to truly connect with the Ursatz as the undamental material or composition, which Schenker reserved or so ew Germanic composers, that will become the psychological underpinnings o the generative scientiic Schenkerian theory. 21 Much more will be said about Schenker s theory, its correlations with the Minimalist Program, and its overall psychological extension. For now, it is suicient to recognize that Schenker can be interpreted as generative in nature, rather than reductive. 21 ibid Ciaramella 17

19 The irst signiicant attempt to link music and language within the paradigm o generative linguistics came rom Fred Lerdahl and Ray Jackendo in 1983 in their work entitled A Generative Theory o Tonal Music. With Lerdahl being a Schenkerian music theorist in addition to a composer, and Jackendo being a student o Chomsky, the work sought to link the principles o Schenker to the advancements o generative linguistics at the time. These authors ultimately ailed in their attempt at a generative theory o tonal music, one which they even acknowledged in their 1983 work by recognizing it as a theory o music perception. 22 Mukherji s dissertation, completed in 2014, is a ar more recent attempt to connect music to language within the generative linguistics paradigm. His attempt is more ruitul than that o Lerdahl and Jackendo both because he works within a dierent, more generative conception o Schenker, and because the ield o generative linguistics has advanced leaps and bounds beyond where it was in 1983 with the advent o the Minimalist Program. Thus, these two distinctions separate his dissertation drastically rom Lerdahl and Jackendo s in Mukherji addresses the shortcomings or Lerdahl and Jackendo s A Generative Theory o Tonal Music in becoming a true application o generative linguistics to music. The irst shortcoming o A Generative Theory o Tonal Music is its inability to account or musical rhythm internally. In their work, Lerdahl and Jackendo recognize rhythm as a completely separate entity to tonal harmony, which is governed by dierent rules unrelated to language in any way. As such, they develop a complicated system or the reduction o metric structures in an attempt to show a generative origin separate rom tonal structure. Their 22 Lerdahl, Fred, and Ray Jackendo. A Generative Theory o Tonal Music. Cambridge, MA: MIT Press, p. 5 Ciaramella 18

20 theory o rhythm employs the process o grouping, which is common to many areas o human cognition. Grouping entails that the human mind chunks a series o elements perceived in linear order into a larger group. Such groups reduce the number o unique elements held in the working memory (which is only capable o holding on average 7 units at any one time), and allows or easier recall rom short term memory into the working memory. 23 Lerdahl and Jackendo proposed a hierarchical arrangement o such groups that conorms to a set o preerence rules which govern the structures that are likely to appear and those that are not. Based on the interaction between rhythmic grouping and their proposed preerence rules, they created a system o rhythmic reduction which occurs concurrently, but separately rom tonal cognition. 24 The main reason Mukherji rejects Lerdahl and Jackendo s theory o rhythm lies in their externalist argument treating the tonal and rhythmic aspects o music separately. Armed with the Minimalist Program, Mukherji rejects this externalist delegation o musical rhythm and employs phonetic orm level o representation ound within the Minimalist Program to account or rhythm internally along with other pitch- based aspects o music. To be discussed more in Sections B and C, the binary character o Merge necessitates that rhythm is created because it requires the ordering o linguistic (or musical) units in space, whether this space is metered or not. For someone working within the Minimalist paradigm, rhythm must thereore be grouped internally along with pitch, since a single mechanism leads to their 23 See Alamia et al., 2016 or an argument that the language centers o the brain also operate by this chunking mechanism. 24 Lerdahl and Jackendo, A Generative Theory o Tonal Music, Chapters 1-4 Ciaramella 19

21 construction. Thus, Mukherji argues or an internalist approach to rhythm. 25 The phonetic level o representation just ensures that the ordering Merge created is capable o articulation by the sensorimotor system in some way. It is thereore at this level that rhythm is realized or the Merge output with the goal o satisying the constraints o our sensorimotor system. Only products which meet the demands o this level, as well as the logical orm level via a conceptual- intentional interace, will emerge as the music we hear. 26 More will be said about this in Section B. The important point at this step is to recognize that through the advancements o the Minimalist Program, there emerges an answer to one o the undamental diiculties that led to the ailed generative account o music by Lerdahl and Jackendo in The second shortcoming which Mukherji acknowledges relates to Lerdahl and Jackendo s amous preerence rule system, on which their theory o both rhythm and pitch is predicated. Lerdahl and Jackendo acknowledge in their irst chapter that a major motivation o their work was to produce an empirically veriiable theory o tonal music, as this was becoming a trend in music theory and speciically music theory that related to cognitive science. 27 Their ocus on empirically veriiable results inevitably orced them to look to musical surace structure (i.e. the notes that are actually heard in music) as the basis o their theory. Speciically, their ocus was on how listeners parse through inormation at the musical surace (which they explicitly heard) in order to arrive at a preerred structural description in their mind. The listener- based and surace- based approach o Lerdahl and Jackendo led them to derive our categories o preerence rules which listeners employ to arrive at a sense o 25 Mukherji, Generative Musical Grammar- A Minimalist Approach, p , p Berwick and Chomsky, Why Only Us, pg Lerdahl and Jackendo, A Generative Theory o Tonal Music, pg. 5 Ciaramella 20

22 musical orm. Their preerence rules were based separately on grouping structure, metrical structure, time- span structure (essentially a combination o the previous two), and prolongation structure. Their theory necessitated that musical surace must simultaneously meet the preerence constraints proposed in each o these our areas simultaneously. Thus, the simultaneous set o constraints governing musical surace limited the potential interpretations listeners were allowed, allowing listeners to come to consensus at a preerred structural interpretation o a piece. 28 Researchers could thereore employ these sets o preerence rules to empirically veriy whether the constraints imposed by the theoretical system conormed with listeners actual interpretation o a piece. Mukherji claims that the constraint- based approach to musical surace at the heart o Lerdahl and Jackendo s generative theory rendered it actually closer to a theory o music perception, rather than generation, and also speciically anti- Chomskyian. A generative theory would begin with the undamental abstract orm o music (which is the inite computational system within the human mind based on the lexicon and Merge) and detail how the mind arises at an ininite number o unique structures, rather than how a listener satisies multiple constraints to arrive at a consensus or structure. Additionally, this separates the processes involved in composition rom listening, since preerence rules apply to listeners interpretation, not composers creation. All o this renders the approach by Lerdahl and Jackendo actually anti- generative and by extension, anti Chomskyian, since Chomsky s generative linguistics speciically views the creator and listener o linguistic structures as abiding by exactly the same 28 Ibid. 1-8 Ciaramella 21

23 mental process. 29 The Chomskyian generative paradigm begins with an abstract computational orm, rather than a constraint- based preerence system. Mukherji thereore separates his attempt to apply the Minimalist Program o generative linguistics rom Lerdahl and Jackendo s attempt on the grounds that it truly is a generative theory which views the process o composing and listening as being governed by the same basic mental aculty, and that this aculty builds on a simple computational mechanism with a inite set o resources, in order to create ininitely many unique outputs. 30 Fred Lerdahl s later publication, Tonal Pitch Space, written in 2001, builds upon his work with Ray Jackendo in A Generative Theory o Tonal Music, and is closer in relation to a true theory o generation than o perception. 31 In Tonal Pitch Space, Lerdahl constructs an algorithm to govern the relative distance between tonal areas as perceived by humans. Closely related tonal areas, like the subtonic in relation to the tonic, or the predominant in relation to the tonic, are perceived as being closer than other tonal areas. The arthest distance within an octave in this theory is the tritone, and is subsequently the least stable in relation to the tonic. Lerdahl quantiies these relations and develops an algorithm to govern overall relatedness given a set o tones. His theory can thereore account or the stability o related keys quantitatively and predict listener perception o stability based on the quantitative result. As such, he is capable o explaining why it is common in Classical music to modulate to the 29 In act, Berwick and Chomsky Why Only Us: Language and Evolution Ch. 1 actually suggests that language evolved as primarily an internal mechanism or thought. The externalization o language is hypothesized to have occurred ater the mental computational system was already present upon evolutionary reinement o the vocal apparatus. 30 Mukherji, Generative Musical Grammar- A Minimalist Approach p The ollowing paragraph ocuses on the general argument put orth in Lerdahl, Fred. Tonal Pitch Space. New York: Oxord University Press, Ciaramella 22

24 dominant or the subtonic, since they represent a stable relationship or listeners. He is also able to account or tonal ambiguity in late Romantic music as well as music o the twentieth century. These genres explore tonal spaces which are arther away in relation to each other, and thus produce a dierent eect on the listener. Lerdahl s Tonal Pitch Space is closer to a generative theory because he seeks the intrinsic musical properties o chords that create the dierent pitch spaces. With this orientation, he is concerned more with how musical structures are generated and why they are constructed in the ways we observe, rather than how they are received perceptually. Where Tonal Pitch Space seems to answer many questions regarding why listeners preer certain sonorities over others by looking to the intrinsic properties o their construction, and how certain groups o pitches creates vastly dierent eects on listeners than others, it still does not answer the question o why music is generated in this manner to begin with. In essence, it characterizes Merge outputs and theorizes as to why these outputs are generated, but does not address the larger system generating these outputs. Thus, Tonal Pitch Space may be useul or classiying musical structures once they exist, but it ails to adequately consider why or how they come into existence at all. The extension o the Minimalist Program into music will provide answers to such undamental questions. Issues surrounding music generation versus perception also weave themselves into research in cognitive psychology and neuroscience. Concurrent with much o the theoretic research into the generation o musical structures and their perception, has been an eort to veriy many o the claims ound in these theories on neuroscientiic grounds. One o the most signiicant claims or the Minimalist Program and its extension to music is that both are governed by the same hierarchical and recursive structure. Thereore, into the twenty- irst Ciaramella 23

25 century, there has been an eort to examine the eect o syntactic changes to musical or linguistic structure and their aects in known language- ocused areas o the brain. 32 Such research oten measures the requency o event- related potentials or speciically ERP 600 s (600 stands or the 600 ms time interval between the stimulus presented and the resulting potential in the brain) which are known to register in the brain when an error in syntax is perceived. 33 For example, Patel et. al present listeners with a harmonic progression that would commonly be ound in common practice Western tonal music and examine brain activity and ERP 600 responses. 34 Then, in the experimental group, researchers would alter one chord, or change the order o the chords in some way that would result in a dierent underlying syntactic structure. These alterations have been shown to cause ERP 600 peaks within the regions o the brain traditionally considered to be involved with processing linguistic syntax. Research o this kind has been replicated in a number o dierent settings and with dierent genres and has generated similar results, leading researchers to iner that the brain is in some way attuned to changes in musical syntax. This has led to a number o theories relating music perception to syntax, some claiming a connection to linguistic syntax, and others claiming 32 See Sammler et. al. 2011, Patel and Gibson 1998, Maess et. al. 2001, Kunert et. al. 2015, Koelsch et. al. 2007, Koelsch 2006 or some examples o this methodology 33 Patel, Aniruddh D. Music, Language, and the Brain. New York: Oxord University Press, Pg Patel, Aniruddh D., Edward Gibson, Jennier Ratner, Mireille Besson, and Phillip J. Holcomb. "Processing syntactic relations in language and music: An event- related potential study." Journal o cognitive neuroscience 10, no. 6 (1998): Ciaramella 24

26 apparent similarity between linguistic and musical syntax, but ultimately denying their similarity Overall, while these kinds o studies are helpul or determining the structures within the brain involved in processing music, and or making observations about the nature o music processing and representation in the brain, they are incapable o providing the level o precision required to generate a theory o music encompassing its natural orm, construction, and implementation in the brain, as a generative theory connected to the Minimalist Program would do. As a result, these studies address similar questions regarding listener perception ound in A Generative Theory o Tonal Music and Tonal Pitch Space, except rom a neuroscientiic standpoint rather than a cognitive one. Thereore, they are open to similar critiques rom someone working within the Minimalist paradigm since they overlook the undamental computational structure o music, which is indispensable to its representation in the mind and implementation in the brain s hardware. Their results have a certain degree o ambiguity which necessarily lead to conjecture regarding the true nature o music. For example, while it might be said that a registered ERP 600 peak in response to an altered musical chord relects a noted change in syntactic structure as represented rom the deeper computational system, it has also been proposed that this response is rather a more general response to a perceived error in the music that may arise rom any number o reasons, such as a amiliarity with the idiom generating a sense o expectancy. This line o thinking has led some 35 Patel, Aniruddh D. Music, Language, and the Brain p covers this in great detail in a chapter entitled Syntax 36 Dr. Mukherji also discusses the relation between neuroscientiic and cognitive work to the Minimalist ramework in Generative Musical Grammar- A Minimalist Approach, p Ciaramella 25

27 researchers to propose that the region o the brain in which these ERP 600 peaks occur is overall responsible or the interpretation o ine- tuned structures, and that more general errors register the ERP 600 peak. 37 Further, designation as an error resulting in an ERP 600 may also be seen to result rom the repeated exposure o an individual to this kind o stimulus, which may have led to a sense o expectancy regarding the perceived correct orm o the music at hand. Development o this sense o expectancy does not necessarily have to arise rom a more abstract computational system, but rather may be developed linearly as a set o probabilities based on perceived pitches which may be received entirely rom one s culture. 38,39 For example, consider how an avid blues listener may perceive a IV chord at the end o the twelve- bar orm to be an error and register an ERP 600 peak. This may represent an alteration o the computational system, or the Merge output, or it could simply arise rom a set o known probabilities relating to the blues, which were acquired linearly by avid listening. The Minimalist Program seeks to avoid such ambiguity by addressing the question o why linguistic structures (or musical structures) are generated, rather than characterizing them once they exist. To do so, it adopts a speciic philosophical paradigm o the human mind as the basis o its theory which is capable o ully representing music as a universal and natural aspect o humanity. This paradigm views the mind as an inormation- processing machine with three levels o operation necessary to describe any phenomenon. These levels are deined as 37 Alaima et. al is a recent example o this. 38 Mukherji, Generative Musical Grammar- A Minimalist Approach pg Berwick and Chomsky Why Only Us: Language and Evolution Ch. 2 entitled Biolinguistics Evolving also discusses an analogous strain o thinking ound in linguistics that argues or a linear, probability based generative process or language. They argue against this stance in great detail. Ciaramella 26

28 computation, algorithm, and implementation. 40 Computation is the most undamental and abstract layer dealing solely with the most basic inputs and outputs o the mind. Minimalist Program is speciically concerned with characterizing the mind s linguistic (or musical) computational system by characterizing the lexicon (inputs) and Merge (the mechanism by which outputs are realized). Products o the computational system are then applied at the algorithm level, which is analogous to the sotware o a computer. At this level, the mind receives input rom the computational system and manipulates it in some way to produce an output. The Minimalist Program claims that the phonetic orm and logical orm necessary to representing language are aspects o this level. The inal level is implementation, which describes the actual neurological structures necessary to construct the system. Broadly, this paradigm claims that one cannot simply look at any level individually, but rather how the principles o each level connect with and airm each other in order to ully understand a phenomenon. 41 David Marr is one o the ounding scholars o this paradigm and applied it to human vision. The above description o this very intricate cognitive theory is extremely brie, but interested readers can ind more on this in Marr, The most important takeaway rom this section on generation versus perception is that where theories o music perception oten describe structures once they exist and characterize their 40 Marr, David. Vision: a computational investigation into the human representation and processing o visual inormation. Cambridge, MA: MIT Press, Berwick and Chomsky, Why Only Us, Ch. 2 entitled Biolinguistics Evolving addresses this process in great detail and argues that its simplicity and eiciency also make its evolution easible rom both the perspectives o bioenergetics and selection. 42 Marr, David. Vision: a computational investigation into the human representation and processing o visual inormation. Cambridge, MA: MIT Press, Ciaramella 27

29 orm, the generative theory o the Minimalist Program seeks to answer the question o why and how they exist at all. Taking Marr s paradigm o the mind, the goals o the work o Lerdahl and Jackendo, as well as much o the neuroscience and psychological research dedicated to music detailed above, are actually to characterize the implementation or algorithm level o music, without addressing the computational level. This will always all short in truly coming to a deep understanding o a phenomenon, since it is an essential pillar o this paradigm that the levels interact and airm each other at a theoretical level. Thereore, the Minimalist Program seeks to work rom the bottom up, beginning at the computational level, and moving up rom there to algorithm and implementation to truly characterize music, as opposed to beginning with a loose sense o perception and characterizing what already exists. Section B: An Overview o the Minimalist Program within Generative Linguistics In this section, I will review the Minimalist Program rom generative linguistics in preparation o establishing its connection to Schenkerian music theory. In doing so, I will not only characterize the mental computational system deined within the Minimalist paradigm, but also put summarize the scientiic methodology which one would use or an investigation o human musicality within this paradigm. Additionally, I also draw substantially upon content rom this section as inspiration or the string quartet associated with this thesis entitled An Exploration o Musical Syntax. The original motivation o the Minimalist Program was to streamline the complex theoretical ramework that already existed within generative linguistics into its most Ciaramella 28

30 undamental and irreducible orm. 43 This motivation arose partially out o concern that the ield o generative linguistics had gotten too complicated and theoretically convoluted to be biologically easible. It appeared as i linguists were over- generating grammar rules governing the so- called universals o linguistic structure in ways that seemed to evade intuitive sensibilities about psychological and scientiic realities. The restrictions became so signiicant that neurolinguists, psychologists, and evolutionary scientists began to notice that the cognitive demand o parsing through the many linguistic syntactic rules subconsciously would likely require the brain to exhaust all o its energetic resources solely on this task. 44 For this reason, the ideas o linguistics came under ire. Concurrently, linguistic theory became suspect rom an evolutionary perspective. 45 The selection advantage conerred by language acquisition is seemingly indisputable, but the process by which language was selected or is a more challenging evolutionary question. It is known that single mutations are easier to introduce to a population than multiple concomitant mutations. Thereore, or language to be easible rom an evolutionary standpoint, it is either the case that language arose quickly by a single, or perhaps very ew, mutations that altered the neural hardware, or that many necessary neural mutations made language adoption occur very gradually over time. I language acquisition occurred gradually in humans, it would be 43 See Mukherji, Generative Musical Grammar- A Minimalist Approach p or an overview o the history o generative linguistics leading up to the Minimalist Program. Page 281 is particularly important in this regard. 44 Berwick and Chomsky Why Only Us: Language and Evolution Ch. 1 entitled Why Now? discusses this point in detail. 45 The ollowing discussion o the evolutionary pressures on language development within this paragraph is also ound in Berwick and Chomsky Why Only Us: Language and Evolution, speciically Chapters 1-3. Ciaramella 29

31 expected that archeological and anthropological indings would relect a gradual adoption over the course o millennia o things like symbolic culture and other similar phenomena used as proxy measures or linguistic ability. These indings, however, are not observed. Instead, it appears as i language developed rapidly on scales o evolutionary time. This would appear to ly in the ace o Darwinian selection, in which mutations conerring an advantage are selected or gradually, especially when involving multiple concurrent mutations. A plausible explanation to reconcile this apparent contradiction, however, is that language was in act the result o one or very ew mutations to the neural hardware. This was recently theorized by Chomsky and Berwick in their 2016 book entitled Why Only Us: Language and Evolution. Perhaps, a single alteration within the neural hardware endowed the human mind with the computational system necessary or language. This would only be possible, however, i this computational system was extremely eicient and simple, as to require ew necessary mutations. This is relevant to establishing a theoretical ramework or linguistics because it supports the idea that linguistic theory must have a simplicity and elegance that relects its evolutionary adoption. With the ideas o biological easibility and scientiic elegancy in mind, the Minimalist Program claims that language can be attributed to a single computational operation, Merge, which acts upon a inite set o word- like inputs with deinable properties, which can generate linguistic structures with ininite complexity and creativity. 46,47 This computational system is 46 In what ollows, see Berwick and Chomsky, Why Only Us: Language and Evolution p or a brie the linguistic computational system and the logic behind its eicient construction, as summarized within this paragraph. 47 In what ollows, see Mukherji Generative Musical Grammar- A Minimalist Approach p or a more detailed description o the linguistic computational system in Minimalist terms, as summarized within this paragraph. Ciaramella 30

32 said to exist or the sole purpose o satisying the biological constraints to language in order to generate interpretable structures with maximal eiciency. These constraints are that the emerging structures meet the demands o a Logical Form which passes through a conceptual- intentional interace within the mind and a Phonetic Form which mandates that it is capable o articulation by the sensorimotor system in some way. Figure 1.1 below illustrates a mental map o the linguistic computational system with each component labeled. Shown in the igure, Merge is the central mechanism mediating the transition rom linguistic lexical items to intelligible linguistic structures. Thus, the ability to carry out Merge operations has been proposed as the undamental characteristic o human language that separates it rom other animal communication systems. Berwick and Chomsky also propose the acquisition o the Merge ability to be the undamental evolutionary change accompanying language s rapid adoption historically. 48 Importantly however, each aspect o the computational system is inseparable rom its other components and they all play an integral role in language generation. This is another key component o the Minimalist Program. Each aspect o the computational system that has been retained is absolutely necessary and described in minimal terms. 48 A very technical argument or this point may be ound in Berwick and Chomsky Why Only Us: Language and Evolution Ch. 2 Ciaramella 31

33 Figure 1.1: A mental map o the Linguistic computational system rom Mukherji, 2014 p. 325 The lexicon can be described metaphorically as a mental dictionary. 49 It stores word- like units with deinable properties that act as the undamental material upon which Merge operates. The term word- like atoms is generally used in place o words to relect the notion that even single words may actually be a combination o more undamental lexical items. For example in English, played is a single word. Linguists view this term as the product o two more undamental lexical units that have already been combined via Merge. Play is viewed as a lexical item with distinct properties such as meaning, pronunciation, syntactic category 49 The discussion o the lexicon is derived rom Carnie, Andrew. Syntax: A Generative Introduction Oxord: Blackwell Publishing, Print p Ciaramella 32

34 (verb phrase, noun phrase etc.), and other lexical properties like the theta criterion (See Carnie, 2002 or a more detailed explanation o this). Linguists also view the - ed as the second lexical item active in the word played. This too has lexical content detailing the tense o phrase. In other languages, this can even be relected as a separate phonological unit that may appear in a dierent portion o the phrase in relation to the verb. Whether existing as a single phonological unit as in played or separated within a given phrase, linguists view this word as a generation rom more basic lexical content. Thereore, the lexicon is a inite set o word- like units, like - ed or play with distinct properties relating to their semantic, syntactic, and phonological detail. 50 Ininite linguistic creativity arises when the Merge acts upon the content o the lexicon. 51 As mentioned earlier, Merge is a binary set theoretic operation that combines lexical items into higher- order phrases. It always acts on two single units and combines them into a single, larger unit. Returning to the example o the English word played, Merge acted upon the two units play and ed and combined them into the single, larger unit, played. Formally, the possibilities o Merge operations can thereore be deined as ollows: (1) A + B à (AB) (combination o two lexical items) (2) C + (AB) à [(AB)C] (combination o a lexical item and a larger Merge product) (3) (AB) + (CD) à [(AB)(CD)] (combination o two Merge products or phrases) Mukherji, Generative Musical Grammar- A Minimalist Approach p gives a concise explanation o the interaction between Merge and the Lexicon. 51 The discussion rom this paragraph through page 37 o this thesis regarding Merge as a binary set theoretic operation working externally or internally stems rom Mukherji, Generative Musical Grammar- A Minimalist Approach p , though situated within a larger discussion o the history o generative linguistics in p See ibid. 318 Ciaramella 33

35 where single letters represent lexical items such as play, and two letter combinations represent single units representative o previous Merge operations (termed phrases). Items grouped in parentheses or brackets represent single phrases generated rom previous Merge operations. In each case, Merge only combines two single units into a larger unit. Importantly, however, Merge cannot actually act upon a phrase itsel as a single unit. Instead, some lexical content rom within the phrase, known as the head o the phrase, projects itsel as the deinable property o that phrase. In essence, the most important inormation governing the content o a phrase projects as the head o the phrase. This is the mechanism by which we obtain verb phrases and noun phrases, among others. Thereore, we can reine options (2) and (3) rom above to say that in the cases o a phrase Merging with a lexical item, or a phrase Merging with a phrase, it is actually true that the head o the phrase is subject to the Merge operation and that the other content o its associated phrase (i.e. its constituents) are carried along with the head into the new Merge product. In this way, we can think o all Merge operations as a case o possibility (1) rom above, whether A and B be undamental lexical items themselves or heads o phrases. This is because a head is really a projection o lexical content rom within the phrase. Thereore, what appears to be a higher- level combination is always representative o multiple consecutive binary Merge operations involving undamental lexical content. Since Merge executes binary combinations, the issue o unit order immediately arises. This can be illustrated ormally with the with the simple example below: (4) C + (AB) à [C(AB)] (5) C + (AB) à [(AB)C] Ciaramella 34

36 (6) C + (AB) à [A(C)B] In the simple case o a lexical item Merging with a phrase (or rather the head o a phrase), three ordering options become apparent. Either the lexical item may be ordered beore the phrase as in (4), the lexical item may be ordered ater the phrase as in (5), or the lexical item may insert itsel as a unique unit somewhere within the phrase as in (6). All three options are possible within the theoretical context o the linguistic computational system. In practice however, a given language only chooses one o the three orderings consistently. This ordering is known as the parameters o a given language. The ield o generative linguistics hypothesizes that when a child is acquiring language early in lie, she is attuned to the syntactic ordering o dierent types o phrases. 53,54 Upon acquiring a given language, the child develops a sense o the order in which Merge must combine units in order or the product to be intelligible within her language. As will be discussed shortly, this does not mean that Merge will not combine units in other orders as well, but that in order or the product to pass through the Logical interace prior to an utterance, it must present itsel with the proper ordering. Earlier paradigms o generative linguistics developed complicated rules or the order in which units may be combined to meet grammatical requirements in a given language. These rules became increasingly complicated trying to account or syntax in each o the world s languages. This is partially to blame or why generative linguistics was called into question as a ield in the early 1980 s. The Minimalist Program does away with the complicated rules o syntactic generation in preerence or the simple and elegant Merge mechanism, which can 53 Carnie, Syntax: A Generative Introduction p. 13, which also suggests that language is an innate instinct within all o humans, rather than something solely learned by external stimuli. 54 Berwick and Chomsky Why Only Us: Language and Evolution Ch. 1 also discusses this process. Ciaramella 35

37 maniest in one o two orms: internal Merge or external Merge. External Merge is the most undamental operation and characterizes syntactic possibilities 1-5 rom the preceding examples. For this to occur, one unit o lexical inormation is simply combined linearly with the next unit, either beore or ater it. External Merge does not inherently impose an order upon the linear combinations. Rather, these arise within a sociocultural speciic context as a language s parameters. The speciic orderings o a given language may arise rom any number o reasons rom cultural or societal norms to sensorimotor limitations and are not o particular ocus or the Minimalist Program. The important act is that external Merge combines units A and B into either (AB) or (BA). This generates what linguists call the D- structure o a linguistic utterance. All utterances in all languages have a particular D- structure that results rom the external Merge operations requisite or a given structure. External Merge, however, does not account or theoretical possibility (6) which results in the structure [A(C)B]. This is instead the product o internal Merge. Internal Merge is the process by which an external Merge product Merges again with itsel. Thereore, internal Merge essentially rearranges the order o constituents within a phrase without changing the lexical content o the overall unit. In order or internal Merge to occur, external Merge must occur irst, generating a D- structure. Then, internal Merge may cause a constituent within the phrase may be reintegrated into the phrase in a dierent place. This results in what linguists call the S- structure o an utterance. This used to be short or surace structure, just as D- structure is short or deep structure. Linguists now resist the terms surace and deep because it relects an older paradigm in generative linguistics in which it was hypothesized that the mechanisms by which the D- structure and S- structure were created were carried out Ciaramella 36

38 separately within the mind and in unique ways. Now, however, it is known that both S- structure and D- structure are a product o a single mechanism, Merge. Linguists now believe that the only dierence between the two is that S- structure is representative o the actual ordering o words heard in a sentence ater all internal Merge operations have been perormed and that D- structure is representative o the same sentence beore internal Merge. One may also ask why internal Merge operations are necessary at all or a linguistic utterance and why D- structures are insuicient. The answer to this question relates to the phonetic level o representation through which all Merge products must pass beore realization. Transormations by internal Merge occur to meet phonological requirements o a language and to streamline the phonological baggage associated with a sentence. Logically, however, a D- structure may be entirely interpretable semantically, but unpronounceable given the morphophonological requirements o the human vocal apparatus, or hands in the case o sign language. Thereore, internal Merge operations alter the phonological content, but not the semantic content o a phrase. As an extension, internal Merge operations are also important or the expressive and aesthetic qualities o language, though these are also particularly culturally deined. The discussion o internal and external Merge brings to light two o the most important deinable properties o human language that set it apart rom other animal communication systems. These are the notions o hierarchy and recursion in syntactic grammar. 55 Hierarchy reers to the idea that consecutive strings o words do not necessarily need to result rom the same Merge operation. Rather, constituents may present with any number o words between 55 Derived rom a personal communication with Dr. Mukherji Ciaramella 37

39 them that may relate at other, higher levels o syntax but not in the immediate Merge operation. This enhances the generative potential o human language by allowing ideas to be embedded within others. Thereore, in a hierarchical grammar, smaller ideas, or modiying ideas, may be embedded within an overarching idea. This powerul aspect o human language allows or precision and complexity o expression and communication. These expressive and communicative qualities are unique to human language, thereore making it a ar more advanced communication system than that o other animals. 56 Additionally, the idea o internal Merge allows or a phenomenon called recursion, in which a syntactic structure is cyclically embedded within itsel, generating a seemingly ininite linguistic structure. For example, consider the sentence Enzo played ball. The phrase the baker may be embedded within this sentence via an external Merge operation ollowed by an internal Merge operation, resulting in the sentence, Enzo, the baker, played ball. A recursive operation would embed another descriptive category o the noun, Enzo, to the sentence in the same. For example, one might say, Enzo, the baker, who is tall, and a riend o Jane, played ball. In this sentence, three phrases o similar syntactic categories (all modiying or adding to inormation about Enzo) were embedded within a single sentence. Formally, one could conceive o repeating this process ininitely and thereore generating an ininite linguistic structure. This is proo that at least in theory, human language holds ininite possibilities and thereore an ininite potential or creativity. 57 This is important to keep in mind whether studying language or music rom a scientiic perspective such as this one. We must take care to showcase the generative capacity 56 Berwick and Chomsky Why Only Us: Language and Evolution Ch. 2 covers this topic in detail. 57 See Carnie, Syntax: A Generative Introduction p or a succinct discussion o recursion. Ciaramella 38

40 o these uniquely human phenomena and treat them in a way that highlights their creative and expressive potential, rather than attempt to reduce them. As mentioned previously, within the Minimalist Program, the sole characteristic o successul Merge operations is that they meet the requirements o both the logical and phonetic interaces within the mind. This is another important acet o the Minimalist approach because it again streamlines the mental map o the computational system to solely the interaction o one computational mechanism with two separate mental interaces. I the product passes through both o these interaces successully, the phrase is said to have achieved what linguists call ull interpretation. This means that the phrase is both intelligible and pronounceable (this includes other sensorimotor operations such as the movements o the hands during sign language). 58 It is important to notice that these are the bare minimum requirements or any linguistic utterance and that the Minimalist Program says nothing about how meeting these requirements may be achieved. In other words, this approach says nothing about the actual qualities o language that express things like emotion, aesthetic impact upon others, or even how it generally sounds. These are let to other sociocultural or anatomical actors that lie outside the scope o this paradigm. 59 The Minimalist Program is only concerned with the pragmatics o generating structures that can be conveyed to others successully with a meaning that is at least interpretable. I will now briely summarize the general aspects o the linguistic logical and phonetic orms. A more in- depth explanation can be ound in Berwick and Chomsky s Why Only Us: 58 Mukherji, Generative Musical Grammar- A Minimalist Approach p Ibid. 326 Ciaramella 39

41 Language and Evolution, which also places their explanations in the context o evolutionary easibility. 60,61 This aids in understanding how and why these structures may have developed within the human mind. The logical orm o language is mediated by a conceptual- intentional interace within the mind and ensures that the orthcoming phrase is interpretable. The issue o interpretability versus interpretation is important to linguistics and centers around the logical interace. To address how the logical interace targets interpretable structures, without automatically applying a speciic interpretation, we must consider the minimum requirements or an intelligible phrase. This can be tricky i one considers the act that a phrase might in act be interpretable without an individual being able to interpret it, since interpretation is dependent on other cognitive actors such as intelligence. Thereore, or linguists to determine i a phrase is interpretable, while bypassing the necessity o their own interpretation, it is important to develop a ormal deinition o interpretability. In a ormal sense, interpretability requires that each aspect o lexical content rom the resulting Merge operations agrees with the others. This accounts or things like subject- predicate coupling, tense agreements, modiiers, and other aspects such as these. This does not necessarily entail that the phrase must be perect grammatically in the sense we learned throughout grammar school, since it is known that most people speak intelligibly in so- called ungrammatical, or dialectic language. Thus, grammar in the common sense o the world has some sociocultural inluence. The ormal deinition o a logical phrase must thereore correspond to a deeper level o linguistic 60 The discussion rom page 39 to the top o page 41 in this thesis derives partially rom Berwick and Chomsky Why Only Us: Language and Evolution Ch. 2 and the reerence in ootnote Also see Mukherji, Generative Musical Grammar- A Minimalist Approach p , Ciaramella 40

42 representation, relating to the agreement o actual lexical content. This is a complicated aspect o the Minimalist Program and one in which this paragraph only scratches the surace. However, or the purposes o applying this methodology to music, recognition that the logical interace works with a ormal, mathematical deinition o interpretability relating to lexical content retained through Merge operations will suice. The phonetic orm o language is mediated by the sensorimotor system within the brain, whose sole purpose is to generate phrases that are pronounceable in some way. An interesting discussion o the sensorimotor apparatus or language and its evolution may also be ound in Berwick and Chomsky s Why Only Us: Language and Evolution. The basis o phonetic orm in language is that the sensorimotor apparatus imposes restrictions on the kinds o phrases that are capable o pronunciation. For example, the vocal apparatus is restricted to only a set range o requencies and only a certain degree o precision or pronunciation. Thereore, Merge outputs that all outside these constraints are incapable o conveying through the sensorimotor apparatus and thereore cannot be realized as language. Interestingly, Berwick and Chomsky claim that language was irst acquired within the mind as a mechanism or thought (a controversial claim indeed). Thereore, Chomsky claims that Merge is not restricted by phonetic orm or thought, but is restricted when we try to convey thought to others in the orm o language. There is also a rich ield devoted to the morphophonological constraints on language leading to the sounds (or sights) we know, but this is also outside the scope o this thesis. For this purpose, it is only important to know that Merge is limited externally by phonetic representation and that language is only realized when Merge products successully pass through both their logical and phonetic restrictions. Ciaramella 41

43 In the interest o making this discussion slightly more tangible, I will briely present a simple example o a linguistic tree to explain how a linguist might interpret the sentence, The students love their syntax assignments, (taken rom Carne (2002) pg. 32). 62,63 Linguists use syntax trees to denote the hierarchical structure o a sentence and represent the operations that took place prior to its inal construction. An example rom Carnie, 2002 shows a tree o the example sentence, though rom a slightly earlier paradigm in linguistics. Still, it serves its purpose here as an example o a linguistic syntax tree and the accompanying methodology. Figure 1.2: A syntax tree o the sentence, The students love their syntax assignments. (rom Carnie, 2002, pg. 32). Within this tree, constituents are represented by lines that extend vertically to the same level. For example, the students are shown as constituents within the noun phrase (NP) portion o this sentence. Every juncture represents the head characteristic o the constituents, and thereore which unit projected its lexical content to a higher level. Returning to the NP, The 62 Sentence example and tree rom Carnie, Syntax: A Generative introduction p. 32. The Merge accompanying this tree on p is my own since this tree is relective o a slightly earlier paradigm in generative linguistics. 63 Additional examples o Merge analyses o linguistic trees may be ound in Mukherji, Generative Musical Grammar- A Minimalist Approach p Ciaramella 42

44 students, it is apparent that the word students (or more precisely, student modiied in number by s ) projected its lexical content as a noun to a higher level o the tree. Importantly, one will notice that every juncture only ever has two lines extending downward rom it. This is representative o the act the Merge always operates in a binary ashion. Thereore, whether Merging with the head o another part o the tree, or with a lexical item itsel, each new juncture only results rom two units. Examining the verb phrase (VP) juncture, the word love Merged with the head o phrase their syntax assignments, which is the noun, assignment. In order to create the phrase, their syntax assignments, our Merge operations must occur. First, assignment must be modiied by with a lexical item by external Merge, resulting in, assignments. Next, assignments must undergo external Merge with the modiier (denoted D), their, indicating possession. Finally, the word syntax must Merge with this phrase, irst externally, beore internal Merge places it between the previous two constituents. Thereore, the larger VP higher in the tree is representative o lexical content indicating that some people are in possession o syntax assignments (the NP) and that they love those assignments (the verb). A inal external Merge operation takes place linking the head o the NP to the head o the VP, resulting in the inal sentence. Beore this sentence was realized, the logical interace would ensure that all lexical properties necessary or interpretability matched rom the given Merge operations, and that the necessary transormations occurred or phonological articulation by the sensorimotor pathway. Ciaramella 43

45 Section C: Schenkerian Music Theory and the Minimalist Program Dr. Mukherji s eort to connect Schenkerian music theory and the Minimalist Program is part o a broader claim that music and language share a common computational system within the human mind. Thereore, attempting this connection depends on the existence o several common structures between music and language. First, there must be a lexicon o musical units analogous to the linguistic lexicon o word- like units. Additionally, there must be evidence o a hierarchical transormational grammar within music, similar to that o a syntactic tree, and that this grammar must show the same binary linear combinations as executed by Merge. Finally, there must exist some kind o logical interace and phonetic interace that limits musical structures to those that are intelligible and capable o articulation. Mukherji claims that arguments or these connections lie within Schenkerian music theory, which I will detail now. 64 The irst, and perhaps most controversial claim necessary or this connection, is the existence o a musical lexicon containing a inite set o musical units with deinable properties. An argument or the musical lexicon originates rom Schenker s notion o stue, or scale- step. Schenker argued each area o a musical passage can be characterized by speciic scale degrees corresponding to their undamental harmonic structure. Thereore, in the case o a musical passage beginning with a tonic in C- major, Schenker would argue that we should view this beginning as an elaboration o the 1,3, and 5 scale- steps. Additionally, a set o harmonies that 64 The remaining content o this chapter expounds Dr. Mukherji s connection between Schenkerian music theory and the Minimalist Program and will thereore only be cited once here. The discussion can be ound in Mukherji, Generative Musical Grammar- A Minimalist Approach p Additionally, aspects o this connection were clariied via personal communication with Dr. Mukherji. Ciaramella 44

46 prolongs a certain passage, such as a plagal cadence in the context o the inal tonic o a piece, can be viewed as a stuengang, or collection o pitches centered around a single scale- step. Thereore, Schenker used the background, middleground, and oreground levels o his analysis method to indicate the primary scale- steps populating a musical passage, in order o importance. These scale- steps generated structural motives at each level corresponding to what we generally think o as a harmonic structure. The Ursatz within the background, which or him was always I- V- I, corresponded to the most undamental scale- steps o the piece s background structure. Middleground elaborations were thereore maniest o subordinate scale- steps to those o the background and served to construct stuengang structures about the background scale- steps. Finally, the oreground served to urther elaborate the stuengang developed through the background and middleground structures, employing voice- leading operations, ornamentations, and even more subordinate scale- steps. Importantly, Schenker believed that undamental content rom the background scale- step projected itsel at each level o a piece in ways that elaborated and expanded upon it. He termed this phenomenon Asckomponierung. Mukherji believes Schenker s idea o a hierarchical organization o scale- steps rom the background to the oreground actually represents the beginning o a generative theory o tonal music. The idea that a scale- step has deinable properties and may be organized in a hierarchical arrangement parallels the idea o word- like units within a lexicon. Further, the idea that a scale- step may project itsel at every level o structure, as those o the Ursatz do, also parallels the idea that lexical content projects as the head o a Merge operation. Thereore, combinations o scale- steps in which one scale- step projects its inormation as hierarchically Ciaramella 45

47 more important rom the background to the oreground can be seen to parallel the idea that when two lexical items are Merged together, one item projects its inormation to higher levels o syntactic representation and deines the content o a phrase. For this claim to hold weight, however, it needs reinement to apply to all musical idioms since as it stands, it would appear that the notion o the scale- step would only apply to polyphonic idioms with harmony similar to that o the Western Classical idiom. Schenker s deinition o the Urlinie substantiates the argument that the universal lexical basis or music might be ound in his theory o the scale- step. Mukherji claims that Schenkerian theory is primarily a melodic one, as opposed to a harmonic one. This originates rom the idea that the Urlinie is constructed rom scale- step tones. Thereore, in the case o the Urlinie, scale degree 3 would come rom the initial tonic scale- step, scale degree 2 would come rom the dominant, and scale degree 1 would come rom the inal tonic. I this is the case, then a melody should already hold the scale- step content it is generated rom and thereore hold the lexical content inherent to scale- steps. The purpose o harmony in this line o thinking would be to externalize the harmony already present in a melody. This is commonly seen in monophonic idioms that oten arpeggiate or unold a choral harmony linearly, thereore serving as evidence that a melody may contain inherent scale- step content. Conversely, music in lead sheet notation may be assumed to contain a Urlinie, even i not outwardly notated, on the basis that it has a logical harmonic progression. This link allows or an extension o Schenkerian theory to potentially all genres o music, since it applies to both monophonic and polyphonic textures. Thereore, Mukherji s conclusion is that there exists a set o chord- like structures, based in Schenker s notion o the scale- step, that serve as the basis or all o the world s music Ciaramella 46

48 and that these are the undamental content upon which Merge operates within the mind s computational system. The only issue remaining is Schenker s sentiment that the basis o music s lexical content must be the projection o a I- V- I Ursatz into a Urlinie. Given the ideological limitations that restricted Schenker to the so- called Germanic master composers, this might be true or music as he understood it. However, in today s global society, it would evade our sensibilities to believe that this truly could be the basis or all music. However, i we view the Urlinie and the Ursatz as culture- speciic artiacts o a more basic computational mechanism, then we can overcome this limitation. Mukherji claims that the Ursatz and Urlinie arise rom Merge operations o basic scale- step content, the structure o which has become part o the logical orm o Western Classical music, thus explaining its prominence. There is nothing intrinsic to this progression, however, that would lend itsel to any kind o universality. Thereore, we would expect that all musical idioms have some orm o an Urlinie and an Ursatz, based in the idea o the scale- step, but that each idiom s structure may not bear similarity to any other. Even the scales used to derive these culturally deined progressions may be dierent rom idiom to idiom. The only necessary commonality is the existence o a hierarchical and recursive grammar centering around a scale- step based lexicon upon which Merge operates. Further, as an aspect o human biology, it would also be expected that the products o Merge be subject to the logical and phonetic interaces limiting their possibilities. In music, the issue o interpretability versus interpretation brought about by the logical interace is perhaps even more pertinent than in language. Meaning in language may be complex, but its nature lends itsel well to a single interpretation. For example, all readers Ciaramella 47

49 would likely understand the sentence, The Godather Part II is my avorite movie, in the same way. Because o this, deducing what might be the ormal, logical basis or interpretability seems manageable with regards to language because we can come to consensus regarding what a meaning is in the irst place. This allows a platorm upon which we can deine the notion o interpretability ormally in terms o lexical, grammatical agreement. Music, however, does not share this characteristic with language. Meaning within music is hotly debated rom all corners o the music academy without even the possibility o consensus. Some even claim that music itsel is meaningless. Among those who acknowledge meaning exists in music, there exists an ininitely many possible interpretations o a piece that can be deended as valid. Given this inherent plurality, the notion o interpretability versus interpretation becomes an ever more important aspect o the Minimalist Program and one that sets it apart rom other analytical methodologies. The logical interace through which Merge outputs are processed beore inalization ensures that the lexical content rom each scale- step within the structure align ormally in a way that is interpretable, but does not actually impose an interpretation to the music. Interpretation, thereore, is not the subject o the mental computational system generating music and something that is applied through other sociocultural orces. Even inormation like harmonic unction is said to arise semantically ater the syntactic Merger is processed through the logical interace. Mukherji explains the concept o harmonic unction as a cultural artiact o the Western Classical idiom that arose as a means o semantically describing Merged syntactic structures within the idiom, but claims that they arise ater the act rather than as a necessary component o the computational system. Ciaramella 48

50 Exploring the characteristics o the universal musical lexicon and its relation to logical orm is an area in need o urther study to substantiate the connection between Schenkerian music theory and the Minimalist Program. Mukherji presents one hypothesized aspect o the musical lexicon as being a scale- step eature relating to the circle o iths. He terms this characteristic the c- eature. A c- eature is a numerical label applied to each pitch in relation to its position on the circle o iths. The actual value o this numerical label is arbitrary, but the dierence between c- values o two consecutive or Merged scale- steps is o importance. Figure 1.3 shows a map o the c- values or each area o the circle o iths. Figure 1.3: c- eature labels or the circle o iths rom Mukherji, 2014 p The c- eature provides a starting point or the ormal logical deinition o an interpretable tonal Merge structure and relects the parameterization o Merge ordering ound in language. For Ciaramella 49

51 the Classical idiom, it is conventional to move in a counter- clockwise direction around the circle o iths. This is made most clear by the prominence o the authentic V- I cadence ending virtually every classical piece. Formally, Mukherji suggests that the parameter o Merge ordering within the Western Classical idiom requires that the Merging o two scale- steps ollow the c dierence, c=01. This is relective o a change between adjacent positions on the circle o iths moving in the counter- clockwise direction. For example, take an authentic cadence between D 7 and G major. This would correspond to the change c=02 to c=01. The dierence between these (02-01) is c=01. Thereore, the Merger would be syntactically valid and order linearly with the D 7 chord moving to G major. Additionally, the Merger o c=00 is always possible in any idiom and would result in no chord change at all. This seems trivial, but is actually necessary or a logically interpretable phrase so that it begins and ends on the tonic. This is the basic idea behind all scale- step changes parameterized within the Western Classical idiom. From this basic discussion, questions immediately arise regarding how a deceptive cadence or a cadence involving a diminished seven chord can be accommodated within this structure. Mukherji claims that there exists a second scale- step lexical relationship between scale degrees related by a third. He calls this a speciic pitch space, just as the circle o iths is a pitch space o ith intervals. In thirds- based space, pitches separated by a third can be seen to essentially hold the same c- value. Evidence or this characteristic is the existence o the relative minor, in which a scale with the same number o accidentals dictates both major and minor depending on the starting note. The order o this operation, however, should be parameterized just as iths- based space is parameterized to move counter- clockwise in the Ciaramella 50

52 Western Classical idiom. Mukherji observes that in Western Classical music, thirds- space is parameterized in moving down a third, as opposed to up. Thereore, C major can be seen to hold the same c- value as A minor, but not E minor. From this, it ollows that c movement may proceed covertly between scale- steps related by a third in order to ulill the syntactic rule that c- values move counter- clockwise in iths- based space. For example, in the case o a V- vi deceptive cadence. It would actually be the case that the initial Merger was between V and I, thereore ulilling the required c=01, and then covert movement between I and its third- space relation vi generated the articulated vi chord. In this case, the I chord is present grammatically and syntactically, but not actually articulated in the structure. This also explains a progression such as (vii o /V)- V- I. While the (vii o /V)- V seems to break the syntactic Merger rule by resulting in c=+05, the structure may be explained by using a covert third- space relation between (vii o /V) and (V/V). In this case, the syntactic Merger was between (V/V) and V, which would generate the proper c=+01, and covert movement occurred within third space moving (V/V) to (vii o /V). The notions o iths- based c- values and thirds- based space allows us to explain other canonical structures within the Western Classical idiom in addition to other Western idioms such as the blues. Take the progression I- IV- V- I, which is the basis or a conventional Western Classical phrase and the origin o Riemannian harmonic areas. Using iths- based c- values and third- based space, we can develop the ollowing syntactic tree or this generic progression shown in Figure 1.4. Ciaramella 51

53 00 IIV(ii)VI C: Figure 1.4: A syntactic tree showing c- values and Mergers or the I- IV- V- I Progression. 00 In the above syntactic tree, lexical items originating rom a letward- up slanting arrow are subordinate to the other lexical item they Merge with, which originates rom a rightward- down slanting line. Thereore, letward- branching units unction to prolong the hierarchically superior unit. Each juncture represents a Merge operation in which either the heads o previous operations or a lexical items are Merged. The resulting phrase links the initial tonic to the inal tonic, resulting in an overall phrase c- value o 00. This is a requirement o Western Classical logical orm, that the overall phrase is characteristically c=00. We can now walk through each Merge operation that resulted in the case o a c=00 Merging with a c=00 to generate the overall phrase. First, the scale- step o hierarchically least importance is the IV chord. This cannot immediately Merge with the V chord because it breaks the c- value syntax rule by creating c=+02. Theoretically, it could Merge with the initial tonic, creating c=+01, Ciaramella 52

54 but this would orbid subsequent Merging with the V chord. Instead, covert third- based movement occurs between IV and ii, which the lexical content o the ii projects. This is noted within the yellow box o Figure 1.4, which takes the c- value o 02. The notion o third- based movement between IV and ii also seems plausible in historical context, since in the Western Classical idiom, IV is oten articulated beore ii in a pre- dominant context. Following third- based movement to the c- value o ii, this scale- step may Merge with the V scale- step, again generating the required c=+01. In each case, the latter scale- step projects its lexical inormation up the tree, relective o the parameterization o Western Classical music. This branch can now Merge properly with the inal tonic, again creating the desired c=+01 and projecting the tonic s c inormation to the highest level o the tree. The inal Merger between the tonic c head o the previous Merger and the initial tonic may now occur, create the permissible c=00 which is also required or a logically interpretable phase. As we can see, the c- value argument between iths- based space and thirds- based space can explain this canonical phrase within the Western Classical idiom, relecting the counter- clockwise parameterization o the idiom or logically interpretable phrases. As mentioned earlier, the c- eature o lexical scale- steps should not be taken as the sole lexical characteristic o musical units. Rather, it is likely just one actor among many others, though more work needs to be done to elucidate these. For example, there must be some modiication to indicate tonicizations versus ull modulations. Additionally, music that exists in other modes may eature other lexical content, or observe a dierent parameterization o the c- eature. For example, Mukherji worked with blues and blues- inluenced rock idioms and revealed that the parameterization o these idioms is exactly the reverse o the Western Ciaramella 53

55 Classical idiom. In these genres, scale- steps proceed clockwise about the c- modiied circle o iths and thereore have the Ursatz o I- IV- I and a c structure o c=- 01. In this argument, a V chord seen at the end o a phrase would represent a transormation o the D- structure I- V- IV- I, as seen in the inal bars o the blues. Thereore, the above argument should not be taken as inal, but rather as the beginning o a more rigorous characterization o the musical lexicon. Still, this will suice or the case studies that will be presented in Chapter two, since they are all rom Western derived idioms. The inal aspect o the musical computational system to describe is the phonetic interace through which music travels prior to realization. This is the most complex and heterogeneous aspect o the computational system discussed thus ar and I will only cover the major points rom Mukherji s discussion here. He irst notices that most theorists treat tonal and rhythmic aspects o music as separate and distinct entities. Thereore, musical rhythm is oten viewed rom an externalist perspective. One major acet o the Minimalist Program, however, is that it cohesively accounts or phonology within language rom an internalist perspective, taking it to be inseparable rom the other aspects o language. In order or the link between music and language within the Minimalist Program to be substantiated, an internalist stance toward musical rhythm must also be taken. Mukherji thereore argues that pitch has an asymmetric inluence on rhythm, but that there is an interplay between the two that generate an overall musical structure. This is done irst through the observation that when two chords are presented, rhythm is inevitable introduced to music. This is because the chords must be ordered in some way, thereore separating their articulation in time. This is the deinition o rhythm. He then Ciaramella 54

56 distinguishes between metered rhythm, which has a regular pulse, and rhythm in general, which only requires the ordering o notes. Metered rhythm can be seen as a special case o the more general rhythm and one whose characteristics are deined by an interplay between ormal syntactic actors and extra musical actors. For example, the Chopin mazurkas purposeully incorporated rhythms known rom Polish dance. Thereore, one may expect to ind an explanation or the speciic accents within the ootsteps o the Polish dances, since there are anatomical limitations to how the human body can dance. This is an extra- musical actor o musical rhythm. The discernment o internal musical actors aecting rhythm are more relevant or the characterization o the musical computational system. To deduce what these might be, Mukherji irst observes that music oten has a regular distribution o harmonic structures in relation to rhythm. Speciically, harmonic units generally appear in divisions o two or our. Mukherji believes that this is not a coincidence or due to external actors. The regular division o harmonic units may be the result o the binary Merge operations. I all rhythmic phenomena are driven by Merge s binary operation, then at an abstract level all rhythm must be binary. This is complicated by the Merging o a head to another head or another lexical item, but the basic premise holds that the origins o rhythm must be binary. Thereore, Mukherji goes on to argue that this binary operation maniests in harmonic structures o two or our units. Further, claims that what might appear to be a deviation o this kind o division is oten resolved at a deeper level o structure. Thereore, a D- structure may present with the proper binary arrangement and by transormations be converted to an S- structure with a seemingly ungrammatical rhythmic structure. Further, voice leading operations and prolongations may Ciaramella 55

57 alter rhythm at the surace, but not at deeper levels. This interaction also works in the other direction. Rhythmic irregularities at the level o D- structure may be resolved by insertion o another beat in to the S- structure, satisying voice leading or other phonological concerns. Mukherji elaborates on this idea to a much greater extent, but the general idea ollows that pitch asymmetrically inluences rhythm through Merge and that D- structures and S- structures interact to reinorce rhythmic structure. Conclusion This chapter developed not only a theoretical basis or a connection between music and language within the Minimalist Program o generative linguistics, but also a methodology rooted in Merge analyses o musical structures. The goal o such analysis is to characterize the process by which the mind generates musical structures with ininite creativity rom a inite set o musical inputs. The next chapter will be devoted to applying this theoretical and methodological ramework to three original case studies and investigating whether it can accommodate musical structures rom variety o musical idioms and time periods. Ciaramella 56

58 Chapter 2: Case Studies rom Western Idioms In this chapter, I present three case studies which investigate aspects o the musical computational system. The irst case study will be the opening phrase o the irst movement o Mozart s K. 332 piano sonata in F Major, which its squarely into the Western Classical idiom. The next two case studies are Georgia on My Mind and Blue Bossa and all under the general category o Jazz, though their inluences are vastly dierent within the idiom. My goal or presenting these analyses is threeold. First, each piece showcases dierent aspects o generative musical grammar and will be used to demonstrate the ability o the methodology presented in Chapter One to accommodate a diversity o musical structures. Second, I will argue or a common grammatical structure underlying each o these pieces and present this as evidence or the validity o the Minimalist Program- Schenkerian music theory connection. Finally, I will expound a theory that the dierence between cyclic and linear song orms lies within the characterization o the inal Merge operation in the piece s grammatical structure and will use Mozart K. 332 as an example o a linear structure and Georgia on My Mind and Blue Bossa as examples o two cyclic orms with dierent grammatical underpinnings. The case studies presented here were chosen because they are each derived rom a Western idiom, but not the same idiom. For a work o the magnitude o a thesis, as opposed to a dissertation, it is useul to choose pieces that broadly all into a similar musical paradigm. This saves the additional work o translating musical structures and terminology rom their original idiom into another in which there might not be an exact translation. By this, I am not suggesting that Western Classical music and Jazz share any particularly strong sociocultural Ciaramella 57

59 connection, but rather that they simply share a similar set o terms by which we describe the music (harmony, melody, etc.) It may be there is some cultural continuity between the idioms and this would perhaps explain some o their descriptive similarities in addition to their musical similarities, but that is beyond the scope o this thesis. This does not discredit cross- cultural investigation within the generative ramework. Rather, these studies are essential to proving the psychological basis or the linguistic/musical computational system. This is only to suggest that such cross- cultural studies oten require the workload o a thesis in and o themselves, i not a dissertation. However, the chosen pieces do allow or strong cross- idiom comparison o musical grammar, which is another key acet o proving the psychological basis o this generative theory. The works presented here span almost two centuries and originated on dierent continents. Commonalities o musical syntax would be expected across this timespan and geographic span i they were relective o a psychological reality, whereas there might not be commonalities i there was simply some loose cultural continuity between eighteenth century Western Europe and twentieth century United States. Thereore, the cross- idiomatic similarities I will present in what ollows will be taken as evidence or an underlying computational similarity. Section A: Mozart Piano Sonata K. 332 Mvt. 1 The irst movement o Mozart s K. 332 F major piano sonata is written in conventional sonata- allegro orm. 65 Theme A rom the exposition, which is the ocus o this analysis, spans mm The theme is presented in F major and consists o three shorter our measure 65 Score used in this analysis was obtained rom Mozart, Wolgang Amadeus. Sonata No. 12 in F Major K. 525 Bryn Mawr, PA. Theodore Presser Company, Ciaramella 58

60 phrases. Phrase one spans mm. 1-4 and arpeggiates an F major triad rom F4 to F5 and eatures a pedal F as the lowest note o the bass arpeggiation. This pedal will be signiicant later or arguing that this entire phrase prolongs the initial tonic. The next phrase spans mm. 5-8 and prolongs the tonic in F major. The melody sequences downward rom F5 to F4 while outlining an F major triad. The inal phrase spans mm and eatures a descending scalar passage outlining the predominant harmony beore an authentic cadence between mm with C major resolving to F major. An investigation o the generative process behind Mozart s construction o the opening phrase depends heavily upon the lens we choose or analysis. For example, i we take a broad lens and view the phrase in context with the entire Exposition, we may see the entire twelve measures as a prolongation o the initial tonic and a single scale degree. Alternatively, we may take a smaller scope and arrive at a dierent conception o the phrase. For the present investigation, we will take mm as a single unit that comprises a coherent musical structure in and o itsel. In other words, we will treat it as a linguist would treat a sentence within a larger paragraph or essay. Within this phrase, Mozart s mind would have employed the Merge mechanism and acted upon the speciic triadic lexical content that is common to the Western Classical idiom to arrive at an interpretable phrase. Our task is to reveal the logical structure inherent within the phrase and visualize the speciic Merge operations requisite or its construction. I we were to perorm a Schenkerian analysis on just the opening phrase, we are immediately conronted with a diicult choice or discerning the Urlinie. The initial ive Ciaramella 59

61 measures outline an F major triad rom F4 to F5. The inal seven measures then descend rom F5 back to F4. Thereore, one could argue that this phrase is comprised o an Urlinie in which the Kopten (highest note o the Urlinie) is revealed ollowing the initial ascent in m. 5. This would require viewing the initial ive measures as a prolongation o the tonic and an elaboration o scale degree one. Following the descent, the dominant chord on the third beat o m. 11, which precedes the inal tonic in m. 12, would then be viewed as the structural dominant o the Ursatz in which scale degree two would be implied and replaced with scale degree seven by a voice leading operation. This analysis, however, leaves questions regarding the integrity o the Urlinie. Schenker seems to generally reserve this Urlinie or larger structures. 66 It is thereore unlikely that the entire scale could descend structurally within the span o seven measures without a sequence or some other measure to harmonically justiy the descent. Additionally, scale degree seven is omitted rom the descent. At its best, this phrase would contain a quick and incomplete Urlinie, i we were to view it this way. Alternatively, we could take scale degree ive on the irst beat o measure two as the Kopten and say that the phrase has a Urlinie. This may seem more plausible, given that it is revealed more quickly durationally and unolds over the course o the entire phrase, rather than the last seven measures. I this were the case, then we might argue that the descent rom scale degree ive to scale degree two is quicker, spanning mm In this analysis, scale degree two would begin structurally on the downbeat o m. 8 in conjunction with the dominant harmony. Mm would then prolong scale degree two by elaborating the dominant with a short phrase beore the inal resolution in mm This would also reveal 66 This idea came about through a discussion with Proessor Shirish Korde. Ciaramella 60

62 the structural dominant o the Ursatz as the C major seven chord on the third beat o m. 11. There are also reasons to question this analysis. First, this would require the initial statement o the Kopten to occur over a V 7 /IV chord. Intuitively, this weakens the statement o the ith scale degree because it is associated with motion to the IV chord, rather than the tonic. Since Schenker believed the Urlinie to derive rom structural tones within the Ursatz, we would expect the statement o scale degree ive to coincide with the tonic, rather than this pre- dominant sonority. Additionally, the only statement o scale degree our within this analysis ollows the Kopten immediately in m. 3. Since IV is the predominant sonority to which the secondary dominant in m. 2 is leading, this would require us to acknowledge that two structural tones o the Urlinie would unold within one phrase area and over the course o two measures. Again, this seems unlikely. A Merge analysis o the opening phrase assists in clariying the proper designation o the Ursatz and Urlinie within the opening phrase. Thereore, I will irst detail the phrase s Merge structure to reveal an underlying logical cohesion rooted in the c- eature, beore explaining the proper Schenkerian diagram o the phrase. Figure 2.1 shows a Merge diagram o the opening phrase. Since this phrase is derived rom the traditional Western Classical idiom, we would expect a parameterization o the c- eature in which scale- steps proceed counter- clockwise around the circle o iths, as demonstrated in Chapter One through the analysis o the canonical I- IV- V- I chord progression. Indeed, this is what we ind within this phrase. The entire structure is constructed o three smaller phrases, each o which embodying some realization o the I- IV- V- I progression. Ciaramella 61

63 Figure'2.1:'MergeAnalysisotheOpeningphraseto MozartK.332Mvt # # # ####################### ############################# ##################### ################## ############################################ ############### ### #################################### ## ### I V 7 /IV IV V 4 3 I(((((((((((((((((( (( V I((((((((((((( ( IV V I The irst step in deriving this phrase s Merge structure is to identiy the major structural components that comprise the head o each section. To begin with the initial tonic, we ind that the F major chord articulated in m. 9 is the head o the initial tonic phrase. Thereore, we can view mm. 1-9 as a letward prolongation o the initial tonic in F major. 67 For this argument, the V chord in m. 8 must irst Merge with the tonic in m. 9, which creates c= 01. I we allow the tonic c=00 content to project as the head o the phrase, then the head may Merge with the tonic elaboration that appears in mm. 6-8, creating the allowable c=00 Merger. The overall projection rom mm. 6-9 would thereore be the tonic c=00 content. Beore Merging m This means that the structurally prolonged tone appears ater its prolongation (See Mukherji, Generative Musical Grammar- A Minimalist Approach p ). Ciaramella 62

64 with the dominant, however, we must deal with the V 7 /IV and IV sonorities in mm To account or this, we must acknowledge that the F dominant seven chord moving to the B lat major chord represents allowable counter- clockwise motion around the circle o iths. Thereore, the chords in mm. 2-3 may Merge to generate c=01 and the lexical content o IV, which is c=- 01, projects as the head o the phrase. This creates the irst dilemma or the Merge structure, in which the c=- 01 cannot Merge with the dominant, since it would create c=02, and it cannot Merge with the tonic in m. 1, because we would be unable to join this with the rest o the phrase. We can circumvent this dilemma by employing thirds- space movement between IV and ii ollowing the initial Merger o V 7 /IV and IV. Now, the lexical content o ii would deine the head o this phrase, which is c=02. This can undergo an allowable Merge with the dominant in m. 4, in which the dominant s lexical content projects as the head o the phrase. This can then participate in a Merger with the tonic phrase rom mm. 6-9, in which the tonic s lexical content projects to the higher order phrase. Finally, this phrase Merges with the initial tonic chord in m. 1, creating a logical phrase o c=00. As we can see, the c- eature o the entirety o mm. 1-9 is actually the tonic s lexical content, indicating that the initial tonic is prolonged over the course o the irst nine measures. To generate the remainder o this phrase, we must take mm. 1-9 as a prolongation o the initial tonic with c=00 lexical content. What remains is an articulation o the canonical I- IV- V- I progression that was detailed in Chapter 1. First, the IV chord in m undergoes thirds- space movement to ii and takes the c value o 02. This undergoes an allowable Merger with the dominant in m. 11, in which the c=01 lexical content project as the head. Next, the c=01 head merges with the inal tonic in m. 12 and generates a c=00 head. Finally, this phrase can Ciaramella 63

65 Merge with the tonic prolongation in mm. 1-9, generating the logical c=00 and an interpretable twelve measure phrase. This Merge analysis helps to reveal the true Urlinie and Ursatz that deines the irst phrase. 68 Shown in Figure 2.2, the opening phrase o the movement is best characterized as a statement o a Urlinie. We can understand the entirety o mm. 1-9 as a prolongation o the initial tonic, in which the tonic s structural tones are arpeggiated upward to F5 in a projection rom Ursatz, and then downward to F4. Finally in m. 9, the Kopten is stated on the downbeat as scale degree three. Thereore, we can view the irst nine measures as a letward prolongation o the Kopten leading up to its articulation in m. 9. This analysis is corroborated by the pedal F underneath the arpeggiated harmony in mm, 1-4, which clues us into what might be Mozart s intuition about the unction o the irst our measures. Further, the two dominant Figure'2.2:'SchenkerianDiagramoMozartK.332Mvt.1OpeningPhrase Foreground Middleground Background I V I 68 Several conversations with Proessor Shirish Korde were also helpul or discerning this phrase s Urlinie. Ciaramella 64