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Thelonious Monk's Prototypical Style: Close andDistant Readings of Jazz StylingsConnor Davisconnorjdavis1@gmail.com

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Recommended CitationDavis, Connor, "Thelonious Monk's Prototypical Style: Close and Distant Readings of Jazz Stylings" (2019). LSU DoctoralDissertations. 4988.https://digitalcommons.lsu.edu/gradschool_dissertations/4988

THELONIOUS MONK’S PROTOTYPICAL STYLE:

CLOSE AND DISTANT READINGS OF JAZZ STYLINGS

A Dissertation

Submitted to the Graduate Faculty of the Louisiana State University and

Agricultural and Mechanical College in partial fulfillment of the

requirements for the degree of Doctor of Philosophy

in

The School of Music

by, Connor Davis

B.M., University of Arkansas, 2013 M.M., Michigan State University, 2015 M.A., Eastern Illinois University, 2016

August 2019

ii

To my wife, Alyssa,

who selflessly supported me

throughout this endeavor, and to

my family who encouraged me

along the way.

iii

Acknowledgements

This document exists as a testament to others’ investment in my life and career. While I

cannot name everyone, I would like to acknowledge a portion of these people. I want to thank my

committee members: Dr. Daniel Shanahan for taking me on as an advisee and helping me

accomplish so much while giving me the freedom to explore; Dr. Jeffrey Perry, whose guidance in

writing and openness to discuss these topics were of great benefit; Dr. Inessa Bazayev, who has

supported me in my endeavors and teaching throughout my time at LSU; Dr. Jon Cogburn, who has

helped shape my philosophical understanding of the world; and Dr. Zevi Gutfreund, who agreed to

serve as my Dean’s Representative.

Next, I would like to thank my colleagues in the music department who have been a

wonderful and welcoming cohort, in particular Sasha Drozzina, Dr. David Baker, Dr. Michael

Palmese, Dr. Jacob Gran, Dr. Adam Rosado, and Elizabeth Monzingo.

I extend a special thank you to my family: to my parents, Rob and Page Davis, for

encouraging me to pursue music and instilling a work ethic to succeed in such an endeavor; to my

brothers, Grant and Ian, for being such wonderful supports and helping me keep perspective; to my

grandparents, Jim and Darrell Rankin, who have supported me throughout this process; to the

various churches I have been a member of during this transient process, Holt Baptist, University

Baptist, Reedemer, CrossPoint, and South Baton Rouge Presbyterian—you are all the body of Christ

here on earth.

I want to thank my beautiful wife, Alyssa. You encouraged me and kept me grounded on a

daily basis. I could not have done this without you. Thank you for your strength and wisdom.

Finally, I want to thank God for his immeasurable love and continued grace.

iv

Table of Contents

Acknowledgements ........................................................................................................................................... iii

Abstract .............................................................................................................................................................. vi

Chapter 1. Literature Reviews and Goals: What Is Prototypicality and How Does It Help? ................ 1 1.1 Introduction ............................................................................................................................................................. 1 1.2 Prototypicality .......................................................................................................................................................... 3 1.3 Statistics as a Categorization Tool ........................................................................................................................ 4 1.4 Epistemological Grounding ................................................................................................................................... 5 1.5 Cognitively Prototypical ......................................................................................................................................... 9 1.6 Concepts in Music .................................................................................................................................................11 1.7 Structural Considerations .....................................................................................................................................12 1.8 Conclusion ..............................................................................................................................................................20

Chapter 2. Establishing a Proptotype: Supervised and Unsupervised Machine Learning Approaches to Solo Categorization ..................................................................................................................................... 22

2.1 Introduction ...........................................................................................................................................................22 2.2 Data ..........................................................................................................................................................................23 2.3 Dimensionality Reduction ....................................................................................................................................31 2.4 K-means Clustering ...............................................................................................................................................34 2.5 Generalized Linear Model ....................................................................................................................................36 2.6 Resulting Prototypical Solos and Their Statistical Features ............................................................................40 Conclusion ....................................................................................................................................................................45

Chapter 3. Close Readings of Prototypical Solos ........................................................................................ 47 3.1 Prototypicality in Cluster 1 ...................................................................................................................................50 3.2 Prototypicality in Cluster 2 ...................................................................................................................................59 3.3 Prototypicality in Cluster 3 ...................................................................................................................................67 Conclusion ....................................................................................................................................................................74

Chapter 4. Thelonious Monk’s Prototypical Style ...................................................................................... 76 4.1 Cluster 1 ..................................................................................................................................................................76 4.2 Cluster 2 ..................................................................................................................................................................83 4.3 Cluster 3 ..................................................................................................................................................................93 Conclusion ................................................................................................................................................................. 103

Chapter 5. "Bloomdido": A Case Study ..................................................................................................... 105 5.1 Charlie Parker ...................................................................................................................................................... 107 5.2 Dizzy Gillespie .................................................................................................................................................... 113 5.3 Thelonious Monk ............................................................................................................................................... 117 Conclusion ................................................................................................................................................................. 121

Epilogue: What About Time Feel? .............................................................................................................. 123

References ....................................................................................................................................................... 140

Appendix 1. Patterns Included in the Model ............................................................................................. 144

v

Appendix 2. Clustering and Distance Metrics ........................................................................................... 146

Vita ................................................................................................................................................................... 159

vi

Abstract

Thelonious Monk’s style has been considered non-conformist, modernist, technically stilted,

intentionally unconventional, even incompetent. His performing is idiosyncratic, to say the least.

However, by what metric is his performing idiosyncratic, or, framed another way, in what ways do

Thelonious Monk’s performances deviate from the prototypical performance? Situated within family

resemblance theories of prototypicality, I utilize supervised and unsupervised machine learning

approaches to categorize jazz solos based on their melodic usage of standard jazz language (novel

corpus of 530 jazz solo improvisations). Using these distant readings to determine which solos are

prototypical, I perform a close reading of these prototypical solos via voice-leading reductions. This

allows for an empirically grounded discussion of how Monk relates to the genre he was so influential

upon.

In chapter 1, I define prototypicality and discuss various difficulties in doing so in a manner

that produces real-world prototypes. Using these premises, I define my goals of studying how

prototypical Thelonious Monk is as a performer, and how that determination is important when

labeling a performer as a non-conformist, modernist, etc. In chapter 2, I employ statistical

methodologies to determine which variables are salient in defining prototypicality, and these

variables are used to create my algorithms for solo categorization. In chapter 3, I explore from a

music theoretical perspective the most prototypical solos in my corpus as identified in chapter 2,

ultimately concluding that these solos find their meaning in deeper middle ground structures.

Chapter 4 examines in detail the three most prototypical Thelonious Monk solos in my corpus. I

conclude that Thelonious Monk’s solos are less about deep structure and more about developing

foreground motives. Chapter 5 is a case study of the tune “Bloomdido,” in which I analyze the solos

of Charlie Parker, Dizzy Gillespie, and Thelonious Monk on the same recording. I conclude the

dissertation with an epilogue entitled “What About Time Feel?”. In this epilogue I introduce future

vii

research and caveats concerning the importance of time feel and rhythmic usage when discussing

performance practice.

1

Chapter 1 Literature Review and Goals:

What is Prototypicality and How Does It Help?

1.1. Introduction

Thelonious Monk (1917–1982) was an American jazz pianist and composer who got his start

as a church musician before becoming a jazz musician, ultimately being schooled in the Harlem

stride tradition. He eventually influenced the Bebop genre, performing much of his career at

Milton’s Playhouse with the likes of Charlie Parker, Dizzy Gillespie, Miles Davis, and Max Roach,

among others. His performance practice has been described as non-conformist, modernist,

technically stilted, intentionally unconventional, even incompetent.1 More systematically, Solis

describes Monk’s music as containing five broad characteristics that capture his style—a unique

approach to time-feel, developmental logic, a unified quality in individual performances, humor and

playfulness, and his music taken as a whole represents an “entire self-created world.”2 The first four

characteristics in this list encapsulate much of what it means for anyone to improvise or compose

well, so it is no surprise that Monk utilizes these features to establish himself as a meaningful

improviser and soloist. However, it is the last point, the self-created world, that is a salient aspect of

Monk’s output. How exactly does a soloist and composer whom usually performs with other

individuals create a world? That is the broadest question of this dissertation—how exactly does

Thelonious Monk play differently than others performers in the jazz genre?3

1 Benjamin Givan, "Thelonious Monk's Pianism." The Journal of Musicology 26, no. 3 (2009), 404. 2 Gabriel Soli. Monk's Music: Thelonious Monk and Jazz History in the Making. Berkeley (University of California Press: 2008), 30. 3 In this document, I define “jazz” in a general sense, similar to Larson’s use, which he describes as similarly related to the term “classical” in so far as its popular usage includes any number of eras, styles, and composers of the western classical tradition (Larson 2009, x). I use the term jazz to encompass the varying styles and traditions from Dixieland, to Bebop, to hard-bop and third-stream. All of these styles share similar influences and connections to the blues, song forms, and improvisation, among other things, as significant aspects of their respective performance practices.

2

Assumed in this claim that he creates a world in his music is the claim that he is somehow

different from other performers, and we can assume it is in his use of the preceding four

characteristics in Solis’ list. For example, how exactly is Monk different from others in his

developmental logic, for example? In order to determine this, there must be a standard by which to

measure the characteristic differences, and a standard implies a certain amount of objectivity by

which someone might say, for example, a Charlie Parker solo is different from a Brad Mehldau solo,

but it is more similar to a Dizzy Gillespie solo. This example would likely be transparently obvious

even to the amateur jazz listener given Mehldau is from a different generation of artists than Parker

and Gillespie, and Parker and Gillespie were collaborators and thus influenced each other directly.

However, that isn’t to say that Mehldau is entirely different than the other two performers, especially

in his more standard lingua franca playing on his albums in The Art of the Trio series.4 There is an

obvious influence of previous generations, and even a culture within jazz of transcribing other

people’s solos and recreating them on an individual’s instrument. This oral tradition creates a

common language in the jazz world.

With this idea of borrowing material from others and inserting it into your own solo (or at

least using this process as a way to absorb a musical language), there has come to be a common

language that people practice even to the point that Jerry Coker assimilated this language into a

collection of idiomatic melodic incipits.5 Coker presents these patterns as a sort of “common

practice” within the genre, the elements that make up the genre’s “identity.”6 These patterns are

short melodic incipits that are often capable of fitting multiple harmonic contexts. For example, see

4 Lingua franca was used by both Thomas Owens (1995, 4) and Giddins and DeVeaux (2009, 607), and it implies a standard jam-session style performance of a head (melody) followed by solos over the chord changes of the head, closing out the tune with a playing of the head; Brad Mehldau (piano), Brad Mehldau Trio. Art of the Trio – Recordings: 1996-2001 (Nonesuch 517129-2, 2001), compact disc. 5 Jerry Coker, Elements of the Jazz Language for the Developing Improvisor (Miami, FL: Alfred Publishing, 1991) 6 ibid, i.

3

figure 1.1.7 This pattern can be, and is utilized in no less than five harmonic contexts. This is one

pattern among many others included in this text and my analyses that begins to highlight how one

might identify a common element that can be used as the yardstick between different performers,

even as they all may have individual time-feels, developmental logic, and a certain humor or

playfulness in their soloing; that is to say, if I want to compare how different Monk was or wasn’t, I

can use melodic language, independent of other musical variables, as a common feature of all

soloists. This usage of a common melodic language allows for the possibility that certain soloists

would be more prototypical than others if that soloist were to utilize more of the patterns that

contribute to jazz’s “identity”.

1.2. Prototypicality

Defining prototypicality within the jazz genre would allow for categorization of solos as

more or less prototypical as a matter of degree, and thus one could discuss not just how similar

Mehldau is to Parker or Gillespie, but one could also discuss how prototypical they are within the

genre as a whole. Moreover, this prototypicality would allow for an exploration of how much a

7 Coker, Jazz Language, 77

Accommodates: Gmin7, C7, Eø, F#7(+5, +9), and B maj7(+5) Pattern starts on: Ninth of the minor 7 chord Thirteenth of the 7 chord Fourth of the ø chord Augmented ninth of the 7(+5, +9) Major seventh of the maj7(+5)

Figure 1.1

The “Gone but Not Forgotten” pattern.

4

soloist sounds like everyone else, or if they are indeed creating a unique musical world, at least from

a melodic perspective.

To define prototypicality in general, it is useful to consider a common example concerning

the prototype of a bird. When considering a bird, it is common to think of something like a robin, a

finch, or even an owl. These species have salient bird-like features that group them all together into

the bird family. However, when considering a penguin, a person might still categorize it as a bird

even though it isn’t as prototypical—this graded structure of what still fits the category of a bird was

introduced by Rosch.8 This discussion is beginning to encroach upon two distinctions of conceptual

categorizations, namely, classical versus natural concepts. Classical concepts are categories that

provide a sufficient definition to categorize something, whereas a natural concept allows for more

grey area (like the penguin being a bird even though it can’t fly). This idea of a natural concept

encapsulates various epistemologies of prototype theory, but in general it is the idea that the

prototype, and thus the concept, is identified not by sufficient a priori conditions, but rather by the

features that are shared most often by members of the group. How to identify this in a real world

example is quite challenging, but valid arguments have been made in favor of statistical

(probabilistic, to be precise) categorization of objects via their internal features.9

1.3. Statistics as a Categorization Tool

Considering our bird example, we could define “birdness” statistically by the number of

common features objects shares with other things that fit within the concept of bird. Robins,

finches, and crows would likely be the most prototypical as they fit the concept of a bird most

closely. Flightless birds like chickens, ostriches, and penguins would be some statistical distance

8 Eleanor Rosch, “Cognitive Representations of Semantic Categories,” Journal of Experimental Psychology: General 104 (1975): 192–233. 9 See Robbins (2002) and Barsalou (1991) for arguments in favor of statistical prototypes, and Salley, K., & Shanahan, D. (2016), van Kranenburg, P. (2005), and Gjerdingen, Robert O. (1986) for operationalization of statistical prototypes.

5

away from those prototypes depending on what other features grouped them together with the

prototypes, but they would none the less still group with birds. If we were to include non-birds in

our dataset, they would be grouped in entirely different categories. For example, a platypus might be

grouped on the border between birds and mammals. Regardless of the real statistical distance and

categorization of this thought experiment, the value is the ability to discuss the relationship of these

various animals to each other and how they do, or do not represent prototypical expressions of their

respective concepts.

Extending this to the topic at hand, when grouping soloists together, it is the likeness of

their musical features that makes them more or less prototypical. Theoretically, the most

prototypical solo would be one that consists exclusively of incipits from Coker’s text, and all other

solos would be a certain statistical distance from this theoretical prototype. Mapping solos to a

distance metric in this way provides a way to compare how prototypical actual solos are in

relationship to one another. This distant reading provides the categorization necessary to explore close

readings of select solos based on how prototypical or non-prototypical they are.10 From there, I can

explore from distant and close readings how Thelonious Monk’s solos fit within the categories of

prototypical solos.

1.4. Epistemological Grounding

As a point of clarification, prototypes are a way of determining concepts—an epistemology

of sorts—and concepts are central to cognition in general; that is to say, a vehicle for categorization

is central to theories of mind, language, psychology, and cognition. Concepts are the ways in which

we can decipher, for example, the statement “all bachelors are unmarried.” The validity of this claim

10 Distant versus close readings is essentially the difference between analyzing an object’s high level features and its relationship to other objects and analyzing an object’s low level features independent of other objects (with the potential to compare, but not implicit in the methodology), respectively. See Moretti (2007) for further discussion of these distinctions.

6

is based on the concepts that are called upon by each of these words, with the words “bachelors”

and “unmarried” being particularly salient. Consider if the word bachelor did not always imply

unmarried men. If that were the case, then our categorization of “all” of this kind of person as

“unmarried” would be incorrect, so this statement would be untrue and essentially meaningless. The

concept of bachelor would even be in question. These conceptual categorizations allow for a

discussion of the inner workings and features of the thing in question. In my case, establishing a

prototypal melodic usage in jazz solos allows for a discussion of the inner workings of all of the

facets that establish the category of “jazz solo,” much like the concept of a bachelor would allow for

a discussion of features other than the marital status of bachelors (not that one would want to

pursue such a venture).

Realism and Nominalism

As with many discussions in philosophy, there is further need for definitional clarity. In my

presentation above, I have thus far ignored an important distinction—realism versus nominalism.

Realism is essentially Platonism in so far as concepts are ontologically prior to the instances of

them.11 Thus, a concept is independent of its actual existence, and the purest form of a concept may

not, and likely does not exist in the real world. This is not the type of concept I am employing. I am

employing the nominal category, which means I define concepts by actual instances of such

concepts. In a sense, this means that concepts are self-creating in so far as they are not ontologically

prior to their existence but are ontologically dependent on their existence.12 My use of a prototype

fits within this nominal definition because I am assuming a certain general category of “jazz solos”

in my data set, but I am allowing the dataset to define, or bring into existence the actual prototype.

11 This is to say that concepts exist prior to their realization in the “real world.” See Bealer (1993), Chrisholm (1996) and Fodor (1975) for further discussion. 12 William Van Orman Quine. Word and Object (Cambridge, Mass: MIT Press, 1960): 6.

7

Given that these distinctions date back to Plato and have contemporary members in both camps, it

is plain that these ontologies are still contested, but for my purposes it is most important that I am

internally consistent in my use of these categories in my analysis.

Prototype Theory

As mentioned above, classical (definitional, or real) concepts often lack real world

applications even as they are easy to work with in thought experiments. It is their exclusivity that can

create logical statements in language, but in their application to real world problems the impossibility

of assigning necessary and sufficient conditions proves a to be most unfruitful. This brings me to the

origins of prototype theory, which is a form of natural (nominal) concept. The first formal instance

of such an idea came from Wittgenstein when he questioned the real world application of classical

concepts and opted for a “family resemblance” definition; which is to say that concepts do their

work in the real world not by definitional necessity and sufficiency, but rather by probabilistic

sufficiency.13 Considering our example of birds, we know a penguin is a bird because it shares a

sufficient number of bird-features with other birds and is thus conceptually a bird. This type of

concept is most useful in the empirical world given the struggle of classical concepts in their

application to empirical data, which is often messy and does not allow for necessary and sufficient

definitions. Rosch and Mervis were the first to apply the idea of family resemblances in an empirical

setting.14 The authors ran six experiments that culminate in the conclusion that the concept of

“family resemblances” is a salient way of defining prototypes in real-world situations. They define

family resemblances as elements that are common between items, but few elements are common

between all items. The authors categorize what is most prototypical by objects that share the most

13 Ludwig Wittgenstain. Philosophical Investigations, 3rd edition, G.E.M. Anscombe (trans.) (Oxford: Blackwell, 1953/1958), 32. 14 Eleanor Rosch and Carolyn B. Mervis, “Family Resemblances.” Cognitive Psychology 7 (1975): 573 – 605.

8

elements with items in their category and least elements with items in other categories. This is the

definition of prototypcality that I will use throughout this document because it allows for degrees of

prototypicality, as well as distance metrics within conceptual categories.

One such instance of the power of this idea applied to real world categorizations is the

selective modification model.15 This study breaks down categories into four values which are

weighted towards the categorization of objects. This model presents four applications involving

varying degrees of adverbial nuance when describing apples (using “slightly red” or “very slightly

red”, for example), and this nuance allows for different features to be weighted differently towards

categorization. For example, roundness was considered less salient than color, and once the authors

added an adverb to the color the model is quite powerful in creating a metric for categorization of

not just apple or not-apple, but also the apple-ness of an apple. The authors conclude that their

model was reasonably successful in providing a quantitative expression of the prototypicality of the

concept “apple” and its varying degrees of redness. It should also be noted that this study has

implications in the qualitative realm in so far as the model involves the combination of different

features, so it allows for not only taxonomic categorizations such as apple or not-apple, but also goal

derived categories as described by Barsalou.16 This model is presented as an example of the power of

quantifying prototypicality for the purpose of making qualitative decisions about real-world

examples, even if those examples don’t have a classical prototype.

15 Edward Smith, Daniel Osherson, Lance Rips, and Margaret Keane, “Combining Prototypes: A Selective Modification Model,” Cognitive Science 12 (1988): 485–527 16 Barsalou (1985) explicates the difference between taxonomic categories and goal-derived categories. Taxonomic categories are most easily expressed as prototypical exemplars, but goal derived categories are not necessarily prototypical in so far as goal derived categories are created through conceptual combination of things that can, but do not necessarily have exemplars/prototypes. For example, “picking a vacation destination” provides the location attribute within a vacation framework. This highlights the idea that one person might think a mountain destination is a better example of a vacation than a beach vacation in so far as the goal of the vacation can be considered—skiing or surfing, for example, which essentially is a consideration of perspective in the decision making process.

9

Considering this philosophical framework provides the ground of epistemic validity to make

such claims pertaining to the prototypicality of the multivariate stimuli that is music. Moreover, it

provides a footing with which to compare disparate musical objects. However, this philosophical

framework lacks an ontology that has most readily been expressed and explored in the cognitive and

psychological sciences. These fields have utilized much of this discussion of prototypicality—family

resemblance in particular—to make claims as to concept acquisition. This is important for my claims

because if I am claiming prototypicality of a musical stimulus, I need to provide evidence as to the

ontological reality of the features I am using to make such claims.

1.5. Cognitively Prototypical

Concepts have been used in the cognitive sciences to talk about how we perceive and

categorize various objects and experiences, thus how we identify things to be, in a sense, real.

According to Zbikowski, Roger Brown demonstrates a most helpful distinction which is that we

categorize utilizing a maximally useful sensitivity in our taxonomy: that is to say, we do not employ

prototypes that are based on the individual (the lowest level) nor the broadest level (highest level),

but rather somewhere in the middle of the taxonomy.17 The power of a mid-level category—hence

forth basic-level—is demonstrated in the following table 1.1.

This table demonstrates the proposed maximal usefulness of basic-level taxonomies. To

start, the basic-level is determined by the object one is attempting to categorize—more on that to

follow—and the various levels in this example could be refined as you move up levels from

17 Roger Brown, “How Shall a Thing Be Called?” Psychological Review 65 (1958):14 – 21; Lawrence Michael Zbikowski, Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Oxford University Press, 2002), 31-32.

10

subordinate to superordinate in so far as superordinate could almost always be taken as an even

higher level of taxonomy than the one presented. Consider first the subordinate category containing

families of birds. If my goal is to group birds with other birds, then I am best to not focus on the

family of finches as I would lose all other types of birds. If I were to increase my sensitivity even

further to the level of the species, then I lose my categorizing power entirely in so far as I am left

with one species of finch, and all other things in the universe are excluded from this category (this is

an absurd example, but my point is illustrated none the less). Moving up past the basic level to the

presented superordinate level, and the problem arises of including too many things in one category,

assuming your goal is to group like animals together, such as birds. That leaves some type of basic-

level taxonomy to provide the maximal usefulness in categorization. I posit that motive at various

structural levels provide is a form of maximal usefulness when categorizing like musical objects. In

the case of the present study, I include surface motives (patterns) as a basic level variable in order to

identify the difference between particular musical performances and group them together with like

performances. When completing my close readings, I explore deeper structural motives as another

Table 1.1 Table demonstrating and examples of differing taxonomic levels.

Superordinate Basic Level Subordinate

Animal Bird Gulls

Finches

Owls

Penguins

Plant Fruit Drupes

Berries

Pomes

Pepos

11

kind of expression of prototypicality. This means that the patterns are a list of variables, and the

structural motives—or lack thereof—are similarly related but are not exclusively of the same kind

and thus provide a different kind of prototypicality. In essence, motives are my basic category.

1.6. Concepts in Music

Lawrence Zbikowski describes via Schoenberg that a fundamental aspect to musical

coherence is motive and that motives must utilize the way in which our mind works in order for

them to be comprehensible to a listener.18 This means that motives must be constructed in such a

way so as to be recognizable to the listener if they are presented in a different context. This unifying

force in music as conceived by Schoenberg and others is more concerned with the coherence of a

particular piece; that is, the coherence that allows a piece to categorize with itself is a matter of the

internal motivic coherence. However, this idea of internal coherence can be extended to genre,

much like the specificity of features of a bird will categorize it into a bird category, even as other

features will specify it as a particular species, and then even further as an individual within the

species—it is a matter of what level category one is attempting to identify that determines what

features are important. Schoenberg’s motives are concerned with individual pieces, so for the

purposes of discussing general style, it is a subordinate category. To discuss genre, the basic category

becomes something that marks that genre to some degree or another. My musical motives that

provide genre coherence, and even subgenre distinction is pattern usage. Beyond categorization as

simply being jazz or not, the frequency of genre-defining patterns would serve as the features that

make something more or less prototypical within the genre. Melodic usage can be readily calculated

18 Zbikowski, Conceptualizing Music, 25.

12

in order to make such comparisons, and these patterns can be explored for their relation to a deeper,

more structural motive.19

1.7. Structural Considerations

Structure in jazz has been discussed extensively by Larson and Martin, among others.20

Additionally, they have framed the idea that jazz improvisation is similar to theme and variation,

relying on the elaboration of an underlying structure. I argue that this is the case, but that it is less

dependent on melody and more dependent on the potential structural pathways in a composition’s

harmonic progressions. This idea of essentially zooming out from a Schenkerian fundamental

structure to a deep middleground level will serve to demonstrate how a performer has freedom to

perform prototypically—even virtuosically, as Martin claims—without being significantly tied to the

structural elements of only the melody.21

Comparing jazz improvisation to a theme and variations is not a new idea. Steve Larson asks

the question of “’Round Midnight,” “What does its internal structure tell us about how it may be

considered a variation on previous themes?”22 Using theme and variations as an analogous form to

consider a jazz composition as a theme sets the foundation to dissect the music to see all of the

19 As an aside, a fundamental aspect in Schenkerian thinking is the unification of tonal music via the Ursatz. While my discussion is different from the particulars of Schenker’s arguments in so far as I am claiming surface patterns as the unifying feature in Lingua Franca jazz, the logic is similar in so far as Schenker’s conception of what made music good was the presence of a common musical structure. 20 See Allen Forte, The American Popular Ballad of the Golden Era, 1924-1950: A Study in Musical Design (Princeton, NJ: Princeton University Press, 1995); Steve Larson, Analyzing Jazz: A Schenkerian Approach (Hillsdale, New York: Pendragon Press, 2009); Henry Martin, Charlie Parker and Thematic Improvisation (Newark, N.J.: Institute of Jazz Studies, Rutgers—The State University of New Jersey, 1996); Henry Martin, “Schenker and the Tonal Jazz Repertory.” Tijdschrift voor Muziektheorie 16, no. 1 (2011): 1-20; Strunk, Steven. “The Harmony of Early Bebop: A Layered Approach,” Journal of Jazz Studies 6, (1979): 4-53; Steven Strunk, “Notes on Harmony in Wayne Shorter's Compositions, 1964-67,” Journal of Music Theory, Vol. 49, No. 2 (Fall, 2005): 301-332. 21 One significant argument in Martin (1996) is that Charlie Parker is performing virtuosically because of his reliance on the underlying structure of the tune as expressed by the melody. I am less inclined to hold the melody as inviolable, and rather argue there are multiple structures that are possible for a performer to be performing virtuosically. Moreover, I argue that this conception of how virtuosic playing can be contradicted by meaningfully avoiding certain deep-structure elements. This will be explored extensively in chapters 4. 22 Larson, Analyzing Jazz, 33.

13

melodic, rhythmic, and harmonic devices that a particular piece might inspire. However, as I will

demonstrate, it is important to not tie the idea of a theme too closely to the actual melody. Miles

Davis’s “Solar” is a salient composition to consider. It is a twelve bar form, and it is tonally

ambiguous with a cyclical structure created by sequential harmonies. Additionally, there is a

misalignment of design and structure which serves to accentuate the different possibilities a soloist

might utilize. I argue that these factors directly influence a soloist’s decisions during their

improvisations by providing them with alternative structural premises for improvising, thus they can

solo virtuosically by Martin’s standards without considering the melody structurally inviolable. For

the purpose of the discussion, I analyze Miles Davis’ recording of “Solar” from the 1954 Prestige

album Walkin’.23

Figure 1.2 shows a sequential reading of the composition.24 The harmonic sequence actually

begins in m. 3 and overlaps the final measure of the form, resolving in m. 1. This is an instance in

which the design and structure are misaligned, creating the possibility for a solo that effortlessly

bridges choruses without any jarring structural cadential figures either melodically or harmonically;

that is, the soloist can use this structural feature of the piece to conceal the beginning of the next

chorus. Also highlighted in this reading is an octave descent in the melody that implicitly resolves in

m. 1, further reinforcing the overlapped sequential reading of the harmony since the final C4 is

implicit and elided with the C5 (m. 1), thus creating a song that in a sense potentially never ends.

23 Miles Davis All-Stars, Walkin’ (Prestige PRCD-30008-2 P7075, 2006), compact disc. 24 Sequential in this situation means a lack of tonality at a structural level. While it may contain a key signature and harmonic motion, it lacks an Ursatz, and, thus, a tonal center.

14

Figure 1.3 shows a reading in E major. As is apparent, there are many similarities

between mm. 1-8 of figures 1.2 and 1.3. The structural line is established at the melodic sequence

break in m. 9. These coinciding events help the listener hear E as a viable option for the tonal

center of this piece. One notable feature of this reading is the D maj7 substituting B 7 for the

interruption on 2. While it may not seem viable at first, I posit that root motion to VII is an

axiomatic dominant substitute; that is, ii7/ VIIà VII7 is sometimes referred to as a “backdoor

ii-V”, substituting ii-V in the tonic key. Given this typical substitute, it is not unreasonable to

consider V7/ VIIà VIImaj7 to be a dominant substitute since it is a similar root motion and

coincides with the end of the melodic phrase.25 Also present in this reading is a tonicization of vi in

E major in m. 1. Given that reading the piece in E major generates an interrupted phrase

structure and an off-tonic beginning, creating possibilities for soloists to use the structure of the

piece to conceal its formal design.

25 This is also easily perceived as a half cadence since the melody ends on the F and restarts to cadence over the bar line. This view of perception is in agreement with the Gestalt Laws of proximity and common direction. Common direction is expressed in the motion from G down to C followed by its modally altered form in m. 10, giving clear motion towards finality on F in m. 11.

Figure 1.2 A Sequential Analysis

15

Figure 1.4 shows a 5-line in C minor. As present in the previous readings, the opening 8

measures contain a sequence. The difference in this reading is that the formal design and structure

are in alignment; that is, the piece begins in m. 1 in the key of C-minor. 5 of the fundamental line is

in line with the melodic sequence break supported by III, and 4 is supported by II. Scale degree

3 is supported as the 9 of the pre-dominant. While chordal extensions are not considered to be

consonant in tonal music or jazz at a structural level, they are part of the sonority of the idiom like

the chordal seventh of a dominant harmony in Mozart; that is, though a ninth may be dissonant, it is

still capable of being part of the fundamental line just as the V7 can support 4 in Mozart.26 Both

Larson and Strunk agree that sevenths, ninths, elevenths, and thirteenths are a part of the modern

jazz sound, even if those extensions “derive their meaning from more stable pitches at a deeper

structural level.”27 Such structural implications cannot by default eliminate their significance in

driving this line towards 1.28 Scale degrees 2 and 1 are implicit in the melodic ascent up the octave

as they complete the descent of the fundamental line during the elision of the form.

26 Steven Strunk. “Notes on Harmony in Wayne Shorter's Compositions, 1964-67,” Journal of Music Theory, Vol. 49, No. 2 (Fall, 2005): 301-332 27 Larson Analyzing Jazz, 32; Steven Strunk. “The Harmony of Early Bebop”, 4-53. 28 Larson highlights chordal extension’s contrapuntal derivations (2009, 7-10). These derivations necessarily carry contrapuntal obligations as well, thus further supporting that the flat-9 of dmin7(b9) is the same E as the third in a C-minor chord (i). Since it is the same E and part of the idiomatic sonority, it is consonant enough be supported by ii7(b9) even as it has an obligation to resolve to 2 ̂ (which is arguably parallel to a dominant chordal 7th having an obligation to resolve to 3 ̂).

Figure 1.3 E Major

16

All three of these graphs are viable readings of the melody to provide alternative

resolutions at various structural points in the piece. However, it is also possible that a soloist might

utilize an entirely new structure that is not presented by the melody. For example, this melody is

built on one of one of the guide tone lines, and there are two such lines in most jazz compositions,

so an alternative structural melody that this composition provides is to follow the second guide

tone.29 The two options for guide tone lines in this piece are presented in figure 1.5, below. The top

line is a reduction of the composed schema, and the bottom line is an alternative schema that a

performer might follow. In essence, this conception of the possibility of multiple structural

pathways—whether they are alternative interpretations of the same pathway or a new pathway

altogether—through a jazz composition moves the importance away from the melody per se, and

shifts the importance to the possible schema that an improviser might utilize to express varying

degrees of structural performing.

29 Guide-tone lines are lines that follow the pattern of chordal-sevenths resolving to thirds of the resolution and then become (often through a chromaticization) the chordal-seventh of the next chord in the harmony. This pattern provides natural pathways through various tunes in jazz compositions.

Figure 1.4 C-minor

17

As an example of a real world application of an alternative interpretation, to elicit a

sequential reading during a solo, a soloist might accentuate the resolution of the auxiliary cadence in

m. 9 and draw attention to the interruption in m. 11 by somehow separating the figure that

retonicizes the top of the next chorus. In Kenny Barron’s fourth chorus of this composition from

his recording Live at Bradley’s, we can see how this concept can be accomplished (see figure 1.5).30

Measures 1-7 are relatively centered tonally and do not draw much attention to the ii-V-I in F in

mm. 3-5. However, he adds clarity to the melodic line with his rhythmic placement of the notes in

mm. 7-8 leading up to a significant rhythmic shift at the resolution of the structural auxiliary cadence

in m. 9. In the recording, he also adds an accent to the downbeat of m. 9. Mr. Barron emphasizes

the interruption by registrally displacing 2, which is accomplished via motion into an inner voice,

from the Bb in m. 12, which is a concept discussed at length in A Generative Theory of Tonal Music.31

30 Kenny Barron (piano), Kenny Barron Trio, Live at Bradley’s (Sunnyside SSC3002, 2001), compact disc. 31 Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Mass: MIT, 1983), 43-49.

&&

bbbbbb

44

44w

w

Cmin

w

w

w

w

Gmin7

w

wn

C7

wn

w

Fmaj7

w

w

wb

wb

Fmin7

&&

bbbbbb

8 w8

w

B b7w

w

Ebmaj7wb

˙b ˙

Ebmin7 A b7w

w

D bmaj7w

˙ ˙n

Dmin7(b5) G7( b9)

w

w

Cmin

©

Figure 1.5 Guide tone lines in Solar as alternative schema

18

When considering the melodic idea that is played in m. 12, I read it as belonging to a cadential

motion into the next chorus rather than a closing figure for the preceding chorus. However, given

that 2̂ isn’t rhythmically separated from the B in m. 12, it isn’t until beat three of m. 12 that the

listener would retroactively consider all of m. 12 as part of a tonicization of the downbeat of the

next chorus.

To imply a c-minor chorus, a soloist might begin clearly in C minor and bring out the

elision of the next chorus. The purpose of bringing out the elision of the next chorus is to close

both the octave descent and the melodic space of the 5 line in C minor. We can see this concept

executed in Bill Evan’s seventh chorus of “Solar” from the album Sunday at the Village Vanguard,

shown in figure 1.6.32 Another way in which a soloist might imply C-minor over other keys is to

consider the first five bars to be a blues, thus creating the expectation that the arrival on Fmaj7 in m.

5 is IV (in C) in a 12 bar blues. While this method is more musicological than Schenkerian, it can be

accomplished by bringing out the melodic line C-B -A , also shown in 1.5

32 Bill Evans (piano), Bill Evans Trio, Sunday at the Village Vanguard (Riverside Records RCD-9376-2, 2005), compact disc.

Figure 1.6 Kenny Barron’s fourth solo chorus.

& bbb 44 œn œ œ œ œ œ œCm(maj7)

œ œ œ œ œœ œ Œ Œ ‰ jœ œ œ œb œGm7

œn œ# œ œn œ œ œb œC7

& bbb œ œ œn œ œ œ# œFMa7

œ œ œn œb œb œ œ œn œ ‰ œ œ œ œ œ œ œFm7

œn œn œ# œ# œn œn œ# œ#B b7

& bbb ˙ ‰ Jœ œ ‰ JœEbMa7

œ œ œb œ œ œn œ œ œEbm7 A b7

œ œ œ œ œ "̇D bMa7

( ) œ œ œ œ œn œ# œn œG7Dm7(b5)

œœCm(maj7)

( )

& bbb œn œ œ œ œ œ œ œCm(maj7)

œ œ œ œ œ œ œ œ œ œ œ œb œ œn œ#Gm7

œ œn œ œ œb œ œ œC7

& bbb œn œ œ œ œn œ œFMa7 œœ œ œœ Œ œœ œ œœ Œ œœ œ œœ

Fm7

Œ œœnn œn œœ ŒB b7

& bbb œœ œ œœ Œ œœ## œnEbMa7 œœ## Œ œœ œn œœEbm7 A b7

Œ œœ œ œœ ŒD bMa7 œœn œ œœ Œ œœn œDm7(b5) G7

& bbb œœn Œ œœ œ œœCm(maj7)

Œ œœb œ œœ Œ œœn œ œœ œœ œ œœGm7 œœnn œn œœ œœ œ œC7 œ œn œ œn œ œ œFMa7

©

>

19

As demonstrated, the structural ambiguities and multiple pathways of this piece create

multiple possibilities for improvisation that might be considered virtuosic by Martin’s standards.

Moreover, it emphasizes that performers might be concerned with differing levels of structure; that

is, Martin extensively demonstrates that Parker solos are about a fundamental line that is derived

from an inviolability of the melody, but the examples above demonstrate a deep middleground

structure with multiple potentialities of interpretation. This idea of multiple potentialities should not

stop at inviolability of the melody. For example, consider Martin’s differing analyses of

compositions over rhythm changes—this further implies that chord changes have multiple pathways

that might be expressed by solos, independent of that head melody that a solo belongs to. This idea

allows for the potential that a performer might utilize a shallow middleground pathway, or a pathway

that jumps between different guide-tone lines, for example, and still be a meaningful improvisation.

Given that many theorists whom analyze jazz from a Schenkerian perspective agree that

improvisation should consider long range planning to some degree or another, it is reasonable to use

these readings as a guide for what is possible; that is, these analyses provide multiple structural and

Figure 1.7 Bill Evan’s seventh solo chorus

&?

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bbb

44

44Ó œ œ œ œ

!

œ œ œ œ jœ œ jœ!

Cm(maj7) clearly in C minor key areajœ œ Jœ œ œ œ œ!

œ œ œ œb œ œ œ œ!

Gm7(b5) œ œ œb œ œ œn3

3

!

C7Motion into IV

œ œb œ œn œ œ3

3

œ œb œ œn œ œ3 3

Fmaj7

&?

bbb

bbbœ œ Œ Ó3

œ œ Œ Ó3

‰ œjœ œ œ

‰ œ Jœ œ œ

Fm7

Œ ‰ Jœb œ œŒ ‰ Jœb œ œ

B b7Œ œ œ œn œb œbŒ œ œ œn œb œb

Ebmaj74 4

4 4

œ œn œb œb œœ œn œb œb œ

Ebm7 A b74

4

œ œb œ œ œnœ œb œ œ œn

D bmaj74

4

Elision into next chorus closing both the octave descent and the five-line in C minor.

œ œ œ œ ˙nœ œ œ œ ˙n

Dm7(b5) G74 4

4 4

ww

Cm(maj7)

( )

( )

©

20

cadential scheme of Solar, so it is within reason that a soloist might consider the options available to

them in this composition (and others). The following Bill Evans quote is significant in our

consideration of the function of a structural analysis, especially one that has multiple structural

readings:

I always have, in anything that I play, an absolutely basic structure in mind. Now, I can work around that differently, or between the strong structural points differently, but I find the most fundamental structure, and then I work from there… I’m talking about the abstract, architectural thing, like the theoretical thing.33

1.8. Conclusion

All of this discussion serves to ground my model and calculations within an epistemically

rigorous tradition. Ultimately, this question lies at the intersection of philosophy, cognition, and

music theory, and all three fields provide a framework on which to hang my claims. To summarize,

philosophy provides definitional clarity, and psychology and cognition provide the ontological reality

as demonstrated by how the mind works to organize our surroundings. Music theory provides the

explanatory power to justify my claims of surface patterns relating to structural considerations,

which will be discussed at length in the following chapters. Ultimately, defining my prototypes

allows me to compare just how prototypical Thelonious Monk was or wasn’t within the genre of

jazz.

To accomplish my prototype categorization, I utilize unsupervised statistical modeling as a

proxy for human cognition. In short—with more detail to follow in chapter 2—I use the capabilities

of artificial intelligence to cluster transcriptions in my corpus by the melodic features. These clusters

have a centroid that the solos are a certain statistical distance away from, so the most prototypical

solos are the ones that are closest to the center. This will provide the probabilistic categorization of

33 This quote is taken from Marian McPartland’s 1978 interview of Bill Evans. For a full analysis of this segment, see Larson Analyzing Jazz, 10-32.

21

solos that allows me to engage in various extensions of probabilistic and statistical interpretations of

the solos, as well as identify solos that will be analyzed in detail using traditional music theoretical

tools.

Thelonious Monk does perform differently than other jazz musicians. The question is in

what ways is his performance practice different from others? In the following chapters, I present the

ways in which Monk’s melodic usage, particularly his relationship to motivic development, is

different from other performers.

22

Chapter 2 Establishing a Prototype:

Supervised and Unsupervised Machine Learning Approaches to Solo Categorization

2.1. Introduction

The following chapter presents two different machine learning algorithms that seek to

provide the statistical grounding—the metaphorical yard stick—by which I will compare how

different Thelonious Monk is from what might be considered a prototypical performance. This

discussion relies on stylometry, which is essentially an attempt to measure the statistical profile of a

genre, artist, author, etc. Stylometry has been used to determine authorship in the Federalist Papers,

Shakespeare, and even J.K. Rowling’s work written under pseudonyms.34 In music, von Kranenberg

explored Bach’s compositional output and determined quite conclusively that the Fugue for Organ

in F minor (BWV 534/2), which was under scrutiny as to whether or not it was Bach’s work, was in

fact composed by Johann Ludwig Krebs.35 It should be noted, that stylometry is understandably

scrutinized as potentially unreliable. While this may be true in certain cases, that does not negate its

usefulness, even as one must be careful not to assert anything that is beyond the scope of this tool;

that is, we must recognize that it is a fallible methodology, so it is best used in conjunction with

other sources such as historical documentation or expertise in a field. In short, stylometry should be

used as a tool, but the results should inform, rather than outweigh musical expertise or historical

findings that may contradict them.

34 Frederic Mosteller, and David Wallace, Inference and Disputed Authorship: The Federalist (Addison-Wesley: Massachusetts, 1964); Thomas Merriam, and Robert Matthews, “Neural Computation in Stylometry II: An Application to the Works of Shakespeare and Marlow.” Literary and Linguistic Computing, 9 (1994): 1-6.; Patrick Juola, “The Rowling Case: A Proposed Standard Analytic Protocol for Authorship Questions.” Digital Scholarship in the Humanities 20 (2015): 100-113. 35 Peter van Kranenburg, “Composer attribution by quantifying compositional strategies.” ISMIR Proceedings (2005): 375–376.

23

When considering stylometry, there are two broad categories of variables to choose from.

The first I discuss is low-level features. These are features that are typically not perceptible and are

generally just statistical profiles of a work. For example, one common measure is the normalized

pairwise variability index (nPVI), which is a method of calculating rhythmic variance.36 Another low

level feature that is often used is a transition probability.37 This is a measure of the probability event X

will proceed to event Y; in music, this is often calculated as the probability that a certain scale degree

X will move to a particular scale degree Y. High-level features are features closer to the surface of

the music. For example, types of dissonance, chords, cadences, and form are types of high-kevel

features. High-level features are helpful measurements because they are features that are often

grounded in more historical analyses in so far as the things that are being measured are tied to some

existing musical theory. As discussed in chapter 1, the only high-level features I include are melodic

patterns. Additionally, the model I use only includes high-level features because low-level features

proved to be problematic in my categorizations.38

2.2. Data

My data comes from a novel corpus of jazz improvisation solos created from the Jazzomat

Corpus, a published collection of Thelonious Monk transcriptions, and various solo transcriptions I

acquired from Corey Kendrick or completed myself.39 My data was converted from both PDF and

.xml formats to Kern format, which is way of notating the “core” aspects of western musical

36 While this feature ultimately is unused in these initial models, rhythmic variance is discussed at length in the epilogue of this document. 37 This is essentially a Markov chain. 38 The problems I encountered pertained mainly to note usage and transition probability—these two features are too correlated. The solos in my corpus generally had too similar note usage and transition probability profiles, so the output in my model did not cluster well. 39 A special thanks are given to my friend Corey Kendrick who provided a substantial amount of transcriptions. These transcriptions can be found at https://ckendrickmusic.wordpress.com/; The Jazzomat Research Project, https://jazzomat.hfm-weimar.de/ (accessed November 2018); The Best of Thelonious Monk: Piano Transcriptions (Milwaukee, WI: Hal Leonard, 2006), 1-120; Thelonious Monk Collection: Piano Transcriptions (Milwaukee, WI: Hal Leonard, 2006), 1-96.

24

notation. Figure 2.1 shows the first measure of Bach’s Fugue no. 2 from the Well-Tempered Clavier,

Book 1. In this format, the music has essentially been turned vertical (each column is called a spine),

and the notes and durations are represented by letters and numbers. I converted my 55 idiomatic

patterns into pattern files (see appendix 1 for a complete presentation of these patterns in musical

notation). An example of a pattern file is shown in figure 2.2. These pattern files were run as a loop

function over my corpus in order to annotate the Kern scores with each occurrence of the desired

pattern. I then utilized a counting function (grep) to count each occurrence of a pattern in the music.

After compiling all of the raw count data of each instance, I standardized the data over the total

number of measures.

Figure 2.1 Kern Format of Bach Fugue no. 2 from

WTC Book 1

25

Corpus Construction

Building a corpus is a task with the goal of producing a representative sample of a

population by which inferences can be made based on the statistical profile of the sample.40

However, with the exception of a truly randomized sample, there are biases that inevitably find their

way into a corpus. Because of these biases, the first stage in developing such a corpus is developing a

falsifiable question that will then provide the filter by which a researcher might explore what is

considered representative. For example, if my goal is to explore questions pertaining to the

harmonic usage of American grunge rock from 1990-1997, I would need to define what exactly is

“American”, “gunge”, “rock”, and “harmonic”. From there, I could filter artists and recording

through the various restrictions I have placed on this genre. However, unless I can say that I have all

examples of such genre—which a person could never claim—I am still only sampling my genre.

This means that I need to test my sample for various attributes that are theoretically rigorous

assumptions in defining a sample to be representative. The first consideration is the central limit

theorem. This was first presented by Abraham de Moivre in 1733, with its necessary and sufficient

40 Rudolph Fruend, William Wilson, and Donna Mohr, Statistical Methods (New York: Academic Press, 2010), 97-99; Justin London, "Building a Representative Corpus of Classical Music." Music Perception: An Interdisciplinary Journal 31, no. 1 (2013): 69.

Figure 2.2 A side-by-side of musical notation represented in “patt” notation. The patt notation reads top to bottom in conjunction with the left-to-right

progression of the musical notation.

26

conditions defined in 1935.41 This is the assumption that population samples of a binomial

distribution will move closer to a Gaussian (normal) distribution as the sample size increases.42

Considering my grunge rock example, if I were to plot this hypothetical corpus, the distribution of

the variables in question—whether they are time series considerations, harmonic usage, or regional

considerations—would ideally look something like figure 2.4, below. If I were exploring questions

pertaining to this corpus, I could reasonably extrapolate my findings to the entire population of this

genre.

When building my own corpus, I did not have access to such a perfect sample, so I largely

relied on convenience sampling, which can be problematic, but did not prove to be substantively so

in my case. My corpus, n= 530, was built from a combination of the Weimar Jazz Database, a select

number of transcription books, sourcing transcriptions from colleagues, and transcriptions I

completed myself.43,44 After converting these files using MuseScore 3 into MusicXML format, and

finally into Kern format utilizing the musicxml2hum command, I was able to begin extracting features.

As mentioned above, I utilized a combination of the patt and grep commands to count the total usage

of idiomatic patterns. I also calculated the note-to-note transition probabilities using the sdmarkov

command found in the humextra toolbox, as well as the normalized pairwise variability index (nPVI)

built by David Huron.45 After calculating all of the discrete counts of pattern usage, I grouped the

41 William Adams, The Life and Times of the Central Limit Theorem (New York: Kaedmon Publishing Company, 2009), xi. 42 More technically, “[i]f random samples of size n are taken from any distribution with mean & and variance '( , the

sample mean ) will have a distribution approximately normal with mean = & and a variance = '( *. The approximation becomes better as n increases” (Freud et al 2010, 100). 43 The Best of Thelonious Monk: Piano Transcriptions (Milwaukee, WI: Hal Leonard, 2006); Thelonious Monk Collection: Piano Transcriptions (Milwaukee, WI: Hal Leonard, 2006); Jazz Collection: Thelonious Monk (Tokyo: Shinko Music Publishing, 2016). 44 See chapter 1 for details on how I defined and limited my genre and selections. My original n=570, but during data processing and cleaning, I removed outliers and lost various files due to corruption or conversion errors. 45 The humextra tools can be found at https://github.com/craigsapp/humextra; These high-level features proved to be mostly unhelpful in my various computational models, but they do provide some musical insight as to the rhythmic homogeneity within the jazz genre which will be explored in the epilogue.

27

various patterns by their characteristics. See table 2.1, below, for a list of these different categories

and appendix 1 for how each pattern was ultimately grouped.

Bebop (BB)

Contrapuntal Elaboration of Static Harmony (CESH)

Digital Patterns (DP)

ii-V Patterns (iiV)

Octatonic Patterns (OCT)

Running Changes (RC)

Whole Tone Patterns (WT)

Quotes (QUO)

Enclosures (ENC)

After summing the total usage of each category, I standardized the count data by dividing

each sum by the total number of measures in the solo. I chose to divide by the measure numbers,

rather than the beats to minimize the effect of meter; for example, consider a solo that is in 3/4

meter, is 12 measures long, and contains five Bebop patterns. If I were to calculate these patterns

based on beats (36 in total), then these five Bebop patterns would be weighted as statistically more

important than five Bebop patterns in a 4/4 example of the same measure length. This would

ultimately lead to meters with less beats weighting melodic usage as more important than in meters

Table 2.1 Categories of Melodic Patterns

28

with more beats. By standardizing the usage, I can compare each solo to another without

considering total length of solo, meter, or tempo factors.46

Figure 2.4 presents the distribution of melodic usage of my corpus overlaid with a normal

distribution. This dataset looks relatively normal enough. However, when run through the Shapiro-

Wilk test for normality, the distribution failed with a W-score of 0.93 (p = 3.54e-15). Given the

distance of this W-score from 1, and the fairly low p-value, I needed to reject the normality of my

distribution.47 Beyond that, the skewness measures 1.2, and the common protocol suggests anything

beyond 1 is considered significantly skewed. However, this is not a significant problem as there are

standard data transformations that simulate the collection of more data, thus they model the central

limit theorem. For right-skewness, which my original distribution possesses, there are three options

of varying strengths that replicate this movement towards the central limit theorem: square root

transformation, cube root transformation, and logarithmic transformation. Given the amount

skewness of my data, I ultimately decided on a cube root transformation (the middle strength

transformation).48 The resulting distribution is presented below in figure 2.5.

46 Rhythmic usage is discussed in the epilogue, but it is otherwise beyond the scope of this project. 47 The Shapiro-Wilk test for normality has a null-hypothesis that the sample is normally distributed, this a rejection of this null hypothesis is evidence that the sample is not normally distributed. The W-score ranges from 0-1, and the closer to 1, the more likely the distribution is normally distributed. However, anything below 0.95 is arguably not normally distributed no matter the p-value or assumed + level. Given this distribution fails the W-score evaluation and any standards of significance levels, this distribution should be rejected as normal. 48 I chose the cube root transformation even though the logarithmic transformation brings the distribution closer to true normal. According to Feng et al. (2014), logarithmic transformations often introduce new problems that are more problematic that the original distribution’s non-normality, including removing characteristic traits from the original data and unreliable significance ratings in hypothesis testing. These problems are not present in square root and cube root transformations.

29

This transformed distribution has a W-score equal to 0.99 (p = 0.0001406). While this p-

value may seem problematic, it is not given the high W-score, the appearance of normality in

comparison to the overlaid normal distribution, and the p-value being close enough to accepted +-

level standards. In addition to this, Shapiro-Wilk testing is highly sensitive to sample size, with

smaller sample sizes not necessarily requiring a p-value of >0.05 as long as the W-score is ≥0.99 and

the distribution roughly matches a true normal distribution. With these common and accepted

transformations and assumptions of my distribution, I can confidently conclude that I can infer

about the population of my solo corpus. Contained within my corpus is a subset of Thelonious

Monk solos. These solos do not have a large enough n (n = 17) to approximate a normal

Figure 2.3 n = 534, & = 0.803, and '( = 0.473

Distribution of Melodic Usage

Standardized Melodic Usage

Freq

uenc

y

0.0 0.5 1.0 1.5 2.0 2.5 3.0

020

4060

8010

0

30

distribution. However, given the nature of their inclusion within a larger dataset that is normally

distributed, I am able to analyze the ways in which Thelonious Monk’s solos relate to the

representative sample even if I cannot make any inferences about the Monk subset independent of

its inclusion in the entire corpus; that is, I can only make statistical inferences about Monk in

relationship to the corpus.

Figure 2.4 n = 534, & = 0.899, and '( = 0.184

Distribution of Melodic Usage

Standardized Melodic Usage

Freq

uenc

y

0.2 0.4 0.6 0.8 1.0 1.2 1.4

020

4060

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31

2.3. Dimensionality Reduction

The first step in any modeling or confirmatory analysis is to explore the characteristics of the

data. To accomplish this, I began with a principle component analysis (PCA). A PCA is an

unsupervised approach to data analysis, meaning that the analysis is completed without any target

value in mind. This provides a way to examine the variance in the data and thus view and

hypothesize as to what components in the data are salient. A PCA essentially works by plotting all of

the data using the total number of variables—I have nine standardized variables represented by the

various pattern types from table 2.1—and rotating it until each data point has the most separation.

Along with these rotations are components totaling the number of variables included in the model,

and each component accounts for a percentage of the total variance in the dataset. The resulting bi-

plot, presented below in figure 2.7, shows the data along an x and y axis, along with the amount of

variance provided by each axis. However, the resulting axes are not one of the original variables. A

PCA must be interpreted using a person’s knowledge of the dataset. My assumption is that the x-axis

(35.4% of the total variance) is representative of style, and the y-axis (12.7% of the total variance),

which is a little less clear, represents either the instrument or the sub-genre (i.e. waltz, swing, Latin,

etc.), with sub-genre being another factor in jazz style. Whatever the interpretation may be, the PCA

accounts for nearly half of all variance in the data, which is a reasonable marker that I have a decent

model to account for variance between each data point (i.e. each performance’s style), though the

clusters are less than apparent at this point.

Figure 2.6 is a loadings plot which presents the features in this analysis that weighed most

heavily in discriminating between the various data points. Principle component 1 (PC1) and

principle component 2 (PC2) are the same components from figure 2.7. The most important feature

32

in determining PC1 is the standardized output of all high-level melodic features.49 In essence, the

most important feature in discriminating the soli was the relative presence of standard melodic

usage. The second most important feature is the standardized usage of “digital patterns”.

Standardized usage of “contrapuntal elaborations of static harmony” (cesh), followed closely by

“running changes” (rc), weighed most heavily in determining PC2. The dispersion of loadings is

further evidence that my melodic feature extraction is a valid approach to solo categorization.50

49 This is calculated by adding all instances of a pattern and standardizing that count over the total number of measures. This feature is interpreted more generally as the overall pattern usage of a particular solo. 50 The inverse of this relationship would be all of the loadings close together on the map, meaning that the melodic features all behaved similarly in the PCA, thus the various melodic features would be shown to be too similar too each other to be a useful metric for further modeling.

Figure 2.5

Loadings plot showing the relative importance in determining the principle component. X-axis is principle component 1 and the Y—axis is principle component 2.

0.2 0.3 0.4 0.5

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34

The separation of the individual data points shown in the PCA biplot reveals that my data is

a valid approach to identifying the various stylistic features of the individual solos in this sample.

Referring back to my question of prototypicality, with my definition relying on theories of family

resemblance, I utilize the unsupervised K-Means clustering to group my data based exclusively on

features of the data. The resulting clusters will represent stylistic groupings which then serve as

proxy for “family” in my family resemblance definition. A byproduct of this type of analysis are

cluster centroids, which serve as a sort of platonic ideal since the centroid is statistically derived and

is not actually a real data point. The solos which are closest to their respective centroids are the

actual instances of most prototypical solos, and the solos on the borders are the least prototypical.51

2.4 K-means Clustering

The first step in calculating a K-means cluster is determining the number of clusters that are

needed for the most meaningful clustering. This is a function of the within sum of square. The final

result is plotted below in figure 2.9. I have identified the elbow at three total clusters for my final K-

means algorithm, though four would have been equally valid mathematically.52 Having determined

my clustering, the final clusters are presented in figure 2.9. For a list of how each solo was clustered,

see appendix 2.

This cluster plot shows three, roughly discreet clusters. Moreover, as to the main purpose of

this project, 13/17 of Monk’s solos included in this corpus clustered together into cluster 3, thus, his

solos comprise 9% of the entire cluster. This is an important first step in determining how different

Thelonious Monk’s performance actually is; that is, given his solos clustered together, it is

reasonable to further explore Thelonious Monk as a performer in relation to prototypes within

51 The overlapping groupings are not necessarily overlapping because this visualization is based on the PCA-biplot, so the visualization is based on just 2 dimensions but it is representing 9. 52 This is again an interpretive tool, and when I selected to group into four clusters, the boundaries and p-values of later tests were negatively affected.

35

cluster 3, and compared to clusters 1 and 2. Aside from this clustering analysis, which will be

explored further below, a generalized linear model can be used to calculate the validity of these three

clusters, as well as provide insight into the relative distinctive features of each cluster.

60

80

100

120

1 2 3 4 5 6 7 8 9 10Number of clusters k

Tota

l With

in Su

m o

f Squ

are

Optimal number of clusters

Figure 2.7 Total Within Sum of Square for

number of clusters k.

36

2.5. Generalized Linear Model

A generalized linear model (GLM) is a supervised machine learning approach to

categorization of non-continuous data; that is, it can be used to predict discrete decisions such as

“yes” or “no” using continuous input data. The continuous data I use is the same data I used to

cluster my data in the above analysis, and the discrete decision is which cluster each solo belongs to.

My model performs with a 97% accuracy (p<.001, [0.9451, 0.9818]). Given the relationship between

the calculations between K-means clustering and GLM’s, it is not a surprise that a GLM performs so

Figure 2.8 Cluster Plot of Complete Data Set

PC1 35.4% of Variance

PC2

12.7

% o

f Var

ianc

e

37

well in such a situation. However, it is a bit surprising as to how powerful this model is in relation to

the minimal training that it takes to calculate such a high accuracy rate. When creating a GLM, a

training set is isolated from the entire corpus. The computer “learns” about the categories from this

training set. The computer then uses this knowledge to make decisions about the remaining pieces in

the corpus, known as the test set. I trained the computer on only 20% of the corpus, and it was able

to correctly categorize 97% of the remaining 80% of this corpus. This is important because it

demonstrates the salience of these melodic features in capturing a solo’s style. Figure 2.10 presents a

confusion matrix of what mistakes were made and corresponding summary statistics. Aside from

demonstrating the salience of these melodic features, the relative importance of each feature can be

considered when assigning each solo to a given category, presented below in figure 2.11. This is

similar to the loadings graph presented above in figure 2.6. To interpret this figure, the closer to 100

that each feature stretches, the more important that feature is in categorizing it into a given cluster,

and each cluster can be compared relatively. For example, the overall use of prototypical incipits,

digital patterns, and whole tone patterns are the most salient attributes when determining a solo to

be in one cluster or another. Considering this figure in relation to the confusion matrix (figure 2.10),

it is logical that the GLM would make the least mistakes when categorizing cluster 3 given it has the

flattest profile comparatively. Musically, this means cluster-3 is marked by an ambiguous profile

relative to the other two clusters. However, this ambiguity should not be considered a lack of

pattern usage, but rather as a less distinct use of patterns. Too conclude this brief discussion, this

GLM provides further evidence as to the validity and salience of these melodic features in

discriminating between different soloists, and thus can serve as a proxy for musical style.53

53 More on this “proxy for style” discussion is to come as the modeling and exploration of the results continues.

38

Accuracy: 97% 95% CI: (94%, 98%)

P < .005

Figure 2.9 Confusion Matrix of Predicted Clusters in GLM with 20/80 Split

Figure 2.10

Relative Feature Importance in Determining Cluster Categorization in GLM

Importance

standardENCLicks

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standardQuoteLicks

standardCeshLicks

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standardRCLicks

standardizedHLFeatures

standardDPLicks

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cluster1

0 20 40 60 80 100

cluster2

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cluster3

39

Determining a Prototype

As discussed at length in chapter 1, I utilize the family resemblance definition of prototypicality

to determine which solo is most prototypical. To calculate the most prototypical, I use the Euclidean

distance from the K-means center.54 To calculate the center point, I took the mean of the PC1 and

PC2 for each data point by cluster as a proxy for x and y coordinates, respectively, since those

components produced the most variance between my data points. From there, I calculated the

Euclidean distance of each point from its calculated cluster center. The resulting most and least

prototypical solos are as follows, along with every instance of Thelonious Monk’s performances and

his relative distance from the most prototypical. Also provided is the Euclidean distance from the

calculated centroid. For a full list of the clustering distances, see appendix 2.

54 Because my data is initially represented in 9 dimensions, the center point/centroid is a scaled point that I am unable to reverse engineer.

Artist Solo Track Cluster Euclidean Distance

From Centroid

Order Within Cluster

J.C. Higginbotham Baby Won’t You Please Come Home 1 0.055 1 (Most Prototypical)

Thelonious Monk I’m Confessin’ (That I Love You) 1 0.631 31 Thelonious Monk Rhythm’A’Ning 1 1.920 107

Don Byas Harvard Blues (Take 1) 1 4.749 133 Roy Eldridge Undecided 2 0.005 1 (Most

Prototypical) Thelonious Monk Ask Me Now 2 2.210 237

Fats Navarro Our Delight 2 3.552 244 (Least Prototypical)

Lee Konitz Wow 3 0.029 1 (Most Prototypical

Thelonious Monk Little Rootie Tootie 3 0.720 36 Thelonious Monk Trinkle Tinkle 3 1.107 76

Table 2.2 Clustering and distance metrics for the most and least prototypical solos in each cluster

along with all instances of Thelonious Monk’s performances.

(Table Cont’d.)

40

2.6. Resulting Prototypical Solos and Their Statistical Features

Table 2.3 below presents all of the standardized usage features of the most and least

prototypical solos. Table 2.4 is a distance matrix of the solos listed in table 2.2, above. These tables

will be referenced throughout the discussion of the statistical features of these categorized solos.

The most prototypical solos from each cluster 1-3 are as follows: J.C. Higginbotham on Baby Won’t

You Please Come Home (1941), Roy Eldridge on Undecided (1950), and Lee Konitz on Wow (1971).55

The least prototypical solos from each cluster 1-3 are as follows: Don Byas on Harvard Blues-Take 1

(1945), Fats Navarro on Our Delight (1948), and Thelonious Monk on Crepuscule with Nellie (1957).

55 J.C. Higginbotham (trombone), Sidney Bechet, The Cradle of Jazz – Sidney Bechet – Chant In the Night CD 2 (Trumpets of Jericho Ltd. 20.3010-HI), compact disc; Lee Konitz, Sax of a Kind (Membran Music Ltd. 222453-444A, 2005), compact disc;Roy Eldridge (trumpet), Zoot Sims, Quadromanio Jazz Edition, Zoot Sims, That Old Feeling, CD 1 (Membran Music Ltd. 222478444, 2005), compact disc; Don Byas (saxophone), Don Byas – Moon Nocturne (Membran Music Ltd. 222414-444/A, 2005), compact disc; Fats Navarro, From Swing to Bebop, Double Talk, Fats Navarro CD 1 (Trumpets of Jericho Ltd. 20.1976-HI, 1998), compact disc; Thelonious Monk, Monk’s Music (Riverside Records RCD-242-2, 2001), compact disc.

Artist Solo Track Cluster Euclidean Distance

From Centroid

Order Within Cluster

Thelonious Monk Well You Needn’t 3 1.213 83 Thelonious Monk We See 3 1.259 90 Thelonious Monk Blue Monk 3 1.564 109 Thelonious Monk I Should Care 3 1.704 112 Thelonious Monk Monks Dream 3 1.793 119 Thelonious Monk ‘Round About Midnight 3 2.147 127 Thelonious Monk Reflections 3 2.271 130 Thelonious Monk Dinah 3 2.830 141 Thelonious Monk Everything Happens To Me 3 3.144 145 Thelonious Monk Ruby My Dear 3 3.325 147 Thelonious Monk Crepuscule With Nellie 3 4.228 152 (Least

Prototypical)

41

Tabl

e 2.

3 St

anda

rdiz

ed F

eatu

res o

f Mos

t and

Lea

st P

roto

typi

cal S

olos

41

42

Cluster 1 Discussion

The most and least prototypical solo from cluster one is J.C. Higginbotham’s 1941 solo on

Baby Won’t You Please Come Home and Don Byas’ 1945 solo on Harvard Blues-Take 1, respectively.

Relatively speaking, these solo score fairly low in melodic usage compared to the other solos

included in the table. Given that both the most and least prototypical solos are from more

traditional jazz soloists, this is not surprising given the solos in this category are generally more

“traditional” recordings, including solos from Bix Beiderbecke, Zoot Sims, Louis Armstrong, and

Lionel Hampton. However, there are also soloists in this category such as Chick Corea, David

Lieberman, and Wayne Shorter, whom would classify more as fusion, or even avant-garde

traditions—Chick Corea’s 1968 solo on Windows is even categorized as the third most prototypical

solo.56 Tentatively, I conclude that a defining feature of cluster 1 is an approach to jazz that doesn’t

fit neatly into my definition of jazz, which is the lingua franca jam-session model, of which these

melodic features are supposed to describe.

Note that Don Byas’ solo registers zeros for all types of usage. His is the only solo in the

entire corpus to not include any melodic incipits. In addition, as you move from the most- to least-

prototypical solos in cluster 1, there is a general trend towards zero. That isn’t to say that these solos

do not contain idiomatic jazz language or prototypical melodic ideas—because they most certainly

do—but it is a different sort of playing. These solos could be considered analogously as the tails of a

distribution; that is, they are still part of the same distribution, but they are a certain standard

deviation from the norm.57

56 Chick Corea, Inner Space (Collectable COL-CD-6910, 2008), compact disc. 57 They may also be playing what Kernfield (1983, 41) identifies as formulas, which is to say an idea that they are playing nuanced variations of the formulas. More on this topic in the close readings of chapters 3 and 4.

43

When considering the feature importance figure 2.12 from the GLM, the three most

important features when determining cluster 1 are digital patterns (DP), running changes (RC), and

whole-tone (WT) patterns. Note that the profile of the mean and most prototypical for this cluster

match the GLM feature importance graph. This provides an insight into the close readings

presented in chapters 3 and 4.

Cluster 2 Discussion

The most and least prototypical solos in cluster 2 are Roy Eldridge’s 1950 solo on Undecided

and Fats Navarro’s 1948 solo on Our Delight. These two solos are from different styles entirely

(swing and Bebop, respectively), and it shows in their usage profiles in table 2.3. Moreover, the

profile of each solo matches that of the GLM feature importance graph. I will ultimately label this as

the more lingua franca cluster given it contains solos with the most uses of patterns.

Considering the GLM feature importance, this cluster is defined by overall high-level

melodic usage, digital patterns, and whole tone patterns, but in different proportions than in cluster

1. What is even more interesting is that the least prototypical solo in this cluster also matches the

same general profile. This suggests a certain clarity and consistency in style that will become

apparent in the cluster as this analysis continues to move towards a close reading.

Cluster 3 Discussion

The most and least prototypical solos in cluster 3 are Lee Konitz solo on Wow (1971) and

Thelonious Monk’s solo on Crepuscule with Nellie (1957). These two recordings are from entirely

different sub-genres and of jazz performance practice, and it shows in their usage profiles in table

2.3. This further confirms my hypothesis that cluster 3 is made up of a rather ambiguous grouping

of solos marked by a pattern usage that is markedly different from clusters 1 and 2. As will be

demonstrated throughout the rest of this document, this is a logical cluster for nearly all of Monks

performances to group. While this will also be further explored throughout, a general reason for this

44

Tabl

e 2.

4 D

istan

ce-to

-Cen

troid

Mat

rix o

f Sel

ect S

olos

by

Clu

ster

with

Hea

t Map

44

45

is the lack of any given melodic usage that marks the solo. For example, Lee Konitz’s solo is most

clearly defined proportionally by DP patterns, but proportionally it contains less clarity in usage of

the other types of melodic patterns. Moreover, the profile of each solo does not match that of the

GLM feature importance graph, further confirming the ambiguity, or lack of clarity in this cluster.

Conclusion

To conclude this discussion on identifying which solos are most prototypical, I rank the

three prototypical solos in order of most- to least-prototypical of the three listed prototypes.

Considering the preliminary discussion on the features of cluster 3 as being an ambiguous cluster (of

sorts), I classify this as the least prototypical prototype. Clusters 1 and 2 both have distinct feature

profiles, but since that the most important feature in cluster 2 is general high-level melodic usage, I

consider this to be more prototypical than cluster 1. The most- to least-prototypical solos are as

follows; J.C. Higginbotham on Baby Won’t You Please Come Home, Roy Eldridge on Undecided, and Lee

Konitz on Wow.

Another perspective to consider as to why this may be the case is the mean distance between

each point in each cluster, which are as follows; cluster 1 = 1.921, cluster 2 = 1.449, and cluster 3 =

1.830. The tightness of cluster 2 further confirms that clarity in this cluster as the most prototypical.

Not only is this the grouping in the center of the cluster plot, but it is also the most tightly grouped.

The spread in cluster 1 paired with the feature importance graph is interpreted to mean that patterns

are still used, though the trend is towards zero usage (i.e. likely containing outliers), so it is a less

clear clustering. The spread in cluster 3 paired with feature importance graph represents an

ambiguity in the clustering and minimal or less distinct usage of patterns, but the cluster likely

contains no outliers.

This chapter serves to establish my metaphorical yardstick. I have demonstrated clear

groupings of soloists and that my tools are ecologically valid. Moreover, these models demonstrate

46

that there is in fact something different about Thelonious, but the above distant readings only provide

generalities about the solos. The following chapters explore close readings that serve to demonstrate

the ways in which these patterns relate to deeper structural issues in improvisation.

47

Chapter 3 Close Readings of Prototypical Solos

Having completed the distant readings, it is important to move beyond essentially pattern

counting and grouping and perform a close reading, which Martin rightfully identifies as a meaningful

step when identifying the makeup of a soloist’s style, but not the end of the discussion.58 Moving

forward, I will present various voice leading sketches. These sketches will include a reduction of the

head-tune as the basis of the structure of the piece. Consider them as a sort of schema. That being

said, I am not borrowing from the more orthodox Schenkerian traditions and am instead utilizing

this notational style to show structure of individual pieces; that is, I am not borrowing the

metaphysics of the Ursatz as a first principle. It is my desire to avoid the debates of Schenkerian

orthodoxy and intend rather to demonstrate the importance of structure and schema when

navigating a particular set of harmonic changes as it relates to the composition, essentially the

“theme”, and a soloist’s “variations.”59

I borrow this middleground logic from David Neumeyer’s work in his 1987 article, The

Urlinie from 8 as a Middleground Phenomenon.60 Figure 3.1, presented below, shows some alternative

Urlinien that Neumeyer explored. The logic of these alternative pathways is similar to that of the 3,

5, and 8 lines in a strict Schenkerian graph in so far as they generally rely on stepwise motion and

end on members of the tonic triad; they don't, however, correspond to Schenker's Urlinie or Ursatz

archetypes. By adopting alternative background structures in my reductions, I intend to show that

jazz still relies on tonality, or at least it still relies on tonal figuration and middleground structures,

58 Martin Charlie Parker and Thematic Improvisation, 5. 59 Variations is taken from Larson’s seminal 1997 work Analyzing Jazz: A Schenkerian Approach, which explores how structure and theme relate in jazz, and how discussions of theme and variations can serve as a proxy for discussing soloists’ varying choruses over a given set of chord change. 60 David Neumeyer, "The Urlinie from 8 as a Middleground Phenomenon”, In Theory Only 9 (1987): 3-25.

48

but it is not bound up in strict, common practice monotonality, nor do I require that all lines must

descend. However, that is not to say that I would discount a gapped line. For example, consider the

reduction below of Sy Oliver’s ‘Opus One’, completed by Martin.61 In this, the importance of 6 is

demonstrated by the melodic figuration centering around that scale degree even as the harmony

changes. This piece also serves to demonstrate how the logic of tonality, which Martin describes as a

“broader ‘modal-tonal’ syntax”, expresses itself at the level of the individual piece.62

This idea of expressing an individual piece is fundamental to the argument of how

prototypicality in surface patterns can also express unique artistry, and even distinguish between

virtuosic playing and sterile playing.63 As discussed in the sample analysis of Solar in chapter 1, these

varying pathways and alternative contextual interpretations provide varying opportunities for

structural and motivic variations. The implicit structure that occurs in pseudo-tonal practices such as

jazz relates to established Schenkerian principles, but the regulations pertain to more local events. As

such, I use these established methodologies in line with Martin, mainly by preferring the harmonic

implications of a soloist’s choices to the diminishment of the notated chord changes; that is to say,

performers often insert chordal substitutions and additions in their solo lines, and these solo lines

take precedence over the written chord changes.64

61 Henry Martin. “Schenker and the Tonal Jazz Repertory.” Tijdschrift voor Muziektheorie 16, no. 1 (2011a): 1–20. 62 Henry Martin. “More Than Just Guide Tones: Steve Larson’s Analyzing Jazz—A Schenkerian Approach.” Journal of Jazz Studies 7, no (2011b). 1: 128. 63 See Martin’s discussion (1996, 111) of patterns and their relationship to virtuosity and sterile playing. 64 This is not an unprecedented idea to de-emphasize the bass. With the exception of Larson, most Schenkerian studies in jazz minimize the roll of the bass. Givan writes, “[w]hereas in Schenkerian theory bass lines are structurally crucial, the sounding bass voice in a typical jazz ensemble - ordinarily played by the double bass and as freely improvised as the other instrumental parts - depicts the a priori harmonies, one way or another, but does not affect them,” and doesn’t even provide anything beyond the melodies with lead-sheet chord changes above the staff in his sketches (Givan 2010, 37).

49

Figure 3.1 Alternative Urlinie recreated from Neumeyer (1987)

50

3.1. Prototypicality in Cluster 1

The most prototypical solo in cluster 1 is J.C. Higginbotham’s performance on “Baby, Won’t

You Please Come Home.” The reduction of the head-tune is presented below in figure 3.3. The

genre of this piece falls under the category of ‘traditional’ in the Weimar Jazz Database and includes

performers Sidney Bechet (soprano saxophone), Henry “Red” Allen (trumpet), J.C. Higginbotham

(trombone), James Tolliver (piano), Wellman Braud (bass), J.C. Herad (drums).65

65 https://jazzomat.hfm-weimar.de/dbformat/dboverview.html

Figure 3.2 Graphic Reduction of Sy Oliver’s ‘Opus One’, from Martin (2011).

51

At the deepest middleground level, this melody primarily centers around 3 as the structural

tone and contains a fairly straight forward binary-form with an interruption of 2 supported by V.

The second phrase re-establishes 3 before descending 2 - 1, supported by the typical V-I motion.66

Continuing to look at the deepest presented level, I have included two motives that are present at a

structural level. The brace demarcates the descent down to 6 and returning to 3, and the bracket

demarcates a lower neighbor, with the brace-motive being more structurally significant than the

bracket-motive. At the middleground, the brace-motive is further explored in more surface level

ideas, as can be seen in mm. 1-2. When first examining the bracket-motive, it becomes plausible that

it may reflect an exploration of the relative minor key area. While I would not strongly posit that this

is the case based on the motive itself, given that the 6 in m. 2 corresponds with the arrival of VI, I

am inclined to at least link it to a possible way to navigate these changes in a solo.67 Moving to the

melody itself at level a, the bracket-motive that is present a structural level can be considered to be

derived from all of the neighbor note motives—chromaticized or otherwise—as marked in the

score.

66 I have decided to imply 2 rather than have a gapped descent that skips this scale degree. The precedent for doing such a thing is well established, and it makes logical sense to adopt a more linear reading of the fundamental line given the interruption in the first phrase. McFarland (2012) discusses this in application to jazz at length when critiquing some of Martin’s analyses that lines that don’t fit in the strict Schenkerian fundamental line. 67 This is analogous to the ‘Solar’ analysis in chapter 1 in which hypothetical pathways through the piece can be conceived of being in either the major or minor mode of a given key signature.

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53

Figure 3.4 below is a graphic analysis of Higginbotham’s solo.68 Chorus 1a at the foreground

demonstrates how Higginbotham navigates the changes while exploring both structural motives, and

the ambiguity of those structural motives.69 For example, he toys with a fairly straight forward

example of the brace-motive in mm. 2-3. This essentially mirrors the structural aspects of the head-

tune analysis. However, in mm. 5-6, he outlines a g-minor triad, thus exploring the relative key-area

during the first a-section. To help move his performance forward, he avoids notes that imply an

interruption in the strict sense.70

In chorus 1b at the foreground, Higginbotham continues his exploration of the open-fifth

brace-motive from the melody’s structure. He also borrows other structural features from the head

such as the bracket-motive and emphasizing the structural importance of 3. As an interesting

feature, he even avoids explicitly playing 2 in the descent to 1 at the cadence of the first chorus.

Unlike his playing to conceal the structural motion at the half-cadence in chorus 1a, he chooses to

present his chorus 2 almost as an entirely separate “variation,” making no effort to connect the lines

between the two choruses. This sectional approach to this transition I think is helpful for the listener

and ultimately is a more artistic decision. Since he has essentially strung together 16 measures

without a structural ‘breath’ in his playing, this is an apt time to insert such a breath in order to allow

the listener to process what has happened and prepare for the next chorus.

68 Each chorus has a 2-measure tag extension, which is why the overall form is 18 measures rather than the original 16. 69 The formal boundaries are marked on the score throughout the document. For example, marker 2A3 is interpreted as the third A-section of the second chorus (the first number represents the chorus number when applicable, the letter is the formal section, and the last number is the occurrence in the form). The presented example would be the aabA of the second chorus. 70 Though there is not an interruption in the melodic line, there is one in the harmony, so the soloist, in a sense, is at odds with the formal structure here as he attempts to keep his solo moving forward even though the formal structure is begging for an interruption. Ultimately, this is an effective artistic decision, and, as we shall see in other solos, it is a fairly common way that soloists avoid playing solos that are too sectional.

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57

The first four measures of chorus 2a are quite intriguing. Structurally, he plays a variation on

the brace-motive by playing it in inversion, with the initial 6 transposed up an octave. This is elided

with a real expression of the motive in mm. 2.4-4. Measures 4-7 is an expression of the beginning of

the fundamental line as he moves into a proper 2 at a structural level in m. 8. As can be seen by

looking ahead at chorus 2b, this is the only time that Higginbotham expresses at a surface level the

structural 2. He even expresses the interruption on a surface level by inserting rests and not

beginning chorus 2b until the middle of the first measure (actual m. 27). Chorus 2b explores a delay

in the reestablishment of 3 until it is supported by III in m. 4 of chorus 2b. Before concluding his

solo, he sounds the brace-motive at a structural and surface level before proceeding to 1, followed

by the tag-extension. Like the head-motive, the structural 2 is implied.

Furthermore, recalling the feature importance graph from chapter 2 (figure 2.11), we can see

that progressions that move the harmony forward are important to the categorization of this

cluster.71 Mainly, the importance of Bebop-patterns when compared to their importance in the other

clusters. Given the nature of these patterns is generally to move the harmony forward, it is logical

that a composition that promotes linear motion at a structural level would also promote linear

motion in the solos. As a result, I interpret a main way in which the patterns relate to structure is

that the patterns that are used promote progression of a structural motive. Given this, it seems that

even a bad solo could be prototypical, and I suppose that mathematically it could be, but at the root

of this claim is that the balance of different patterns is a product of playing more structurally; by this

I mean that patterns are used as vehicles to navigate changes on a surface level, but which (type of)

patterns are used is in a conversation with musical structure. That isn’t to say that good players

71 Given the lower importance of overall high-level features, this is interpreted to mean that each feature carries more weight than in cluster 2.

58

always engage in deep structural playing, as we will see in the cluster 3 analyses, but it is to say that

deep structural ideas are a characteristic of one type of virtuosic and prototypical playing.

In this solo, Higginbotham demonstrates an attention to not only the natural structural

pathways that are present in guide tone lines, but he also demonstrates an ability to play a unique

solo that relies on the structural aspects of the head-motive while utilizing a fair amount of

patterns.72 What makes this fact particularly interesting is that this recording doesn’t actually include

a playing of the head-motive, so J.C. Higginbotham imposes elements that communicate at the

foreground, middleground, and deep-middleground levels that this is indeed ‘Baby, Won’t You

Please Come Home’ even though we never actually hear the tune.73 This type of “theme and

variation” is similar to a structural variation that was discussed in chapter 1, and much like Martin

points out in his 1996 book, this is a way to play virtuosically, as opposed to only playing surface

level patterns, like jazz improvisation is an etude over different chord changes.

The surface features of this solo were most like the features of other soloists in this cluster.

One characteristic of that clustering is that there needs to be enough uses of patterns in order for

this solo to cluster with other solos; that is, there are enough patterns at the surface level in this solo

that it could potentially be a sterile solo, but it is none the less structurally meaningful when

considering the deeper level progressions. Additionally, it is characterized by movement in the

structural lines at middleground and deeper middleground levels.74 This brings me to a claim

72 See the discussion of this cluster and solo in chapter 2 for more detail concerning the use of patterns in this solo and cluster. 73 I will avoid a discussion on the intent of the performer to communicate any particular melody in his solo. Rather, I assert that expression of structural features is likely caused by Higginbotham’s expertise in playing this music. He likely knew the tune well, so playing over the chord changes, even though there is no head, is not a substantive difference for his performance practice than if, for example, he didn’t play until the 8th chorus; he may not have heard the head in 5 minutes, but that doesn’t mean he doesn’t know the head—in a meaningful way—while he is soloing over the chord changes. 74 As opposed to deeper structures that may have more static lines with minimal linear progressions or structural motion. Consider the Neumeyer (1987) example, above, which lists Urlinie that only move 8 - 7 - 8. This would be considered more static than the structures of both this head tune and this solo.

59

regarding prototypicality in jazz performance: soloists utilize surface patterns that relate to the genre

as a whole, but one way that a jazz performance is prototypical is how these surface features relate

to essential aspects of an underlying structure. This claim is similarly related to Martin’s claim that

Parker’s performances are incredible not just because of his mastery of patterns, but his mastery of

use of those patterns to express deep structure in music.75 However, I am extending this claim to

other artists and that this is actually a feature of prototypical playing in jazz. It is balancing patterns

with their expression of structure that is prototypical of a virtuosic jazz performance.

One way to express prototypicality is through utilizing standard patterns to express deep

structure that relates directly to the head tune. However, as will be seen in the analyses of cluster 3 in

particular, this type of relationship between patterns and deep structure is not the only thing that

makes a performance prototypical.76

3.2. Prototypicality in Cluster 2

The most prototypical solo in cluster 2 is Roy Eldridge on Charles Shavers’ “Undecided”

(figures 3.5 and 3.6). Recorded in 1950 and categorized in the Weimar Jazz Database as “swing”, this

recording features Roy Eldridge (trumpet), Zoot Sims (tenor saxophone), Dick Hyman (piano),

Pierre Michelot (bass), Ed Shaughnessy (drums), Anita Love (vocals).

75 Additionally, Martin defines three categories for how the head-tune can relate to the solo (Martin 1996, 38-39): 1) paraphrase improvisation in which the head tune is only related at the surface level; 2) thematic improvisation, in which the head-tune relates to the structure motives; 3) harmonic improvisation, in which the solo is unrelated to the head-tune. This solo would fit within the thematic improvisation category. However, these categories derived by Martin are merely logical categories resulting from process of elimination. They are not claims as to what happens prototypically. 76 Moreover, the influence of a particular type/genre of jazz composition becomes important when discussing what is prototypical and what isn’t. There is more discussion on this topic in the conclusion to this chapter, but, in essence, it becomes a question of cause; is the performer playing prototypically, or is a particular composition, with its limited pathways more prototypical than another?

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B A3

62

The form of this composition is AABA song form in the key of B� major. The A-section

can generally be considered to be in I, and the B-section—like many B-sections—moves briefly into

IV before tonicizing V and returning to the A section. At the deepest level, this piece doesn’t

actually move anywhere: it is merely an expansion of 1 (8). This schema matches one of David

Neumeyer’s proposed alternative Urlinie. How the improviser relates to this structure will be

demonstrated below. At the middleground, a brace-motive demarcates the lower neighbor 7 - 8 - 7

followed by a minor third skip down to 6. One feature of this motive is its covering the distance of a

minor third. As a result, I have divided this motive into two parts, the neighbor tone and the

spanning of a minor third.77 Both of these features are important at a structural level, as well as the

surface level, though their structural importance is very close to the foreground. For example, in

mm. 5-6, the neighbor figure is followed by a descent from �3 - 1.

In the B-section, the structural significance can be seen in the elaboration of the neighbor

note 2 from mm. 9-12 and again in mm. 13-16, though at 16 we come to realize it functions as a sort

of interruption that tonicizes I for the return of A, so the second expression of this is more of an

incomplete neighbor that is interrupted before it resolves back to 1. Additionally, there is a linear

progression from 8 down to 5 as the harmony moves through the tonicization of IV and the

tonicization of V.

At this point, I need to reconcile my deepest middleground analysis with the harmony and

melody present in the middleground and foreground. The trouble area is mainly present in the final

two measures of the B-section when the middleground sketch is on the incomplete neighbor 2

supported by V. In essence, I believe this is not a true interruption. Rather, I interpret this to be a

77 The minor third will at times be considered generically as just a third.

63

retonicization of I as the piece moves back to the A-section; that is, the V and the upper-neighbor

derive their significance from I and 1, respectively. This piece should provide interesting ways for

the soloist to relate pattern playing to structural elements of the piece—namely which patterns are

used to prolong the static structure and the brace-motive.

First, concerning the deepest middleground I have analyzed in the solo, the importance of 1

is apparent—all of the A-sections are essentially prolongations of 1, just like the melody.

Additionally, Eldridge’s navigation through the B-section matches the middleground analysis of the

head-tune. So, like cluster 1, this solo at a deep structural level matches the deep structural events of

the head tune. However, the structure of the head-tune promotes a different use of patterns than is

present in cluster 1. As discussed in chapter 2, this cluster is characterized by the use of digital

patterns.78 Since Bebop patterns often imply harmonic progression, it is logical that cluster 1 would

have more structural motion in the solos. This may or may not correspond to the structure of the

head-tune, since a head-tune is often as much a product of the potential pathways as the solos are,

but given this head-tune has little motion at deeper structural levels, it is logical that this solo would

cluster here.

Concerning the middleground, the elaboration of 1 is readily apparent, namely through

pentatonic and blues-scale ideas. Referring back to the importance of digital patterns in this cluster,

consider the pentatonic scale in relationship to digital patterns; that is, the first five notes of the

major-pentatonic scale is a digital pattern. When considering the lack of structural melodic motion

that is present in the pentatonic and blues scales, this solo expresses the static motion of the

78 Digital patterns are combinations of chord tones 1,2,3 and 5. See chapter 1 for further discussion as to the construction of different patterns and appendix 1 for musical notation.

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68

structural level by relying heavily on patterns that do not move the harmony forward. Consider the

third most important feature when determining this cluster, whole tone patterns. These patterns are

so static that they are not even capable of moving the harmony forward given their symmetrical

construction.

However, the presence of Bebop patterns is not unimportant when defining this cluster.

This is where the structure of the B-section becomes important, namely that it is a ii-V-I in IV,

followed by a ii-V-I in V. This progression allows Eldridge to exploit the implicit linear motion in

these progressions by playing Bebop patterns. For example, in B1 at the level of the middleground,

Eldridge follows the same structure as the head-tune. That being said, when examining the

foreground analysis, we can see that he follows the logical localized sol-fa-mi progression over each ii-

V-I pattern. This example in particular demonstrates how surface level patterns can be elaborated to

match the structure of the piece; that is, although the surface of the music follows the ascending

harmonic ii-V-I from key area IV up to key area V, the deeper structure matches the linear descent

in I from 8 down to 5 through an altered 7.

Cluster 2 is particularly helpful when considering the role of patterns in promoting structure.

This prototype is marked by patterns that do not ultimately move the structure forward, but rather

serve to prolong at the middleground and deep middleground a more static structure. It is

intertwined with some linear progressions, as seen in the B-section of this head-tune and solo, but it

is ultimately defined more by the lack of structural motion, intermixed with some middleground

progressions.

3.3. Prototypicality in Cluster 3

The most prototypical solo in cluster 3 is Lee Konitz on “Wow,” written by Lennie Tristano.

Recorded in 1949 on Tristano’s album Sax of a Kind, recording features Wayne Marsh (tenor

saxophone), Billy Bauer (guitar), Arnold Fishkin (bass), Harold Granowsky (drums), Lennie Tristano

69

(piano), and Lee Konitz (alto saxophone). Additionally, this recording is categorized as “cool” jazz

in the Weimar Jazz Database. Voice leading reductions are presented below in figures 3.7 and 3.8.

This is in a 32-measure AABA song form in the key of F major. Arguably the most salient

feature of this composition is its lack of a coherent deep structure when considering the harmony

and the melody together. The harmony consists of fairly parsimonious voice leading, even if the

chords used present less than typical progressions. It has some chromaticized substitutions, like in

m. 4; the Amin7 could be part of a ii-V pattern leading to the Gmaj7 in m. 5, but if considered as a

“failed” tritone substitution—failed meaning it is that it is not a dominant and is instead a major 7.

One reason for this is twofold: the desired chromatic bass voice-leading paired with the G in the

melody force this sonority.79 An alternative reading might be that the chords and bass motion are

chosen not because of their traditional voice leading, but rather because of their directed bass

motion towards F (i.e. their chromatic motion towards F), and the melody forces certain chord

qualities. The reason for this is that much of the harmony can be parsed independent of the

melodic construction, almost as though the bass motion and the melody are at odds with each other.

Since the melody consists mainly of motivic structures that sometimes follow voice-leading

principles and at other times do not, I argue that the structure in this piece lies in two areas that

ultimately work together but are also independent. The first aspect is the harmonic voice leading that

can be represented in Schenkerian notation, independent of the melody, and the second part is the

melody, which is of course consonant with the harmony, but is generally more about expressing

79 It could be proposed that the melody could have easily been changed to G�, but I believe doing so would force the melody too far astray. While it might not be the most tonally clear piece, the melody at least grounds the piece to the key of F major. The G� would likely have produced an unstable aesthetic with the modular nature of the harmony.

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73

unique surface motives at varying pitch levels, particularly the motive (and its constituent parts)

demarcated by the brace. For example, the first 3 measures consist of a typical ii-V-I in F major, but

the melody is an ascending repetition of the brace-motive. This reasoning points to surface motive

being somewhat independent of a fundamental line, even if that structure is present in the chords.

Concisely, surface motive in this head-tune is more important than structural lines, even as the two

interact. This is a salient feature of cluster 3.

Konitz only solos over the first 16 measures of this composition. Generally speaking, he

follows much of the voice leading from figure 3.7. Moreover, his solo is mostly scalar. When

considered against the Feature Importance Graph in chapter 2 (figure 2.11), this is a logical

prototype for this category given the importance of the ambiguity of patterns when profiling this

cluster. Additionally, the most important feature aside from ambiguity of patterns are running

changes patterns. When Konitz is not playing a scale that matches the chord, he is often simply

running the changes. These scale patterns are related to the foreground motives in the head in so far

as he is taking the language he has available to him, scales, and moving it around to match the

chords. In this way, Konitz is mimicking the construction of the melody.

This solo and composition are distinctly different from both the prototypes in clusters 1 and

2. It is marked by the most non-traditional fundamental line in the composition, and the harmonic

voice-leading is less than standard. This ambiguity comes out in the performance in which the

performer must rely less on expressing deep structures and rely more on foreground motives; that is,

a performer must rely on ideas that clearly express the given chord and may not have a convenient

pathway to the next chord. While there are convenient pathways in this piece, they are very limited

and not standard. In fact, while creating the voice leading sketches in figure 3.7 and 3.8, I often

struggled to justify why I was making one choice over another. In many places, this piece lacks

standardized voice-leading syntax, like a ii-V pattern, or one of its many substitutions. Because of

Figu

re 3

.8

74

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Com

p: L

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(197

2Le

e K

onitz

75

this, both the melody and improvisations will be forced to find non-prototypical pathways through

the chord changes. These non-prototypical ways are likely more modular in conception, lacking a

“proper” resolution point like a ii-V pattern or a Bebop pattern, so as to be applicable in any

moment, independent of what preceded the current chord or what will come after it. Because of

this, the performer is inevitably forced to develop motives that are closer to the foreground.

Cluster 3 is marked by foreground development, rather than deep structural development.

This likely forces a performer to rely less on their pattern vocabulary and more on foreground

motives and ideas that fit a given piece. In the case of “Wow,” Konitz relied on his understanding of

chord-scale relationships to work through this rather challenging piece. As is discussed extensively in

chapter 4, Thelonious Monk’s performances are marked by this type or foreground-development.

Conclusion

Cluster 1 is marked by motion in the fundamental line and patterns that inherently push the

line forward. Cluster 2 is marked by a relatively static fundamental structure when compared to the

cluster 1 prototype, and thus the patterns are generally more static. Cluster 3 is marked by a

diminishment in the importance of the fundamental structure when considering the melody but may

still have voice-leading built into the harmony even if it is less than traditional. This static line in

cluster 3 promotes the use of harmonically static patterns. The performer is often left to play

foreground ideas that can be moved from chord to chord, independent of context. As a result, the

patterns that a performer chooses will likely rely more on expressing a single harmonic function,

rather than something like a ii-V pattern, which inherently implies forward harmonic motion.

Clusters 1 and 2 are closely related as the meaning of these compositions is related to deep

structural playing; that is, a performer could fill their solo with patterns, like Charlie Parker often

does, yet still create a unique and virtuosic performance because the foreground ideas are not where

the development occurs. The development in the clusters occurs at deeper levels. Cluster 3 is

76

marked by surface playing and less traditional uses of patterns. How these ideas relate will continue

to be explored in more detail in chapters 4 and 5.

These three analyses serve as the yardstick by which to measure Thelonious Monk’s playing.

In the following chapter, I discuss the ways in which he does or does not fit these molds. For

example, do his performances in a cluster 1 solo rely heavily on the motion of a fundamental

structure? Is there something inherent in his soloing style that caused his performances to essentially

all be clustered into cluster 3? Does he express a relatively static structure in his cluster 2

performances? In the case of all of the clusters, how do his surface motives and patterns translate to

a deeper structure? Do they even translate in a meaningful way?

77

Chapter 4 Thelonious Monk’s Prototypical Style

The aim of this chapter is to explore the musical profile of Thelonious Monk’s performance

practice. While some of this chapter will compare and contrast his performances to others, the main

purpose is to identify Monk’s style.

4.1. Cluster 1

The most prototypical Monk solo in Cluster 1 is “I’m Confessin’ that I Love You,” recorded

on his 1965 album Solo Monk (figures 4.1 and 4.2).80 This piece is in an AABA 32 measure song form

performed in the key of A� major. He plays through the entire head before soloing over the first

16 measures. Remembering the prototypes of this cluster, we should expect to see a structural deep

middleground that contains forward motion. This forward motion may unfold over the course of

the solo itself, or extend through the composition as a whole and include the solo.

This composition presents a few interesting ideas. Namely, what are the most structurally

essential pitches, the ones that determine the deepest level of structure? After considering several

analyses that started on more traditional tones such as the initial 5 in the melody, I found them to be

unsatisfying. They didn’t capture what seemed to be happening structurally throughout the piece.

My final analysis at a deep middleground level follows the tones 7 - 8 in the A-sections, with the 7

initially supported by I, and the resolution to 8 in the seventh measure of each A-section. My

analysis of the B-section moves to 2, followed by an upper-neighbor 3 in mm. 22-23, which moves

back to 2 in m. 24. There is an interruption of sorts in m. 24 before the final

80 Thelonious Monk, Solo Monk (Columbia, Legacy CK62533, 2003), compact disc.

Figu

re 4

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ont.)

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80

repeat of the A-section.81 At the middleground, the motive labeled with a brace proves important in

the resolution of the ‘top’ of the motive always resolves to the structural tone on beat 1. Even in the

B-section this is the case. So, much like the background structure is moved forward by surface level

details in “Baby, Won’t You Please Come Home,” so is true of this composition. Now the question

becomes, how does Thelonious Monk navigate this structure?

We have a limited data since Monk only solos over the first two A-sections, but it is

sufficient to demonstrate how he would navigate such a structure utilizing the patterns that grouped

this performance with cluster 1. At the deepest level, Thelonious Monk avoids the 7 – 8structure

from the head-tune. In fact, he prolongs only 8 throughout the half-chorus. At a deeper level,

Thelonious Monk avoids the structure that is presented in the head tune, which will prove to be a

hallmark of his style; that is, while he does play solos that have some fundamental structural motion,

his solos generally lack meaningful structural motives.82 He often plays surface ideas that express

middleground and fore ground structures, but his solos often lack a deeper internal logic, or at least

seem to be about something other than deep structure. This, as we will see, is a characteristic feature

in the way that Thelonious Monk solos. While his surface level features might be similar to another

81 It is challenging to call this an interruption in any strict since because each A-section resolves to 8, so the B-Section is more independent that derived from the A-section; that is, is it really an interruption when the line already resolved? I think that is something that could be argued for either way. For the purpose of this analysis, I will call it an interruption because it matches the idea that the B-section comes before a da capo marking, which implies a restart, rather than a continuation. 82 As was discussed in chapter 3, this idea of the authority of the structure presented by the head-tune may or may not be a way that a soloist might navigate changes. It might be that a soloist finds an all-new pathway through the harmonic structure, and this pathway might even on the surface reference the original head-tune, but at a structural level it may be entirely “new”. Something that is interesting in the conception of a “theme and variations” in jazz improvisation is the variations might avoid the head-tune all together and be a very broad conception of the idea of variations. For example, it might be that it is only a variation in the sense that it generally follows the harmony, assuming there are even any chordal substitutions, and it is the same formal structure. In that sense, it might be more like some of the variations in Bach’s Goldberg Variations, in which the overall formal structure, delineated with a few harmonic sign-posts is the only thread connecting a particular variation to the theme. Because of this idea of alternative pathways, there are inevitably alternative structures to the chord changes of a given tune.

Figu

re 4

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81

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83

performer, and at times they imply quite a bit of forward motion, he is more often concerned with

surface elaborations that shift the focus to the foreground.

In this particular solo, we can see that he has some linear-progressions that surround a third

in the middleground. For example, the 8 - 7 - 6 progression that is supported by the II in m. 4.

However, this progression unfolds from the 8 that is present throughout. Another linear

progression we see in this same period is the inner voice motion from 3 - #1, which is part of a

running changes pattern that moves the VI to II. Here we can see how Thelonious Monk often

avails himself to more surface prolongations to move the local harmony forward, but, in this case at

least, it is somewhat circular as the line that moves 3 - #1 is ultimately the line that is part of a

motion from an inner voice as the upper voice progression from 8 - 6 is shown to be a motion to an

inner voice.83 This motion that serve to both move away from, and to 8 is a way in which Monk

allows himself to continue running changes in a similar way, thus drawing attention to his

development, or at least repetition of, certain middleground and foreground ideas. For example, he

essentially plays the same running changes pattern over ever VI chord. Additionally, he plays a

similar Bebop pattern over every V chord that comes before a signpost harmony.84 To summarize

how this represents a prototypical Monk performance, it is the case that he employs similar patterns

as other performances in this cluster. However, he uses them more as surface ideas than ways to

navigate deeper structural patterns.

It might seem inconsistent to say that he doesn’t elaborate a deep structure while identifying

a fundamental line that doesn’t move beyond 8. However, my point is not that a structure cannot be

83 This is not necessarily prototypical of Monk, but it is an interesting way in which his surface explorations of various motives can sometimes work for him. In this example, which is essentially single-line polyphony, Monk is shown to prolong 8 through various linear intervallic patterns, unfoldings, etc. 84 A signpost harmony is a harmony that occurs at a hyper-metrically important position, usually occurring at 4 or 8 measure intervals.

84

found; very often a soloist performs over chord changes that have pathways that implicitly express a

deep structure. My point, however, is that the logic and motion in Thelonious Monk’s solos

frequently lies on the surface of a solo. His ideas generally have the characteristic of cluster 3

performances, in which the ideas are more towards the surface. In this sense, Thelonious Monk’s

elaborations are generally readily apparent to the listener.

4.2. Cluster 2

The most prototypical solo in cluster 2 is his performance on “Little Rootie Tootie” (figures

4.3 and 4.4). Recorded on the 1954 album Thelonious Monk Trio, this performance features

Thelonious Monk (piano), Gerry Mapp (bass), and Art Blakey (drums).85 This is also in a 32-measure

AABA song form. As will be shown, the harmony of this piece follows more of the spirit of many

AABA forms from this period in so far as the harmony lacks any chord changes in the A-section or

traditional motion by fifth or common substitutions in the B-section. It relies more on a modular

construction, similarly conceived as the most prototypical composition from this cluster, but it is less

predictable and is more of a collection of rather unpredictable changes.

Given the A-section is I chord, it is logical that there is no possible motion of a deeper

structure.86 The clear purpose of this A-section is to sound the surface motive. Looking forward to

the B-section, there is some motion that centers around 1. As a result, I retroactively assign the

structural head as 1. This tone holds at the deepest middleground level until m. 4 when 2 gains

85 Thelonious Monk (piano), Thelonious Monk Trio, Thelonious Monk Trio (Prestige PRCD-30164, 2007), compact disc. 86 I am not considering Monk’s Db chord that occurs every other measure to be a harmony, but rather a texture, or color.

Figu

re 4

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87

control. 1 regains its structural importance at the return of the final A-section. I do not consider this

to be an interruption, but rather that the entire line moves 1 - 2 - 1.

Considering the middleground B-section, the upper neighbor is significant both in the

melody and the harmony. For example, the chromaticized #1 moving to 1 in m. 17 is mimicked in

the arrival of 2 at m. 4. This chromatic upper neighbor can be considered as a middleground

expression of the deep middleground 1 - 2 - 1 neighbor motion of this alternative fundamental

line.87 The last feature of this graph I would like to draw attention to is m. 21, in which there is an

imbedded chromaticized neighbor note that allows for the support of 2 above VI. If considering

this VI (F-major) as an isolated chord, it would seem that 2 is an unsupported tone. However, if

considering this F-major chord to actually be derived from the F-minor chord of the following

measure via a chromaticized A�, however, then the 2 is actually being supported by an F-minor

triad. This fourth above the bass of a minor triad is arguably consonant in this context.88

To summarize, this piece is structurally rather flat.89 At the deepest middleground it lacks any

motion in the A-section, which is 75% of the composition, and only contains an upper neighbor in

the second half of the B-section. There are some more local level upper neighbor motions in the

middleground, but overall the concern in this composition seems to be the exploration of the

87 It might also be considered as part of the A-section surface motive, namely the “top” of that motive resolves down by step to the consonant tone above the harmony. However, I think this is logically too far of a leap. The only thing I might consider to this more structural upper neighbor relating to the middleground is the motion to the deep middleground 2, which is preceded by a sort of over-reaching with a #2 that resolves to 2. This moment is even harmonically unexpected given that #2 is the third of a V/III that harmonically moves to II before proceeding to III, almost as if to emphasize that the #2 most certainly should go to 2. Given that this piece is composed by Monk and middleground and foreground motives are more characteristic of his style, it would be expected that such an odd harmonic interpolation would be present. I will engage with the idea of Monk as a performer and Monk as a composer at the end of this chapter as it is relevant to the question of what is prototypical of his performance. 88 I argue that this is consonant because of its prevalence in the harmonic language of jazz. For example, the famous “So What” chord is constructed by placing a fourth above the bass of a minor chord as the lowest sounding voice other than the root of the chord. 89 The normal performance practice of the A-sections usually doesn’t involve any chord comping or walking in the bass, rather, each performer plays the melody.

88

surface motive presented in the A-sections. All of that being said, as we have seen with other

compositions, there often is the possibility for alternative pathways that provide more motion at a

deeper structural level than is expressed in the head-motive.

Moving on to Thelonious Monk’s solo, the main concerns are the ways in which he develops

motives and the extent to which he relies on deep middleground, middleground, or foreground

structures to develop his solos. A graphic analysis of his solo is presented below in figure 4.4.

At the deepest middleground, Monk follows the 1 - 2 - 1 fundamental line. This isn’t

particularly interesting on its own, but the way in which Monk transforms the middleground in

relation to the foreground further demonstrates a significant aspect of Monk’s prototypical playing.

Looking at the middleground in the A-section, we can see that Monk develops the neighbor ideas at

the foreground and the middleground. Measure 1 sets up the idea that he will develop throughout

his solo. While it may appear this is derived from the deepest structure of the piece, I argue it is

more a surface level feature. The reason for this is that he implements these foreground ideas more

readily than other prototypical performances do; that is, while other performers often utilize patterns

to navigate deeper structures, Thelonious Monk employs motivic ideas to do this, and he uses the

patterns to navigate local chord changes. For example, in the solo choruses, the chord changes

utilize ii-V patterns that return the harmony to I, rather than simply just having a I chord throughout

the A-sections. He performs various Bebop and running changes patterns to cycle through these

local harmonies (as in mm. 5-6), only to return

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93

to the neighbor idea in various forms, be it a lower neighbor or a chromaticized neighbor. This type

of surface development of foreground motives is seen throughout his performances.

Tracing this foreground neighbor, we see it presented as a chromaticized lower neighbor at

the start of A2, which is expanded rhythmically until he moves again into more pattern playing over

ii-V’s. Moving into the B-section of the first chorus, Monk plays a handful of patterns that fit this

rather modular construction, but at a middleground level, these neighbor ideas are still prevalent,

even audible to a listener who is accustomed to listening to Monk’s developmental schemes. For

example, the chromaticized neighbor note above 2 from mm. 21-23. This even corresponds with the

chromaticized upper neighbor from 1 that is sounded in the left hand.

In the last A-section, Monk emphasizes what his solo has been “about” by simply playing a

series of lower neighbors for six of the eight measures before playing a descending arpeggiation that

contains a lower-neighbor below 5. This descending pattern brings him to the return of the head,

entering back in on the B-section.

A second surface motive of this solo is more about a sonority than a particular motive. That

sonority is a fully diminished seventh chord. We first see this sonority enter in m. 6 when he

arpeggiates the #IVdim. He draws attention to this sound in both A-sections by playing similar

arpeggios each time the harmony occurs. In the B-section, he draws attention to this sonority by

outlining diminished fifths whenever possible; he sprinkles his solo with tritone spans in places that

many other performers would use stricter patterns. For example, in m. 21 he oscillates between B

and F, and in m. 20 he outlines the chordal third and seventh of a C7 chord. In m. 19 he leaps from

the �9 to the #4 above a G7 chord, emphasizing his tritone idea. Finally, and much like in the

section labeled 2A1, he brings the tritone to the surface by simply repeating an open diminished-5th

for the entirety of this A-section.

94

What this solo demonstrates is that unlike other prototypical performances examined thus

far, Thelonious Monk relies heavily on surface motives that are less about expanding a deep

structural idea and more about developing surface ideas and sonorities. Moreover, the motives he

chooses are unique to each piece. As we proceed, this type of performance strategy becomes

apparent yet again. Thelonious Monk does rely on patterns, but his use of them is quite different in

that they are not used to navigate or connect to deep structure, but they are rather used as

foreground ideas that serve as a bridge between his exploration of surface motives. As a result, this

analysis shows how Monk is similar to other performers; that is, he uses patterns to find his way

through common chord changes. However, he does not rely on them as other performers do, which

is demonstrated by nearly all of his performances clustering in the group that is marked by a less

distinct use of patterns.

4.3. Cluster 3

“Ask Me Now,” recorded in 1964 and released on the album Solo Monk, features a solo

performance in a stride style (figure 4.5).90 This piece is in an AABA song form and was composed

by Thelonious Monk. It is an interesting case study in the intersection between Monk the performer

and Monk the composer because he did not release a recording of himself playing an improvised

solo on this piece, but rather performed it each time as an embellished melody.91 In this particular

recording, he plays through the composition twice, with the second time through being more

90 Thelonious Monk, Solo Monk (Columbia, Legacy CK62533, 2003), compact disc. 91 Monk released this composition on two other studio albums, 5 by monk by 5 (1959) and The Genius of Modern Music 2 (1951). On both recordings he did not improvise, but embellished the melody, much like he does in this performance from Solo Monk.

95

embellished than the first. Below is an analysis of the entirety of this performance. The piece is in

the key of D�major, with the deepest level expressing a static 5 throughout.92

Moving to the middleground, the chromatic motion from 7 to 5 in the first the three

measures of the A-sections is apparent in both the harmony and the upper-voice of the melody.

What is also apparent is the motive that generates much of this motion—demarcated by a brace—is

both important to the foreground coherence and the middleground motion. Here we see Monk’s

prototypicality in exploring foreground and shallow middleground ideas. This motive can be

conceived of broadly as an arpeggio followed by a resolution to the next harmony. In the case of the

first presentation, and the more explicit presentations of this motive, that resolution is often

followed by, or preceded by a skip or leap, as seen in mm. 1 and 6, respectively. In the middleground

of the B-sections, monk prolongs the 5 by motion into an inner voice to 2. This is similar to the

acquisition of 5 in the A-section, but the goal of 2 sets up the expectation to return to the A-

section.93

Looking ahead to the second chorus, both the middleground features and the deepest

background are the same. Moreover, the foreground is nearly unchanged. There are instances in

which the fills between measures involve very local motion, such as the neighbor ideas in m. 1 of the

second B-section. However, these fills are more idiomatic to Thelonious Monk, particularly

92 One could argue for a bit of motion in the B-section at the deepest middleground, but that seems like confirmation bias. I think a more consistent analysis keeps the fundamental line on 1 throughout, and the motion to other voices is reserved for middleground and foreground analyses. 93 This is not dissimilar to the other B-sections analyzed up to this point in the document. The B-section very often sets up the expectation for a return to A by either presenting an interruption or simply landing on 2 at a middleground level. In this analysis, I think an interruption is more appropriate given how stark the separation is between what I label as a half-cadence at the end of B and the return of A.

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103

his use of whole-tone runs and ideas. This again points to Monk’s concern for surface motives; that

is, the ‘point’ of this piece is not necessarily deep structure, but foreground motives he is developing.

This type of motivic playing drives the piece forward. It is the exploration of this motive that

provides the virtuosity in this composition and performance.94 As far as how this piece fits into

cluster 3, this cluster is marked by running changes and other patterns that do not implicitly drive

the harmony forward. While I have called final note of the brace motive a resolution, it is most often

part of a running changes pattern, even if sometimes it does in fact resolve to the next harmony.

Moreover, this cluster is marked by a static structure, which, given the deepest middleground is

essentially a static 1 with the only significant motion being analyzed at the middleground, this

composition even fits that solo construction. As a result, this solo is correctly catalogued not just by

its surface details, but also by the structural aspects the piece communicates.

As was stated in the introduction to this analysis, this piece doesn’t feature a solo, per se.

However, it is arguably the most prototypical Monk performance. It captures his concern for audible

motivic development, as shown in the establishment of the fundamental line in mm. 1-3 and the use

of the brace motive from m. 1. It presents his developmental logic by presenting two choruses of

the same idea, but the second is developed more via certain idiosyncratic patterns like the insertion

of whole-tone runs between statements of a theme. Also, much like was shown in the analysis of

cluster 2, he utilizes more prototypical patterns when navigating common changes, but these are

used more to provide variety as he develops foreground features that are unique to a particular

performance; that is, his B-section is where he employs more ii-V type patterns, but they serve as a

94 This is in opposition to Martin’s claim that virtuosity and interest derives exclusively from deep structural elaborations.

104

contrast to his motivic development rather than a vehicle for his structural development (as is also

the case with the prototypical solos analyzed in chapter 3).95

Conclusion

Prototypical performances from other soloists are most often marked by an elaboration of a

fundamental structure. The patterns utilized often directly relate to this structure by pushing the line

forward, or, the antithesis, choosing patterns that hold the structure static like that underlying static

harmony. These performers relate their use of patterns not necessarily as a vehicle for variation, but

as a way to navigate and express structure. Comparatively, Thelonious Monk proves to be much less

concerned with deeper structure. While he often communicates middleground linear progressions,

these progressions are arguably not what mark his style, but they are rather a byproduct of playing

over harmonies that implicitly communicate some sort of middleground structure. Monk is

concerned with surface-level motivic development. He employs patterns not as vehicles for deeper

structural development, but rather as variation from his foreground motivic development. This type

of performance is likely due to Monk also being a composer. As is seen in his work “Ask Me Now”

and “Little Rootie Tootie.” Monk not only concerns himself with surface motives in his solos, but

also in his compositions.

This begins to blur the line between Monk the composer and Monk the performer. The

similarities between the logic of his solos and his compositions demonstrate a thoughtful musician

who was consistently concerned with motivic development, balance, and variation. While some may

claim his technique was poor—it intentionally was—and others may claim his solos are

incompetent, it would be incorrect to say he was not as virtuosic or thoughtful as someone like

95 There is also a lot to be said about rhythm in Monk’s performances, but that is mostly beyond the scope of this document. However, I will begin to address this topic in the epilogue by discussing his use of rhythmic variance when compared to every other performance in this corpus.

105

Charlie Parker, who (as Martin has demonstrated) was virtuosic because of his use of patterns as

they relate to deep structure. Monk is virtuosic because he mastered motivic development and

variation over chord changes that others were navigating in a fundamentally different way. Monk

was indeed unconventional (at least for his time) and even, in a sense, non-conformist. However, he

was a master of his craft, demonstrating a sensitivity to certain musical parameters in a way that

other musicians were not.

106

Chapter 5 “Bloomdido”: A Case Study

In the preceding chapters I propose that Thelonious Monk may have utilized patterns similar

to those of other performers, but that his concern for perceptible motivic development is the thing

that marks his prototypical motivic playing; that is, he performed often in a way that developed one

or more, interlacing those developments with pattern playing. I also demonstrate that Monk’s

performances may have implicit deep structural ideas, but those deep structures are often

byproducts of the composition and genre, rather than the ‘point’ of his solos, which was the

foreground motivic development. In this chapter, I analyze a solo that is outside of this corpus,

“Bloomdido,” written by Charlie Parker. This recording from the album Bird and Diz, recorded in

1950 and released in 1952. This track features Charlie Parker (alto saxophone), Dizzy Gillespie

(trumpet), Thelonious Monk (piano), Curley Russel (bass), and Buddy Rich (drums).96 This

composition is a 12-bar blues with fairly typical chord changes, excluding the D�minor chord in m.

8. An analysis of the composition can be found below in figure 5.1. This performance was chosen

because it features solos Parker, Gillespie, and Monk, so it is ripe for a comparative analysis to see

the ways in which these performers navigate a solo even on the same performance. It should be

predicted that both Parker and Gillespie utilize more patterns, and they use them in a way that

relates to a deeper structure, while Monk utilizes more idiomatic or surface motives that are

interspersed with patterns that provide variation and move him through the necessary chord

changes.

96 Bird and Diz (Verve Record 314 521 436-2, 1997), compact disc.

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108

At the deepest middleground, this piece is a three line. The 3 is established in m. 2. There is

a lower neighbor �3 in mm. 5-6, which moves back to the natural 3 in m. 7. Measure 8 moves

through a chromatic passing tone to 2 in m. 9 before finishing the line on 1 in m. 10. There is a re-

tonicization of I as the form folds back in on itself at the repeat of the

head, a standard practice when playing a blues. At the middleground, a series of Bebop lines push

the background forward as well as elaborate the more local harmonies. Given this piece is so short

and is rather harmonically and thematically simple, it might be expected that the solos would also be

as such, but as will be demonstrated, all of these performers create interest in different ways. The

first solo to be analyzed is Charlie Parker’s, who solos first on the record. My graph is presented

below in figure 5.2.

5.1. Charlie Parker

Parker essentially treats each chorus as a new structure.97 Moreover, he expresses a different

structure through each chorus of his solo. The first chorus is a motion from 8 - 5, essentially

utilizing the guide-tones to navigate the changes. The patterns he utilizes move the deep-

middleground motion. For example, the motion from A�- G is propelled forward via an octatonic

pattern in m. 8 of the first chorus. The second chorus explores the space from 8 - 3 by dividing the

octave at 5. Once again, the patterns propel the deeper structure. Considering mm. 7-9, we can see

that the deeper structure is moved forward by a Bebop pattern (m. 7), followed by a ii-V pattern (m.

8), which resolves to the 4 (m. 9). This chorus ultimately resolves to 3 in m. 11, but it is displaced by

an octave.

97 It is also present in his use of space in so far as each chorus seems to close before the next begins; that is to say, Parker could have ended his solo at the end of any of his four performed choruses and it would have been a logically complete solo.

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Chorus three expresses the melody’s structure of 3 - 1. It even contains the lowered 3 in

mm. 5-6. Again, the structure is pushed forward by pattern playing. For example, mm. 8-9 contain a

digital pattern that moves the motion from 3 - 2. What is particularly compelling about

this use of patterns is their relationship to the fundamental structure, which in Schenkerian terms is

still a 3 supported by I when the pattern begins, but the final note and resolution occurs over a ii

chord. This metric placement forces what is normally a harmonically stable pattern to become a

dissonance that needs to resolve; that is, when the pattern begins, it is the third of a I chord, but

when it ends it is the ninth of a ii chord, which must resolve to a chord tone. The re-

contextualization of this note as the harmonies change provide a compelling forward motion of a

pattern that is otherwise often used as a stabile expression of a harmony.

Parker’s fourth and final chorus expresses a 5 line. As demonstrated in the previous three

choruses, the patterns push the deeper structure forward. Similar to the second chorus, Parker

pushes the line forward using a ii-V pattern in m. 8 (G7-Cmin7). This is a particularly salient insight

into Parker’s use of patterns in his playing; the use of the same pattern in the same formal moment

that pushes the structural tone forward demonstrates one of my main claims concerning a way in

which performers other than Thelonious Monk relate pattern playing to the background structure.

In Parker’s performance, he consistently uses patterns to clearly express forward structural motion.98

A main point of Parker’s performance is deep structural motive. Because of this, his playing often

utilizes recognizable surface patterns that can be utilized in different contexts, but the point is not

the surface patterns. This is in contrast to Thelonious Monk’s performances, which, as has been

98 This structural forward motion via patterns is made even more explicit aurally in these moments by using exact iterations of the textbook patterns, rather than modified or embellished versions. While I intuitively think this is the case for Parker at least, I am hesitant to over extend this claim regarding clarity of pattern usage at specific structural junctions.

114

demonstrated, shift the motivic development to the surface of the performance rather than the

background.

5.2. Dizzy Gillespie

Dizzy Gillespie solos second on this recording, and, much like Parker, treats each chorus as

an independent structure. The first chorus expresses a 3 line, but it is not exactly the same as the

melody’s motive because Gillespie leaves out, or, at least, underemphasizes the lowered third. At a

middleground level, he displaces the lowered third an octave, but it is arguably more about matching

the local chord than a structural alteration. Furthermore, Gillespie even plays the � 3 a measure early

(assuming the alteration is merely a local, and not a structural change), contradicting the chord

played at the piano by Thelonious Monk. The structural line moves to 2 in m. 9. Gillespie moves

the line forward with a surface level enclosure. Furthermore, this enclose is part of a major Bebop

pattern.99

Dizzy’s second chorus is another 3 line. The arrival of 2 is marked by an arpeggiation, which

is part of the overall resolution of the chordal seventh of the IV chord. This is an interesting motion

that bypasses the surface harmony in favor of a more traditional resolution of the chordal seventh;

that is, in this blues structure, the lowered 3 in m. 4, which is part of the major-minor IV7 chord,

does not resolve properly according to traditional resolution tendencies in common practice music

and much of jazz literature. However, in this moment, Gillespie avoids playing the 3 over the I

chord in m. 7, ultimately fulfilling the voice leading obligation of the minor-7th to resolve down by

step. Dizzy inserts a chromaticized 2 as a passing to on the way to 1 before beginning his thirds and

final chorus of the recording.

99 This embellished Bebop pattern would not have been found by my algorithm.

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Like Parker, Gillespie utilizes patterns ubiquitously in his solo. These patterns function to

embellish, elaborate, and develop the fundamental line of each chorus. That is to say, the patterns

relate to the underlying structure by shifting the purpose of the solo to a deeper motivic

development. That isn’t to say that surface development is nonexistent, but rather that the motivic

development at a deeper structure is more meaningful, the part of the development that relates to

the interest of each chorus, the forward motion of each chorus, and “virtuosity” of the

performance.100 In essence, the point of this solo is not the surface patterns or elaborations. The

point is motivic development at a deeper structural level, and the patterns serve to elaborate that

structure, which helps provide part of the answer for why these patterns can be used so ubiquitously

throughout jazz improvisations and still be interesting as a genre.

5.3. Thelonious Monk

Thelonious Monk performs the third solo on this recording (figure 5.4).101 Similar to Parker

and Gillespie, Monk plays each chorus as a separate idea. Like the analyses in previous chapters, the

fundamental line is not only challenging to find using generally accepted Schenkerian techniques, it

is also arguably not a very meaningful expression of what is happening in the solo. I have analyzed

both of Thelonious’ choruses as 3 lines that match the fundamental line of the melody. However, as

is one of my main arguments surrounding Monk’s playing, this isn’t the level of analysis that

generates interest in Monk’s performance. The interest comes from his development and use of

foreground motives that are often unique to each performance.

The first motive to be examined is the arpeggiation from 5 to 1, demarcated by the bracket.

Much like the ubiquitous nature of patterns in other performers’ solos, this motive is used as the

100 Martin, Charlie Parker and Thematic Improvisation, 111. 101 Buddy Rich performs a two chorus drum solo before the ensemble plays the head out.

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121

material to be developed, though this development is surface level as opposed to material that is

developing a deeper motive. It is more about executing a hook, something that can be understood

on the first listen and without a structural understanding of soloing. One development of this

motive is the alteration of B�to B�. This development is brought to the surface by the metric

placement. Instances of this motive are presented either after at least a half rest (m. 8, 12-13, and

15), thus drawing attention to the entrance, or as quarter notes, which if performed by other players

might be considered too heavy or stilted (m. 9 of chorus 2).102 Stylistically, this quarter note

figuration is in opposition to the expectation of rhythmic syncopation that other Bebop players are

well known for. A less transparent development, but one that is still towards the surface of the

music, is a substitution of 5 for 7, as shown in the first measure of the second chorus. The motive is

presented clearly leading into the first measure of the second chorus. All of this being said, one very

important insight into this motive being a conscious development for Thelonious Monk’s

improvisation is not even in his solo, but is actually in the introduction to the piece, presented in

figure 5.5, below. As is apparent, the motive that is explored in the solo is the same motive from the

introduction. This argument bolsters the idea that Thelonious Monk explores motives that are

unique to a piece, rather than patterns that are universally utilized in the genre.

102 The stilted or awkward nature of this rhythmic figure aids in the description of Monk’s being non-conformist, etc.… While I am not much concerned with time feel in this document, I do discuss rhythmic usage in the epilogue.

Figure 5.5 Piano Introduction

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The second motive to explore in this solo is resolution of D�to D�, which finds its origins

in the fundamental line of the melody. This motive is less distinct that the arpeggiation from 5 to 1.

However, it is still plainly heard as a surface motive. The development of this motive is mainly

through rhythmic variation. For example, in m. 10 of the second chorus, Monk toys with this motive

by rhythmically separating the resolution of the D� to D�, and he explores it further by making it

part of the figuration in mm. 11-12 of the second chorus.

Concerning pattern playing in this solo, there are only two patterns present—the whole tone

patterns in mm. 10 and 16 and the arpeggiation that leads to a Bebop idea in mm. 9 and 22-23.103

The whole tone patterns are a feature of Thelonious Monk’s idiom. However, the limited pattern

usage in this solo in general demonstrates my claim the Thelonious Monk is not a pattern player in

the same way that Parker or Gillespie are (even though he arguably could be if he so chose—his

approach to pattern playing seems to be intentionally different). His concern for surface motives

leads him to play different kinds of ideas, ideas that are often derived from the melody or some

other compositional feature such as the introduction. Thus, he at least utilizes patterns more

sparingly so as to not distract from his desired form of surface development. For example, in the

solo just discussed the arpeggiation is used sparingly as a break from the pattern playing. This might

be considered a reverse approach to what, for example, Gillespie did. In Gillespie’s solo, he utilizes

non-pattern moments to contrast his virtuosic Bebop playing (mm. 1-2, for example), which relies

heavily on patterns or embellished patterns.

Conclusion

In the opening paragraphs of this document, I pose questions surrounding Thelonious

Monk’s non-conformity within the genre. I discuss how Monk might play in a way that represents an

103 The chromaticized Bebop idea is not included in my algorithm.

123

“entire self-created world.”104 The preceding chapters demonstrate that Monk accomplishes this by

approaching motivic development in a way that is quite different from other performers. He

performs at the surface. That is not a negative assessment. In fact, it is quite the opposite. This

surface playing is the way that Monk so readily fulfills the needs of his world building. He performs

in a way that pulls the listener in by presenting a limited number of easily recognizable motives that

are developed throughout his solo. This non-conformity is demonstrated by his limited use of

patterns, which are ubiquitous in the playing of other performers as the musical material that serves

to develop a deeper structural motive. His use of patterns is idiosyncratic not due to a total lack of a

common language, but by the placement of the patterns and the apparent intent of the usage as a

way to break up his surface motives. Thelonious Monk’s melodic usage is unique because of its

diversity and uniqueness to individual pieces.

104 Solis, Monk’s Music, 30.

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Epilogue: What About Time Feel?

The scope of this dissertation limited my discussion to consideration of motivic

development and pattern usage. However, it is necessary to discuss the rhythmic usage and time feel

of this unique performer and composer at least to some extent. Most importantly, it is vital to

articulate how Monk’s rhythmic usage differs from that of other composers and performers. To

address this point, I utilize a rhythmic variance metric called the normalized pairwise variability

index (nPVI).105 This metric calculates the amount of variance between note onsets and it is

normalized to an output of 0-200.106 For example, see 6.1 below. What this information provides is,

in a sense, a proxy for rhythmic usage because it serves to calculate the variety of rhythmic patterns a

performer utilizes in a solo. Moreover, this metric has been shown to function as a proxy for style.

For example, a Katherine Vukovics and Daniel Shanahan found a relationship between intended

national style and nPVI, which contributes to the broader discussion of the role of rhythmic usage

as a proxy for style or genre.107

To demonstrate the role of rhythmic variance as a proxy for style in this corpus, I will utilize

a similar methodology as that in chapter 2 of this document. Namely, the supervised machine

learning algorithm (GLM) that will attempt to categorize a solo as Monk or not-Monk. This model

utilizes the same low-level features (the patterns) included in original model, but it also includes each

performance’s nPVI. The purpose of this analysis is to show that rhythmic variance is a feature of

Monk’s performing that further sets him apart as non-prototypical. Additionally, this model serves

105 See, Esther Grabe and Ee Ling Low, “Durational Variability in Speech and the Rhythm Class Hypothesis,” Papers in Laboratory Phonology 7, 2002. Initially, this metric was utilized as a way to categorize the rhythm differences between stress- and syllable-timed languages.

106 *PVI = 100×[ 2342356(8358356)

:/(< − 1)>4?

@A? , where d is the duration of the kth object and m is the total number of

note onsets. 107 See Vukovics and Shanahan (2018), Daniele (2016) and VanHandel (2016).

125

to reinforce the arguments from the preceding chapters that Thelonious Monk’s performance

practice is holistically different enough from other performers that a computer should even be able

to recognize his style.

I trained my model on 20% of the data and tested it on 80% of the data. Keep in mind that

this training process only examines two Thelonious Monk performances, so it is a reverse test; that

is, the computer will learn about the features of other performers and essentially be blind to

Thelonious Monk’s performance practice given there are not enough samples on which to train the

computer. This is by design given the characteristics of the corpus—essentially how many Monk

performances are included relative to other performers. For example, consider a training set that

contains 80% of my data, which is 423 samples in total, 13 of which are Thelonious Monk. This

model would test on 20% of the corpus, or 106 in total and 3 Monk solos. Running this analysis

produces a success rate of 98% ± 2% and p=0.42. I attribute this failure to overfit, thus the results

Figure 6.1 Example of nPVI ratings of folk tunes. The durational values are calculated as

a proportion of the first onset. Recreated from Daniele (2003, B40).

126

are unreliable.108 This is to be expected given the limited test data. However, if the logic of this test is

reversed, essentially learn the features of the non-Monk category with the goal of identifying

negative results, then the model demonstrates that Monk was different, even if the model hasn’t

learned enough characteristics of Monk’s playing to positively identify his performing; that is, the

goal is to demonstrate that Monk was non-prototypical, even if the model isn’t powerful enough to

identify in what ways he is non-prototypical and is only able to say that his solos do not fit the not-

Monk category.

When running the model on the appropriate partition (20/80 split), the training set contains

103 non-Monk performances and three Monk performances. This means that the driving force of

the model is to implicitly determine that Monk is different from other performers. The model

performed at a 98% ± 1% accuracy and p<0.05. Moreover, the specificity is 0.99 and the sensitivity

is 0.77. Specificity relates to the ability of a model to correctly identify a true negative. In this case, a

true negative is “not-Monk.” Sensitivity relates to the ability of a model to correctly identify a true

positive, which in this case is correctly categorizing Monk as himself. 109 It should be noted that the

validity of the sensitivity of this test is questionable because of the limited sample size; which is to

say, this is not necessarily the computer’s ability to positively identify Monk, but rather it is the

computer’s ability to positively identify not-Monk (the specificity), and, thus, only negatively identify

Monk. A confusion matrix is presented in table 6.1 below. This table visualizes this sensitivity versus

108 Model overfit is occurs when a model is too specific a given dataset and is thus incapable of categorizing any “new” data beyond the training/test sets. The inability for this model to successfully categorize outside of the corpus means the results aren’t actually real when discussing Monk’s style. This can happen for a number of reasons, but I believe this 80/20 model suffers from that problem because of the limited number of chances the computer had to correctly asses that a solo was Monk. Additionally, the relative number of Monk versus non-Monk solos likely means the computer has learned too much about both categories, especially when considering that it only had 3 chances to correctly asses Monk. There is a problem with this relative scale because if Monk is indeed markedly different from other performers in the model, then the computer has been given too much information about both categories and thus if Monk did play similarly to others, the nuance of his performance would be lost. 109 Colloquially, I might label this with a double negative, “not-not-Monk” since the sensitivity is unreliable.

127

specificity discussion in so far as the sensitivity is shown that the model is successful at correctly

identifying something as not-Monk given that only three of the not-Monk category solos were

incorrectly attributed to the Monk category. Since I am relatively confident in the claim that Monk is

substantively different enough from others that his performances are not even grouped with others,

the features that loaded on this decision should be explored.

Presented in 6.2 is the feature importance graph for this model. Like the importance graph

from chapter 2, the further the line stretches from left to right, the more important that feature is in

determining the category. As is apparent, the most important feature by far in determining a solo

belongs to Monk is nPVI. This type of categorical modeling gives credibility to the idea that

rhythmic usage as expressed by mathematical variance in onsets demonstrates significant difference

in Monk’s playing. Though we are interpreting this analysis negatively in so far as the sensitivity of

this test is dubious, it is reasonable to assume that given the significant importance of this feature in

determining something is Monk, the inverse is also true—low nPVI is something we can certainly

attribute to not-Monk solos in this particular corpus.

No Yes No 437 3 Yes 3 10

Reference Pr

edic

tion

Accuracy: 98% ± 1% P < 0.05

Figure 6.2

Confusion Matrix of Predicted GLM with a 20/80 Split

128

Considering the validity of this claim requires a little more data analysis, namely the actual

nPVI ratings between our two groups. The boxplot shown in figure 6.3 shows the nPVI profile of

Thelonious Monk next to all other solos in the dataset. A few key things to note about this figure;

first, the mean nPVI between both categories is dramatically different, with the not-Monk category

mean nPVI equal to 52.7 and Monk’s mean nPVI roughly double that at 105.7. This disparity is

evidence to confirm that rhythmic variance significantly marks Monk’s playing. Musically, comparing

these two numbers could be explained by multiple variables, from unpredictability to a reliance on

more levels of subdivision, which may be less common in other players.

As the transcription below demonstrates, it seems more likely that a general feature of

Monk’s soloing is a reliance on more levels of subdivision. A second characteristic of Monk’s playing

Figure 6.3 Feature Importance Graph of Monk vs. Not-Monk GLM

129

compared to that of others as revealed in this boxplot is a general homogeneity in rhythmic usage in

the not-Monk data.110 With a mean of 52.7, a median of 53.0, and an inner-quartile range of 15.7, the

not-Monk data implies a general rhythmic usage that is not only lower than Monk’s, but is also fairly

homogeneous. To speculate, I hypothesize this relates to pattern usage given most patterns that

performers learn and utilize exist at one metric level throughout the entire pattern. Given the

conclusions in the analyses from previous chapters concerning Monk’s sparing use of these patterns,

it is reasonable to propose that the variance of both categories are also a product of their use of

patterns as they pertain to motivic development at differing hierarchical levels.111 As a demonstration

of these generalized characteristics, a transcription of the solos with mean nPVI variances are

reproduced below in figures 6.3 and 6.4.

Regarding Mulgrew Miller’s performance on “If I Were A Bell”, the general rhythmic usage

of eighth notes and quarter notes is apparent at first glance.112 With the exception of a handful of

triplet figures and a short double time run towards the end of the piece, Miller’s solo primarily

incorporates only two rhythmic levels. When comparing this excerpt to the excerpt of Monk’s solo

on “Reflections”, the disparity in rhythmic usage is ever more apparent. Most importantly, Monk’s

use of differing rhythmic levels throughout the solo (as opposed to primarily operating in eighth and

quarter notes).

110 For reasons similar to the arguments made regarding the comparative sample sizes of Monk versus not-Monk, I believe it is helpful to avoid inferring too much about the homogeneity or lack thereof in the Monk boxplot. 111 I do not want to over extend my conclusions but given Monk’s reliance on unique motives interspersed with patterns, this seems like a probable cause, even if it is just one component of this variance question. 112 Barron, Kenny (piano), Kenny Barron Trio, Live at Bradley’s (Sunnyside SSC3002, 2001), compact disc.

130

To conclude, Monk’s rhythmic usage is significantly different than other performers. Not

only does he use more levels of subdivision during his performances, but he also utilizes them in

arguably less predictable ways. His performances are marked by a general freedom in rhythmic

usage, often exploring—as can be seen in the transcriptions from previous chapters—subdivisions

that are smaller than sextuplets, and he even explores divisions of the beat that are arguably ametric,

even if some form of division has been attributed to the rhythm for the purposes of notation (like

his whole tone runs that span odd durations, e.g. 11-notes in the space of one half note).113 Further

113 See m. 12 of Monk’s solo on Ask Me Now, figure 4.5.

Figure 6.4 Boxplot of nPVI for Monk (1) and not-Monk (2) categories.

131

research exploring this component of his performance would do well to not just explore notational

variance, as I have limited myself to in this epilogue, but also real performance timing variances.

This would likely result in even more clarification in how Monk utilized time feel and rhythm

differently than other performers. Furthermore, the relationship between pattern usage and

rhythmic variance is a route that could be explored further. While I hypothesize that pattern usage

and rhythmic variance are correlated, to what extent these features correlate is an important

question.

More generally, the question of influence is of the utmost importance to such a discussion of

pattern usage considering the premise of this argument is that certain patterns are learned by all, and

thus they influence all, jazz practitioners. Given that Monk’s pattern usage is markedly different in

their application, to what extent does Monk’s performance practice influence the next generation?

As was noted in chapter 2, Monk often groups with performers that are a generation or two beyond

his own contemporaries. Is that Monk’s influence? Was Monk ahead of his time? What is Monk’s

relationship to future performers? These are all questions that could be explored that extend beyond

his motivic and developmental logic.

Overall, Thelonious Monk is a musical non-conformist. His idiomaticism is apparent, and he

was clearly after a different aesthetic than others in the genre. I agree with Solis’ claim that Monk

created a “world” in his performances. His ambition to create something new in his solos via

foreground developmental logic arguably relates more to composition per se than improvisation. His

control over melodic material allowed him to guide the listener into a new place, somewhere

different than other soloists of his generation were attempting to take their audience.

132

Figure 6.5

& bbbb 44 ‰ œ œ œ œn œ ≈ œb œ œb œn œ3

A bmaj7 G b7 F 7(#11) E7(#11)

œ œ œ œ œ œn œ œn œ œ œ œn œ œn3B bmin7 Eb7( b 9) œb œ œ .˙A maj7 B bmin7 Bmin7

& bbbb4

œ œ œ œ œb œ œ œ œb œ œ œ œn œ œ œ3

C ø F 7( b 9)

œ œ œ œ ÓB bmin7

‰ œ œ œn œ œ œ œ œ œ œ œn œ œ œ3

Eb7( b 9)

& bbbb7 ‰œ œ œ œ œ œb œ œ œ œn œn œ œ3 3

A bmaj7 A dim œ œ œb ≈ œ œ œ œ œn œ œn œ ≈ œn œ œn œ3

3

B bmin7

‰ œ œ œ œn œb œ œ ≈ œ œn œEb7( b 9)

& bbbb10 Œ ≈ œ œ œ œ œ œn œ œn œ œn œ œn3A bmaj7 G b7 F 7(#11) E7(#11) œb œ œ œ œ ŒB bmin7 Eb7( b 9)

œ œ œ œ œb œ œ œ œb œ œ œn3A maj7 B bmin7 Bmin7

& bbbb13 Ó ≈ œ œ œ œ œ œ œ3

3

C ø F 7( b 9) œ œ œ œ# œ œ œ œ œn œb œ œn œ œnB bmin7

œ œ œ œ œ ‰ . rœEb7( b 9)

& bbbb16

œ œb œ œ ≈ œ ≈ œ œ œ œ œn œ œA bmaj7 A dim

‰ jœ œ œ œ .œ Jœ3

B bmin7 Eb7( b 9)

jœ ‰ œ œ œ Ó3A b7 A bmin7D b7

& bbbb19 ‰ œ œ œn œ œ œ ≈ œ œ œ œ œ œ œ œn3

C 7( b 9)

œ Œ ÓFmin -maj7-min7

Œ œ œ œ œ œ ‰ œ3

Fmin7

& bbbb22 ˙ ˙B b7sus B b7( b 9)

œ œ œ .œ jœB bmin7

œ œ œ œ œ œ œ œn œ œn œ œn œ œn œEb7sus A 7

Reflections Comp: Thelonious Monk

©

Score

As performed on "Thelonious Monk Trio"

(1954)Thelonious Monk

& bbbb25

œ œ ‰ Jœ œn œ œ œ œ œb œb œA bmaj7 G b7 F7(#11) E7(#11)

œ œ œ œ œ œ œ œ œ œn œ œn œ œn œ œ œ3

3

B bmin7 Eb7( b9)

œb œ œ .˙3

Amaj7 B bmin7Bmin7

& bbbb28

œ œ œ œ œb œ œ œ œb œ œ œ œ œ œ œ3

C ø F7( b9)œ œ œ Ó

B bmin7 œ œ œ œ œ œ œ œ ‰ jœ œ œ œn œEb7( b9)

& bbbb31 ≈ œ ≈ œ œ œ œ œ œb œ œ œn œ œ œ œ œb3A bmaj7 Adim

œ œ œ œ œ œ œ œ œ œ œ œ œ œ3

2 Reflections

133

Figure 6.6 (cont.)

& b 44 ww#nG 7

‰ Jœœ ..˙˙#C7

œœn ..˙˙bFmaj7

Ó œ œ œ œ œ .œ JœAmin7(b5)

wD 7

& b7 œ œ œ .œ JœG 7

œ# Œ ÓC7

Œ œ œb œ œb œ œbFmaj7

œ œ œ œB b7

.œ jœ œ œ œ œFmaj7

& b12 ∑Emin7(b5)

A 7

‰ jœ œ œ œDmin7 /C œ œ œ Œ œ œ#

Bmin7 E7

œ œ# œn œ œ# œ# œn œbAmaj7

œ œ Œ œ œ œ œ

& b17 œ œ œ œ œœb ŒG 7

Ó Œ œ# œC7

œ œn œb œ œ œ œb œFmaj7

œb œb œ œn Ó

& b21

œ œb œ œ œ œb œ œAmin7(b5) œ œ œ ˙D 7 œ# œœ œ œ œnG 7

Jœb .œ œn œ œC7 ˙ ÓFmaj7

& b26 œ œ œ œ œB b7 œ œ jœ# ..œœ JœFmaj7

wD 7

Œ ‰ Jœ œ œGmin7 œ œ œ œb œC7

& b31 ‰ œb œ œ œ œb œ œbFmaj7 œ œb œ œ œb œ œb œbD 7

wG 7

Œ œ œ œC7

Ó œ œ œFmaj7

& b36

œ œ œ œ Œ Ó œb œ œAmin7(b5)

œ œb œ œ ŒD 7

œ# œ œ œ œnG 7

œb œ œb œn œ œC7

If I Were A BellComp: Frank Loesser

Score

Performed on "Live At Yoshi's" (2003)Mulgrew Miller

134

Figure 6.6 (cont.)

& b41 œ Œ ÓFmaj7 œb œn œ œb œ œb œ œ

B b7

œ œ œ œFmaj7

˙ œ œ œ3

Emin7(b5)A 7

œ œ œ ‰ jœ œDmin7 /C

& b46 Œ œ# œn œ œ œ œ#Bmin7 E7

œ œ# œn œ œb œb œ œbAmaj7

œ œ œ œ œ œb œ œb œ œ œb œ œn œ œb œnG 7

& b50 œ œb œ( ) œb œ œb œC7

Œ œ œ œ( ) œ œ œFmaj7

œ( ) œ œ œ œ œ# œ œ œn ‰ .œ ÓAmin7(b5)

& b54 œb œ œ œ œb œ œ œ œD 7

œb œb œ œb œ œ œn œG 7

œ œ œ œ œ# œC7

Ó œ œ œ œ œFmaj7

& b58 œ œ œ œ ÓB b7 œœ œb œ ‰ œ œ œFmaj7 œ œ œ# œb ‰ Jœb Œ

D 7

Œ ‰ jœ œ œ œGmin7

jœ# ˙̇ œ œ œC7

& b63 œ œn œ œ#Fmaj7

˙ œ œ œD 7

jœ# wG 7

Œ œ œ œ ‰ œC7

œ œ ‰ œ ˙Fmaj7

& b68 Œ œ œ œ ‰ œ œ œ ‰ œ ˙Amin7(b5)

Ó œ# œ ‰ œD 7

.˙ œn œbG 7

œ œ# œ ˙C7

& b73

˙ jœ# œ œFmaj7

˙ jœ# œ œB b7 œ œ œb œ œb œ œFmaj7

.œ Jœ œ œ œEmin7(b5) A 7

œ œ œ ÓDmin7 /C

& b78 Œ ‰ Jœ œ œ œ#Bmin7 E7

‰ Jœ# œ ˙Amaj7 œ œ# œn œ œb œb œ œb œ œ œ œ œ# œG 7

˙# ÓC7

2 If I Were A Bell

135

Figure 6.6 (cont.)

& b121 ‰ œb œn œ œb œ œ œ œ3

Fmaj7 œ œ œb ‰ Jœ œnB b7

œ œ œb œ œœnb œ œbFmaj7

œ œb œ œb œ œ œ œD 7

& b125 œ œ œ œ ŒGmin7

œb œb œb ÓC7

œ œ œ œn œ œ œFmaj7

œ œ# œ œn œ œ# œ œD 7

œœb Œ ÓG 7

& b130 ‰ Jœ œ œ œC7 œ œ œ œFmaj7 .œ Jœ œ œ œb ˙ ÓAmin7(b5) œ œn œb œb œ œb œ œbD 7

& b135 œ œ œ# œ# œn œn œnG 7

œ œ œb œb œ œbC7

œn œ œ œ œ œ œFmaj7

œ œ ‰ œ œb œ œb œbB b7

& b139

œ œ œ œFmaj7

œ œ œ œEmin7(b5) A 7

wDmin7 /C

˙ ‰ œ œ œ#Bmin7 E7

œ œ# œn œ œœ# œAmaj7

& b √144 Ó Œ œ œœ œœ Œ Œ jœ# œG 7 œœ œœ Œ Œ œ# œC7 œ œb œ œ œ œ œ œnFmaj7

œ œn œ œ œ œb œ

& b149 œ# œ œ œ œ œ œ œAmin7(b5)

Ó Œ ‰ jœ JœbD 7

‰ œb œ œb œ œ œ#G 7

œ œœ œ œ ŒC7

œ œ œ œFmaj7

& b154 œ œ œ œ œ œB b7

œ ‰ jœ# Jœœ ˙Fmaj7

Ó ‰ œ œb œD 7 œn œb œb œ œb œnGmin7

& b158œb œb œb œ œb œb œ œ

C7

œ œ Œ ˙Fmaj7

Ó œ œD 7jœ# ..œœ Jœ œn œ œ œœbG 7

4 If I Were A Bell

136

Figure 6.6 (cont.)

& b83 œb œ œ ˙Fmaj7

œ œn ‰ œ ˙ œb œb œ ˙Amin7(b5)

∑D 7

‰ œ œb œ œn œ œb œnG 7

& b88 œb œb œn œ œb œ œb œbC7

œ œ œ œFmaj7

œ œ œ œ ‰ jœ ŒB b7

Ó œ œ œ œ œb3

Fmaj7

& b92 œ œb œ œ ‰ œb ‰ œ#D 7

œ œ œ œ œœ œœbbGmin7

œœ Œ Œ œC7

œ œb œ œ œ œ œFmaj7

& b96 œb œn œ œb œ œb œnD 7

œ .˙G 7

jœ# œ œ jœ# .œ JœC7 œ œ œ œ Œ

Fmaj7

∑

& b101 Óœ œb œbAmin7(b5) œ œ œ œ œb œ œn œD 7

œb œn œb œb œ œb œ œbG 7

œ œ œn œ œb œ œ œC7

& b105 œb œ œb œb œ œn œn œFmaj7

œ œ œ œ œ œ œ œB b7œ œb œ œb œ œ œ œ

Fmaj7

œ# œ ˙Emin7(b5) A 7

& b109 ‰ œ œ# œ œ œb œDmin7 /C

‰ jœ œ œb œ ŒBmin7 E7

œ# œn œn ‰ œb œb œ œbAmaj7

œ œb œ œ œ œ œ œb

& b√

113 œ# œ ‰ œb Jœ# .œG 7 ˙ œb œ œ œC7

Œ œ œn œ œ ŒFmaj7

œ# œn œ œb œ œn œb œ

& b√117 œb œb œ œ œ œb œ œ

Amin7(b5)

œb œ œb œb œ œb œ œD 7

jœ# œ .˙G 7

∑C7

3If I Were A Bell

137

Figure 6.6 (cont.)

& b√

162 ‰ jœ# ..œœ œ œ œC7

œ œn œ œ#Fmaj7

œ Œ œ œ œb œœ œb œ œ œ œ œb œAmin7(b5)

& b(√) √

166 œ œb œ œn œ œb œn œbD 7 œŒ Œ

œ œ œb3

G 7 œ œb œ œ œ œ œb œC7

œb œb œ œ œ œ œb œFmaj7

& b(√) √170 œ œ œ œ œ œn œ œbB b7

œ œ œ œ œ œ# œ œnFmaj7

œ# œ œn œb œ œ œ œEmin7(b5) A 7

œ œ œb œ œ œ œb œ œb3Dmin7 /C

& b (√)174 œ œb œ œb œ œ œn œBmin7 E7

œ# œ œ œn œ œb œb œ œb œ3

3Amaj7

œ œ œ œ œn œ œ œ œ œ3

3

& b177 œb œ œb œ œ œb œ œ œ œ3

3G 7

œ œ œ œ œ œ# œ œC7

œb œb œb œ œ œ œFmaj7

jœ .œ œ œ# œn œ#& b181 Œ œb œb œb œn Œ

Amin7(b5)

œb œ œb œ œ œb œ œD 7

˙ œ œ œG 7

œ œ œ jœb ˙̇nC7 œœ œ œ œ œœ ŒFmaj7

& b186 œœ œ ‰ œ œœ ŒB b7 œœ œ œ œ œœ œ œ œ

Fmaj7 œœ ‰jœ# Jœ ˙D 7

Ó Œ œGmin7 œ# œ œ œn œb œC7

& b191 œn œ œb œ ŒFmaj7

Jœb .œ Jœ .œnD 7

Jœb .œb Jœ .œnG 7

œ œ# œb œn œ œ œnC7

& b195

Jœb .œb œ œn œn œ#Fmaj7

œ œ œn ˙ jœ .œ jœ# .œAmin7(b5)

œ œ œ œ œb œb œ œbD 7

5If I Were A Bell

138

Figure 6.6 (cont.)

& b199

œ œ œ œ œ œb œb œbG 7

œ œb œb œb œn œ œ œC7

œb œb œ œ œ œ œb œFmaj7 œ œ œ œ œ œ œbB b7

& b√

203 œ œ œ œ œ œ( )Fmaj7

œ# œ œ œ œ œb œb œ œ œb œ œ3

33 3

Emin7(b5) A 7

œb œb œ œ œb œ œn œb œn œ œ œ3 3 3 3

Dmin7 /C

& b(√)

206 œb œn œ œ œ œ œ œb œb œ œ œb œ œ3 3

Bmin7 E7

œ# œ œ œn œ œ# œ# œn œb œ œ3

33

Amaj7

& b(√)

208 œ œ œn œ œ œb œn œ œ œ œ œ œ œ3

3 œ œ œ œ œb œ# œ œ œ œ œ#3

3 3

G 7

œ œ œn œb œ œ œ œb .œ Œ3

C7

& b√ √

211 Ó œ œ œ œFmaj7

œ œ œ œ œ œ œ œ œ œ œ œ œ œAmin7(b5)

œ# œ œb œ œn œ œ#D 7

œ œœ œœ œG 7

& b (√)216 œ œœ œœ œœC7 œœ œœ œœ œœFmaj7 œœ Œ ‰

œ œ œB b7 œ œœ œœ œFmaj7 œœ# Œ ‰œ œ œD 7

& b221 œ œœ œ œœGmin7 œœ Œ ‰ Jœ œ œ œ3

C7 œ œœ œ œœœFmaj7 œœ Œ ‰œ œ œD 7 œ œœn œœ œœG 7

& b√

226œœ ‰ Jœ œ œ œC7 œ œœ œ œœFmaj7 œ Œ ˙b œ œb œ œ œ œb œ œAmin7(b5) ˙̇ œ ‰ Jœ#D 7

& b(√)

231 œn œb œb œn œb œb œ œbG 7

‰ œb œ œ œb œ œn œnC7

œb œ œn œ œb œ( )œ œbFmaj7

œn œ œb œ œ œ œb œB b7

6 If I Were A Bell

139

Figure 6.6 (cont.)

& b235

œb œb œ œ œ œ œn œFmaj7

œ œb œ œb œ œ œ œbEmin7(b5) A 7 œ œ œ œDmin7 /C œ œ œ œ œ œ œ œ3 3

Bmin7 E7

& b239 œ œ œ œn œ œ# œ œ3

Amaj7

œ# œ# œn œb œ œ œb œ œ œb œ œb œ œb œ œbG 7 œœ œb œ œ œC7

& b√

243 Jœ .œb œ œ œbFmaj7 ˙ œb œn œ œ Œ œ œ œ œAmin7(b5) œ œb œ œ œ œ œ œbD 7 œ Œ ÓG 7

& b(√) √

248 œb œ œ œ œ œ œb œ œ3

C7

œ œ œ œ œ œ œ œnFmaj7 œœ œœ ÓB b7

Œjœ ..˙̇

@Fmaj7 ˙̇ œ œ œ œD 7

& b√253 œ œœb œœn ˙̇Gmin7

Œœœ œ œ œ œC7

œ jœ# œœ ˙Fmaj7

Ó ‰ œ œ œD 7

œ œ œ œ œ œb œb œbG 7

& b258 œb œb œb œb œ œ œC7

œ œ œ œ œb œb œn œFmaj7

œb œ œ œb œ œ œ œ œ Œ Œ œb œAmin7(b5)

& b262

œ œ œ œ œb œb œ œbD 7

œ œ# œ œ œ œG 7

œ# œ œ# œnC7

œ œb œ œbFmaj7

œ œ œ œB b7

& b267

œ# œ œ œFmaj7

œ œ œ œEmin7(b5)A 7

œ œ œ œDmin7 /C œ œ œ œ# Jœ œ JœBmin7 E7

œ œ# œ# œ# œ œ# œ# œ#Amaj7 œ œ# œ# œ#Ó

& b√273 jœ# ˙̇ ˙G 7

jœ# ˙̇ œ œb œœnC7

‰ œ Jœ œ œFmaj7 jœ# œœ œ œ œ ‰ jœ Jœœ

7If I Were A Bell

140

Figure 6.6

& b√277 œœ œ œ œœ Œ

Amin7(b5)

∑D 7

œ œ œ œ# œ œb œbG 7

& b280 œ œ œb œ œb œb œ œC7

œ Œ œœ œœFmaj7 œ œ œ œb œB b7 .˙ œ œFmaj7 .˙ œœ œœ

D 7

& b285 œœ œœ œœ œœ œœGmin7 œœ œœ œœ œ

C7

wFmaj7

∑D 7

8 If I Were A Bell

141

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Discography

Barron, Kenny (piano), Kenny Barron Trio. Live at Bradley’s. Sunnyside SSC3002, 2001, compact disc.

Bird and Diz. Verve Record 314 521 436-2, 1997, compact disc.

Byas, Don. Don Byas – Moon Nocturne. Membran Music Ltd. 222414-444/A, 2005, compact disc.

Corea, Chick. Inner Space. Collectable COL-CD-6910, 2008, compact disc.

Eldridge, Roy (trumpet), Zoot Sims, Quadromanio Jazz Edition, Zoot Sims, That Old Feeling, CD 1. Membran Music Ltd. 222478444, 2005, compact disc.

Evans, Bill (piano), Bill Evans Trio. Sunday at the Village Vanguard. Riverside Records RCD-9376-2, 2005, compact disc.

Higginbotham, J.C. (trombone), Sidney Bechet. The Cradle of Jazz – Sidney Bechet – Chant In the Night CD 2. Trumpets of Jericho Ltd. 20.3010-HI, compact disc.

Konitz, Lee. Sax of a Kind. Membran Music Ltd. 222453-444A, 2005, compact disc.

Mehldau, Brad (piano), Brad Mehldau Trio. Art of the Trio – Recordings: 1996-2001. Nonesuch 517129-2, 2001, compact disc.

Miles Davis All-Stars. Walkin’. Prestige PRCD-30008-2 P7075, 2006, compact disc.

Monk, Thelonious. Monk’s Music. Riverside Records RCD-242-2, 2001, compact disc.

———. Solo Monk. Columbia, Legacy CK62533, 2003, compact disc.

——— (piano), Thelonious Monk Trio. Thelonious Monk Trio. Prestige PRCD-30164, 2007, compact disc.

Navarro, Fats. From Swing to Bebop, Double Talk, Fats Navarro CD 1. Trumpets of Jericho Ltd. 20.1976-HI, 1998, compact disc.

145

Appendix 1. Patterns Included in the Model

& œb œ .˙ œ œ .˙ œb œn œb œ .˙

& œ œ œ œ ˙b œ œ œ œb Ó

& ‰ Jœ œ œ œb œ œb Œ œ œ œ œ œ œ œ œb œ Ó

& œ œ œ œb jœ .œ

& œ œb œN œ Jœ .œ

& œ œ œ œ œ œb œ œ œ œb œ œb

& œ œb œb œb œ œ œ œ œ œ œb œ œ œ

& œ œb œb œb œ œ œ œ œb œ œ œ œ# œb œ#

Enclosure

C.E.S.H

"Cry Me A River" Lick

"Gone But Not Forgotten" Lick

enca encb

cesha ceshb

ceshc ceshd

cry

gone

encc

Running Changesrc1 rc2a/d rc3

rc4 rc5a/d rc6

rc7a/d rc8 rc9a/d

& œ œ œ œ ˙D-7 G7

œ œ œb œ ˙Dø7 G7

& œ œ œ œ œ œ œ œD-7 G7 œ œ œ œ œ œb œ œ

Dø7 G7

& œ œ œ œ œ œ œ œD-7 G7 œ œ œ œ œ œb œ œDø7 G7

& œ œ œb œ ˙ œ œ œb œn ˙

& œ œb œ œ ˙ œ œ œ œ# ˙

& œ œ œb œ Ó œ œb œn ˙

& œ œ œb œ œ œ Œ œ œ œb œ œ œ Œ

ii-V's

iiVa1 iiVa2

Bebop

iiVb1 iiVb2

iiVc1 iiVc2

bba1 bba2

bbb1 bbb2

bbc1 bbc2

bbd1 bbd2

146

& œ œ œ œ œ œ œb œ œ œ œb œb

& œ œb œb œb œ œ œ œ œ œ œb œ

& œ œ œ œ# œ# œ œ œ œ# œ œ#

& œ œb œb œn œ# œ œ œ œb œ œ# œ#

dp1a/d dp2a/d dp3a/d

dp4a/d dp5a/d dp6a/d

Digital Patterns

Scalar Ideaswt1 wt2

oct1 oct2

147

Appendix 2. Clustering and Distance Metrics

Cluster Center 1 -2.287 -0.090 Cluster 1 1.151Cluster Center 2 -0.049 0.132 Cluster 3 1.020Cluster Center 3 2.015 -0.148 Cluster 2 1.331

File PC1 PC2 ClustersDistance To

CenterNumber in

ClusterjCHigginbotham_BabyWontYouPleaseComeHome -2.207 -0.143 1 0.096 1lesterYoung_DestinationKC -2.207 -0.115 1 0.084 2chickCorea_Windows -2.207 0.045 1 0.157 3benWebster_DidYouCallHerToday -2.207 0.015 1 0.132 4dickieWells_IGotRhythm -2.207 0.182 1 0.284 5sonnyRollins_PlayinInTheYard1 -2.207 0.098 1 0.204 6jJJohnson_CrazyRhythm -2.207 -0.084 1 0.080 7steveLacy_LetsCoolOne -2.207 -0.396 1 0.316 8milesDavis_Oleo2 -2.207 -0.414 1 0.334 9dexterGordon_Montmartre -2.207 -0.441 1 0.361 10zootSims_DancingInTheDark2 -2.207 -0.108 1 0.082 11benWebster_NightAndDay -2.207 -0.371 1 0.292 12milesDavis_Oleo1 -2.207 -0.488 1 0.406 13gerryMulligan_WalkingShoes -2.207 -0.482 1 0.400 14chickCorea_SambaYantra -2.207 0.359 1 0.456 15woodyShaw_IfIWereABell -2.207 -0.500 1 0.418 16wayneShorter_SpeakNoEvil -2.207 -0.283 1 0.209 17lionelHampton_Dinah -2.207 0.087 1 0.194 18davidLiebman_Pendulum -2.207 0.203 1 0.304 19wyntonMarsalis_YoureMyEverything -2.207 0.381 1 0.477 20milesDavis_EightyOne -2.207 0.040 1 0.153 21milesDavis_KCBlues -2.207 0.040 1 0.153 22jJJohnson_Teapot -2.207 -0.397 1 0.318 23rexStewart_Perdido -2.207 -0.600 1 0.516 24henryAllen_BabyWontYouPleaseComeHome -2.207 -0.386 1 0.307 25mccoyTyner_PassionDance -2.207 -0.046 1 0.091 26lesterYoung_SixCatsAndAPrince -2.207 -0.011 1 0.112 27curtisFuller_DownUnder -2.207 -0.218 1 0.152 28bobBerg_NatureOfTheBeast -2.207 -0.142 1 0.095 29steveColeman_DoubleVision -2.207 -0.526 1 0.443 30theloniousMonk_imConfessinThatILoveYou -2.207 0.503 1 0.598 31paulDesmond_BossaAntigua -2.207 -0.123 1 0.087 32wayneShorter_Orbits -2.207 0.380 1 0.477 33milesDavis_Walkin -2.207 0.122 1 0.226 34

CENTROID X,Y Mean Distance to Centroid

148

milesDavis_BluesByFive -2.207 -0.753 1 0.669 35johnColtrane_BodyAndSoul -2.207 0.553 1 0.648 36curtisFuller_BlueTrain -2.207 0.558 1 0.653 37woodyShaw_SteppingStone -2.207 0.076 1 0.184 38herbieHancock_Agitation -2.207 0.519 1 0.614 39jJJohnson_Elora -2.207 0.588 1 0.683 40johnnyHodges_EarlyMorningRock -2.207 -0.380 1 0.301 41woodyShaw_InACapricornianWay -2.207 -0.584 1 0.500 42buckClayton_DickiesDream -2.207 0.619 1 0.713 43wayneShorter_AdamsApple -2.207 -0.769 1 0.684 44royEldridge_KingDavid -2.207 -0.152 1 0.101 45lesterYoung_AfterTheatreJump -2.207 0.709 1 0.802 46wayneShorter_InfantEyes -2.207 -0.442 1 0.361 47steveColeman_Segment -2.207 0.364 1 0.461 48wyntonKelly_ThisIDigOfYou2 -2.207 0.767 1 0.861 49louisArmstrong_GutBucketBlues -2.207 0.694 1 0.788 50royEldridge_St.LouisBlues -2.207 -0.747 1 0.662 51bixBeiderbecke_Margie -2.207 -0.839 1 0.754 52johnColtrane_TranesBlues -2.207 0.532 1 0.627 53steveColeman_TheOracle1 -2.207 0.589 1 0.683 54donByas_BeBop -2.207 -0.203 1 0.139 55steveColeman_TakeTheColtrane -2.207 0.324 1 0.421 56donEllis_YouSteppedOutOfADream2 -2.207 -1.113 1 1.027 57sidneyBechet_BabyWontYouPleaseComeHome -2.207 -0.940 1 0.854 58louisArmstrong_OnceInAWhile -2.207 -0.826 1 0.740 59cliffordBrown_Sandu -2.207 -1.126 1 1.039 60milesDavis_VierdBlues -2.207 -0.927 1 0.841 61kidOry_WhosIt -2.207 -0.089 1 0.080 62kidOry_GotNoBlues -2.207 0.953 1 1.046 63louisArmstrong_BigButterAndEggMan -2.207 1.046 1 1.139 64leeMorgan_TotemPole -2.207 -0.657 1 0.573 65milesDavis_BitchesBrew2 -2.207 -0.111 1 0.083 66milesDavis_BitchesBrew1 -2.207 -0.586 1 0.503 67dickieWells_JoJo -2.306 1.124 1 1.214 68charlieParker_Segment -1.373 0.831 1 1.298 69donEllis_JohnnyComeLately -1.030 -0.550 1 1.339 70bixBeiderbecke_ImComingVirginia -2.009 1.174 1 1.294 71buckClayton_DestinationKC -3.354 -0.687 1 1.222 72freddieHubbard_DownUnder -1.907 -1.347 1 1.313 73wyntonMarsalis_UMMG -1.969 -1.363 1 1.313 74milesDavis_TranesBlues -3.001 -1.129 1 1.261 75steveLacy_Work -3.521 0.098 1 1.248 76

149

paulDesmond_Alianca1 -2.775 -1.302 1 1.307 77herbieHancock_Riot -2.495 -1.396 1 1.323 78patMetheny_NothingPersonal -1.336 0.926 1 1.392 79kennyDorham_InNOut -1.550 -1.285 1 1.405 80milesDavis_ESP -1.739 -1.385 1 1.407 81paulDesmond_TheGirlFromEast9thStreet -2.983 1.083 1 1.364 82davidMurray_BodyAndSoul2 -1.640 -1.387 1 1.450 83louisArmstrong_MuskratRamble -2.673 1.259 1 1.403 84milesDavis_MilesRunsTheVoodooDown1 -1.542 -1.356 1 1.469 85dickieWells_AfterTheatreJump -2.068 1.342 1 1.448 86milesDavis_MilesRunsTheVoodooDown2 -2.797 -1.421 1 1.426 87kaiWinding_TinysBlues -2.006 -1.550 1 1.487 88MilesDavis_NoBlues -3.640 -0.569 1 1.435 89lesterYoung_DBBlues -2.074 -1.583 1 1.508 90lionelHampton_Avalon -3.619 -0.638 1 1.441 91donByas_HarvardBlues2 -3.739 -0.003 1 1.454 92sonnyRollins_PlayinInTheYard2 -1.678 -1.521 1 1.556 93kennyGarrett_BrotherHubbard1 -1.174 -1.214 1 1.582 94steveColeman_CrossFade1 -1.526 -1.475 1 1.580 95curtisFuller_KillerJoe -1.203 -1.308 1 1.631 96dickieWells_DestinationKC -3.822 0.020 1 1.539 97ericDolphy_DahomeyDance -0.607 -0.295 1 1.692 98paulDesmond_Alianca2 -2.507 1.536 1 1.641 99kidOry_SavoyBlues -3.457 1.053 1 1.635 100louisArmstrong_BasinStreetBlues -1.257 1.303 1 1.732 101bixBeiderbecke_SinginTheBlues -3.656 0.814 1 1.640 102steveLacy_AloneTogether -3.009 1.434 1 1.686 103johnColtrane_BessiesBlues -1.291 -1.563 1 1.779 104kidOry_GutBucketBlues -3.348 1.272 1 1.726 105milesDavis_SoWhat -3.807 0.813 1 1.768 106theloniousMonk_rhythmANing -1.740 1.770 1 1.938 107fatsNavarro_TheSkunk -1.093 -1.655 1 1.968 108kennyDorham_Doodlin -1.827 1.809 1 1.953 109lionelHampton_RunninWild -1.689 1.787 1 1.970 110kennyDorham_Punjab -1.190 -1.794 1 2.027 111milesDavis_Orbits -1.345 -1.885 1 2.028 112johnColtrane_GiantSteps2 -1.071 1.545 1 2.037 113natAdderley_BohemiaAfterDark -1.353 -1.907 1 2.044 114milesDavis_Agitation -2.222 -2.122 1 2.033 115wyntonMarsalis_CherokeeII -0.912 -1.762 1 2.166 116buckClayton_AfterTheatreJump -3.333 1.729 1 2.098 117cliffordBrown_JoySpring -0.268 -1.039 1 2.232 118

150

louisArmstrong_CornetChopSuey -2.618 2.059 1 2.174 119benWebster_WhereOrWhen -1.609 -2.206 1 2.223 120johnnyDodds_GotNoBlues -1.793 2.084 1 2.230 121milesDavis_Dolores -1.508 -2.223 1 2.271 122dickieWells_SixCatsAndAPrince -4.353 0.945 1 2.311 123bixBeiderbecke_RiverboatShuffle -1.224 2.109 1 2.442 124zootSims_DancingInTheDark1 -4.733 0.185 1 2.461 125steveLacy_AskMeNow -1.687 2.400 1 2.561 126milesDavis_TuneUp -0.862 -2.248 1 2.587 127cliffordBrown_I'llRememberApril_AlternateTake2 -0.455 -2.089 1 2.712 128zootSims_KingDavid -4.967 1.461 1 3.096 129bennyGoodman_HandfulofKeys -2.837 3.034 1 3.171 130dickieWells_DickiesDream -5.485 1.367 1 3.514 131kidOry_MuskratRamble -5.751 0.494 1 3.513 132donByas_HarvardBlues1 -6.912 0.637 1 4.681 133royEldridge_Undecided -0.042 0.137 2 0.009 1joeLovano_LonniesLament -0.100 0.150 2 0.054 2natAdderley_WorkSong -0.168 0.144 2 0.120 3bobBerg_Angles 0.026 0.253 2 0.143 4davidLiebman_ThereWillNeverBeAnotherYou -0.126 0.026 2 0.131 5leeMorgan_JustOneOfThoseThings -0.166 0.233 2 0.155 6artPepper_Anthropology -0.040 -0.018 2 0.150 7michaelBrecker_Peep 0.114 0.149 2 0.164 8bennyGoodman_RunninWild 0.090 0.258 2 0.187 9joeHenderson_In'NOut2 -0.159 -0.002 2 0.173 10johnColtrane_Oleo 0.139 0.217 2 0.206 11steveColeman_SlippedAgain -0.221 -0.043 2 0.246 12steveTurre_StevesBlues -0.266 0.288 2 0.268 13stanGetz_Insensatez 0.086 -0.095 2 0.263 14kennyKirkland_Chance_bootleg -0.218 0.349 2 0.275 15branfordMarsalis_UMMG 0.228 0.022 2 0.298 16bennyGoodman_TigerRag1 -0.173 -0.141 2 0.300 17bennyCarter_ItsAWonderfulWorld2 0.254 0.062 2 0.311 18chickCorea_IHearARhapsody 0.259 0.220 2 0.320 19johnnyHodges_Bunny -0.292 0.343 2 0.322 20michaelBrecker_MidnightVoyage -0.212 0.418 2 0.329 21bobBerg_NoMoe -0.177 0.437 2 0.331 22freddieHubbard_SocietyRed 0.194 -0.092 2 0.331 23stanGetz_CrazyRhythm -0.364 0.023 2 0.334 24sonnyRollins_StThomas2 0.283 0.044 2 0.343 25kennyWheeler_SlippedAgain 0.254 -0.055 2 0.356 26lionelHampton_Whispering -0.314 0.402 2 0.378 27

151

johnColtrane_GiantSteps1 -0.420 0.124 2 0.372 28chickCorea_Matrix -0.113 -0.232 2 0.370 29kennyKirkalnd_MrJC -0.301 0.435 2 0.394 30wyntonKelly_FreddieFreeloader -0.140 0.522 2 0.401 31steveColeman_TheOracle2 0.320 -0.013 2 0.396 32wyntonKelly_DigDis -0.018 -0.273 2 0.406 33steveColeman_Processional 0.028 0.550 2 0.425 34gerryMulligan_LineForLyons -0.439 0.311 2 0.430 35charlieParker_Ornithology 0.198 0.500 2 0.442 36chrisPotter_Rumples -0.480 0.313 2 0.467 37johnnyDodds_OnceInAWhile -0.484 -0.026 2 0.463 38johnnyDodds_HotterThanThat 0.339 0.416 2 0.480 39fatsNavarro_Anthropology_No1 0.386 0.338 2 0.481 40chuBerry_BodyAndSoul2 -0.306 -0.297 2 0.500 41aulDesmond_SambaCantina1 0.309 -0.234 2 0.512 42woodyShaw_Rosewood 0.348 0.491 2 0.535 43gerryMulligan_Bunny 0.494 0.218 2 0.549 44sonnyRollins_StThomas 0.287 0.574 2 0.555 45hankMobley_LadyBird -0.004 0.687 2 0.557 46leeKonitz_BopGoesToLeesel -0.347 -0.321 2 0.543 47johnColtrane_262 -0.368 0.589 2 0.557 48chickCorea_StellaByStarlight 0.328 0.552 2 0.564 49colemanHawkins_ItsOnlyAPapermoon 0.420 -0.228 2 0.591 50charlieParker_ThrivingOnARiff -0.152 0.728 2 0.605 51kennyKirkland_MyIdeal -0.209 -0.436 2 0.590 52cannonballAdderley_ThisHere 0.218 0.681 2 0.610 53paulDesmond_BlueRondoALaTurk 0.517 0.389 2 0.622 54donEllis_ILoveYou -0.661 0.169 2 0.613 55dizzyGillespie_HotHouse 0.560 0.021 2 0.618 56sonnyRollins_Airegin 0.548 -0.045 2 0.622 57sonnyRollins_TenorMadness -0.455 0.617 2 0.633 58charlieParker_YardbirdSuite -0.281 0.733 2 0.644 59branfordMarsalis_GutbucketSteepy 0.079 0.777 2 0.658 60johnnyDodds_MyHeart 0.369 -0.361 2 0.646 61davidLiebman_IveGotYouUnderMySkin -0.264 0.763 2 0.666 62kennyKirkland_Dienda 0.409 -0.378 2 0.685 63steveTurre_IfIWereABell -0.519 0.650 2 0.700 64milesDavis_Oleo 0.452 0.635 2 0.709 65wyntonKelly_DigDis2 0.592 -0.170 2 0.708 66branfordMarsalis_HousedFromEdward2 0.260 -0.500 2 0.703 67sonnyRollins_TheEverywhereCalypso1 0.421 0.681 2 0.722 68dizzyGillespie_BluenBoogie 0.571 -0.223 2 0.715 69

152

horaceSilver_TheBackBeat 0.687 0.126 2 0.736 70michaelBrecker_DeltaCityBlues -0.590 0.650 2 0.750 71sonnyRollins_StThomas1 -0.661 0.574 2 0.755 72woodyShaw_Solid 0.537 -0.350 2 0.758 73freddieHubbard_DolphinDance 0.509 0.668 2 0.773 74davidLiebman_Milestones 0.608 -0.259 2 0.764 75gerryMulligan_TheRedDoor -0.646 0.624 2 0.773 76chickCorea_Spain -0.774 0.410 2 0.777 77chickCorea_MagicCarpet -0.340 -0.578 2 0.767 78dizzyGillespie_CognacBlues -0.573 0.717 2 0.786 79michaelBrecker_NothingPersonal 0.658 -0.206 2 0.784 80paulDesmond_AloneTogether 0.649 0.509 2 0.793 81jimmySmith_AuPrivave 0.118 0.911 2 0.797 82chetBaker_YoudBeSoNiceToComeHomeTo 0.698 -0.126 2 0.790 83steveLacy_Skippy 0.165 -0.629 2 0.790 84sidneyBechet_ReallyTheBlues 0.730 0.329 2 0.803 85stanGetz_ImGladThereIsYou -0.700 0.601 2 0.802 86sonnyRollins_BlueSeven3 -0.842 0.228 2 0.799 87stanGetz_BluesInTheCloset 0.559 -0.391 2 0.802 88joeHenderson_UMMG -0.853 0.136 2 0.804 89miltJackson_BemshaSwing -0.699 0.626 2 0.817 90milesDavis_Airegin -0.619 0.728 2 0.825 91davidLiebman_NicasDream 0.753 -0.073 2 0.828 92wyntonKelly_SoulStation -0.571 0.790 2 0.840 93colemanHawkins_StompinAtTheSavoy -0.673 0.693 2 0.839 94kennyKirkland_YesOrNo 0.782 0.279 2 0.844 95kennyKirkland_DelfeayosDilemma 0.135 0.970 2 0.857 96cannonballAdderley_StarEyes 0.414 -0.575 2 0.845 97branfordMarsalis_ThreeLittleWords -0.761 0.602 2 0.853 98kennyKirkland_Chance 0.776 -0.108 2 0.859 99herbieHancock_Orbits -0.796 -0.278 2 0.852 100wyntonKelly_ThisIDigOfYou1 -0.288 0.977 2 0.878 101joeLovano_LittleWillieLeapsIn 0.688 -0.333 2 0.871 102harryEdison_DidYouCallHerToday -0.258 0.992 2 0.885 103johnColtrane_Countdown 0.773 -0.182 2 0.879 104kennyKirkland_YouAndTheNight 0.662 0.670 2 0.891 105joeHenderson_TheSidewinder -0.776 -0.357 2 0.877 106dexterGordon_StanleyTheSteamer -0.873 0.481 2 0.895 107redGarland_Oleo 0.834 0.307 2 0.900 108paulDesmond_SambaCantina2 0.803 -0.148 2 0.896 109fatsNavarro_GoodBait 0.829 0.355 2 0.906 110patMetheny_MidnightVoyage 0.449 -0.617 2 0.899 111

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philWoods_OnASlowBoatToChina 0.806 0.452 2 0.913 112dizzyGillespie_Anthropology 0.143 -0.748 2 0.900 113joshuaRedman_HomeFries -0.550 0.898 2 0.916 114jJohnson_BluesInTheCloset -0.711 -0.482 2 0.903 115colemanHawkins_BodyAndSoul 0.443 0.916 2 0.925 116johnColtrane_BluesByFive -0.956 0.298 2 0.923 117donEllis_YouSteppedOutOfADream1 -0.823 -0.367 2 0.921 118warneMarsh_Wow -0.220 -0.775 2 0.923 119chickCorea_TonesForJoansBones2 0.885 0.220 2 0.938 120woodyShaw_StevesBlues -0.984 0.126 2 0.935 121michaelBrecker_SongForBilbao -0.446 -0.711 2 0.932 122chetBaker_LetsGetLost 0.767 0.628 2 0.954 123kennyWheeler_DoubleVision -0.997 0.081 2 0.950 124joeLovano_Work -0.091 -0.814 2 0.948 125mulgrewMiller_PressingTheIssue -0.908 -0.288 2 0.957 126michaelBrecker_CabinFever -0.381 1.044 2 0.971 127wayneShorter_ESP -0.561 -0.681 2 0.961 128jJJohnson_BlueMode 0.607 0.865 2 0.984 129charlieParker_ScrappleFromTheApple 0.201 1.085 2 0.985 130chrisPotter_Anthropology 0.063 -0.832 2 0.971 131sonnyRollins_VierdBlues 0.935 0.226 2 0.989 132colemanHawkins_Perdido 0.711 0.774 2 0.995 133johnColtrane_MyFavoriteThings2 -0.926 -0.315 2 0.985 134cliffordBrown_Cherokee 0.881 -0.227 2 0.996 135wyntonMarsalis_Caravan -1.036 -0.014 2 0.998 136wayneShorter_DownUnder 0.605 0.923 2 1.026 137kennyDorham_Serenity -0.124 -0.882 2 1.017 138davidLiebman_NoGreaterLove -1.066 0.011 2 1.025 139chetBaker_LongAgoAndFarAway -0.308 -0.854 2 1.020 140hankMobley_Remember 0.567 -0.689 2 1.027 141chetBaker_TwosBlues -1.078 -0.009 2 1.039 142woodyShaw_ThereWillNeverBeAnotherYou -0.307 -0.878 2 1.043 143wayneShorter_EightyOne 0.693 0.895 2 1.064 144sidneyBechet_Summertime -0.785 -0.629 2 1.059 145benWebster_ByeByeBlackbird -0.700 -0.713 2 1.067 146herbieHancock_OneFingerSnap_AlternateTake 1.032 0.046 2 1.084 147bennyGoodman_Whispering -0.975 0.710 2 1.092 148herbieHancock_HandJive -0.976 -0.432 2 1.085 149zootSims_NightAndDay1 0.797 0.849 2 1.109 150chickCorea_MyOneAndOnlyLove -0.316 -0.931 2 1.096 151woodyShaw_RahsaansRun -1.146 0.033 2 1.102 152wayneShorter_Dolores -0.335 -0.936 2 1.106 153

154

johnColtrane_BodyAndSoul_AlternateTake -1.144 -0.056 2 1.111 154kennyDorham_BluesInBeBop -0.833 -0.655 2 1.111 155johnAbercrombie_RalphsPianoWaltz -1.155 -0.011 2 1.116 156freddieHubbard_SpeakNoEvil -0.849 -0.665 2 1.130 157leeKonitz_MeanToMe 1.088 -0.022 2 1.147 158kennyDorham_PrinceAlbert 0.598 -0.810 2 1.143 159johnColtrane_Impressions_1961 -1.098 0.603 2 1.150 160philWoods_CrazyRhythm -1.130 -0.248 2 1.146 161joeHenderson_Serenity 0.591 -0.819 2 1.146 162donByas_UnAmourPleurait -0.575 1.164 2 1.158 163cannonballAdderley_HighFly 1.022 0.580 2 1.161 164johnColtrane_Impressions_1963 -1.163 0.463 2 1.162 165wyntonMarsalis_JohnnyComeLately -0.356 1.265 2 1.174 166joeyDefrancesco_TheChamp 0.936 0.782 2 1.180 167lesterYoung_DickiesDream -0.651 1.152 2 1.184 168lesterYoung_LesterLeapsIn -0.558 1.211 2 1.193 169davidLiebman_SoftlyAsInAMorningSunrise -0.555 -0.937 2 1.183 170bennyCarter_JustFriends 0.999 0.716 2 1.200 171zootSims_AllTheThingsYouAre -1.209 0.408 2 1.192 172donEllis_SweetAndLovely -1.224 -0.095 2 1.197 173sonnyRollins_IllRememberApril_AlternateTake2 0.681 1.102 2 1.214 174stanGetz_MyFunnyValentine -0.202 1.344 2 1.222 175patMetheny_AllTheThingsYouAre -0.747 1.136 2 1.223 176charlieShavers_LimehouseBlues -1.109 0.742 2 1.223 177bobBerg_IDidntKnowWhatTimeItWas 0.597 -0.935 2 1.247 178steveColeman_PassItOn 0.276 -1.086 2 1.261 179leeMorgan_TheSidewinder -0.665 -0.979 2 1.271 180milesDavis_Pfrancing -0.610 -1.010 2 1.273 181davidMurray_BodyAndSoul1 0.191 -1.126 2 1.281 182cliffordBrown_ANightInTunisia 0.146 -1.136 2 1.283 183royEldridge_BodyAndSoul 0.437 -1.060 2 1.288 184sonnyRollins_BlueSeven2 -1.351 0.279 2 1.310 185dexterGordon_Cheesecake -0.295 -1.169 2 1.324 186chickCorea_TheSlide -1.376 0.272 2 1.334 187joeHenderson_JohnnyComeLately 0.991 0.987 2 1.346 188wyntonMarsalis_AprilInParis -0.145 -1.195 2 1.331 189donEllis_OutOfNowhere -1.372 -0.109 2 1.345 190vonFreeman_PassItOn -0.802 -0.982 2 1.345 191leeKonitz_Marshmallow -0.458 -1.154 2 1.349 192johnnyDodds_HeebieJeebies -0.362 1.472 2 1.376 193artPepper_InAMellowTone -0.955 1.178 2 1.384 194steveLacy_EasyToLove -1.413 -0.043 2 1.376 195

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herbieHancock_GingerbreadBoy -0.623 -1.126 2 1.383 196davidMurray_AskMeNow -0.287 -1.242 2 1.394 197davidLiebman_DayAndNite -0.750 -1.094 2 1.412 198royEldridge_TheGasser2 0.270 -1.251 2 1.419 199kennyGarrett_BrotherHubbard2 -0.022 -1.305 2 1.438 200lionelHampton_HighSociety 0.183 1.584 2 1.471 201lesterYoung_BodyAndSoul 0.101 1.611 2 1.487 202jJJohnson_MyFunnyValentine -0.392 -1.300 2 1.473 203herbieHancock_Dolores -0.397 -1.308 2 1.481 204chetBaker_ThereWillNeverBeAnotherYou1 -0.370 -1.322 2 1.489 205joshuaRedman_BluesOnSunday 0.870 1.367 2 1.539 206philWoods_CottonTail 0.842 1.388 2 1.539 207louisArmstrong_GotNoBlues -1.520 0.593 2 1.542 208chetBaker_JustFriends 0.173 -1.403 2 1.551 209patMetheny_CabinFever -0.542 1.621 2 1.569 210gerryMulligan_ScrappleFromTheApple -0.027 -1.428 2 1.560 211miltJackson_DontGetAroundMuchAnymore 0.969 1.353 2 1.589 212bennyGoodman_NobodysSweetheart -1.602 0.578 2 1.616 213chetBaker_IFallInLoveTooEasily 1.153 1.247 2 1.640 214sidneyBechet_ImComingVirginia -0.094 1.782 2 1.650 215redGarland_IfIWereABell 1.098 1.325 2 1.655 216bennyGoodman_Avalon 0.050 -1.504 2 1.639 217royEldridge_TheGasser1 0.457 -1.431 2 1.643 218herbieHancock_HubTones_AlternateTake 1.509 0.824 2 1.705 219taddDameron_HotHouse 0.701 1.682 2 1.722 220billEvans_AutumnLeaves 0.853 1.603 2 1.725 221bennyGoodman_TigerRag2 -1.292 1.325 2 1.723 222bennyCarter_LongAgoAndFarAway1 0.994 1.518 2 1.735 223davidLiebman_PablosStory -0.789 -1.426 2 1.725 224wyntonMarsalis_Cherokee -0.069 -1.625 2 1.757 225artPepper_BluesForBlanche 0.080 -1.681 2 1.817 226zootSims_NightAndDay2 0.361 1.933 2 1.847 227charlieParker_KoKo 0.484 1.912 2 1.858 228cliffordBrown_Daahoud 0.710 -1.573 2 1.866 229leeKonitz_Tautology 0.065 -1.745 2 1.880 230charlieParker_DonnaLee 0.886 1.821 2 1.930 231sonnyStitt_BluesInBeBop -0.697 -1.685 2 1.930 232joeHenderson_Punjab 0.021 2.154 2 2.024 233jJJohnson_Walkin 0.425 2.135 2 2.058 234warneMarsh_Tautology 0.421 2.188 2 2.109 235chetBaker_ThereWillNeverBeAnotherYou2 -0.346 -1.972 2 2.125 236theloniousMonk_askMeNow 0.669 2.232 2 2.219 237

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wyntonKelly_SplitFeelins 0.261 2.689 2 2.576 238sidneyBechet_LimehouseBlues 1.117 2.549 2 2.683 239johnnyDodds_MuskratRamble 0.586 -2.461 2 2.669 240peterBernstein_Ceora 0.622 2.747 2 2.699 241donByas_CognacBlues 0.025 -2.596 2 2.729 242chickCorea_TonesForJoansBones1 1.233 2.730 2 2.897 243fatsNavarro_OurDelight 0.224 -3.410 2 3.552 244leeKonitz_Wow 2.030 -0.123 3 0.029 1johnColtrane_MrPC 1.979 -0.230 3 0.090 2charlieParker_BluesForAlice 2.000 -0.260 3 0.113 3dexterGordon_SocietyRed 1.874 -0.148 3 0.141 4michaelBrecker_Confirmation 2.149 -0.044 3 0.170 5mulgrewMiller_RelaxinAtCamarillo 2.122 0.000 3 0.182 6freddieHubbard_Birdlike 1.863 -0.254 3 0.186 7mulgrewMiller_IfIShouldLoseYou 1.791 -0.110 3 0.228 8mulgrewMiller_OGrandeAmore 1.798 -0.011 3 0.257 9mulgrewMiller_TimeAndAgain 2.042 -0.412 3 0.265 10warneMarsh_Crosscurrent 1.716 -0.251 3 0.316 11mulgrewMiller_TheFarSide 1.998 -0.512 3 0.364 12chrisPotter_Togo 1.847 0.177 3 0.366 13philWoods_StrollinWithPam 1.658 -0.068 3 0.366 14dexterGordon_TheRainbowPeople 1.636 -0.249 3 0.392 15wyntonKelly_Remember1 2.036 -0.564 3 0.416 16michaelBrecker_IMeanYou 2.088 0.265 3 0.419 17donByas_BodyAndSoul 1.647 0.131 3 0.462 18sonnyStitt_GoodKick 1.630 0.111 3 0.464 19wyntonKelly_remember2 1.948 -0.627 3 0.484 20oscarPeterson_CJamBlues 2.460 -0.365 3 0.494 21wyntonKelly_SoftlyAsInAMorningsSunrise 1.607 -0.438 3 0.500 22chuBerry_BodyAndSoul1 1.501 -0.233 3 0.522 23freddieHubbard_245 1.705 -0.575 3 0.527 24joeLovano_BodyAndSoul1 1.966 0.385 3 0.536 25joeLovano_ICantGetStarted 1.934 0.408 3 0.562 26patMartino_AlongCameBetty 2.395 0.275 3 0.569 27billEvans_Witchcraft 2.366 -0.597 3 0.570 28lennieTristano_LineUp 2.586 0.139 3 0.639 29leeMorgan_Moanin 1.669 -0.733 3 0.679 30branfordMarsalis_HousedFromEdward1 1.370 0.065 3 0.680 31miltJackson_SoftlyAsInAMorningSunrise 2.075 -0.829 3 0.684 32kennyKirkland_AnaMaria 2.548 0.295 3 0.693 33kennyKirkland_Later 1.844 -0.847 3 0.720 34mulgrewMiller_IfIWereABell 1.945 0.568 3 0.720 35

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theloniousMonk_littleRootieTootie 2.040 0.578 3 0.727 36johnColtrane_Soultrane 1.625 0.472 3 0.733 37joshuaRedman_SweetSorrow 1.589 -0.758 3 0.744 38dizzyGillespie_GroovinHigh 1.327 0.185 3 0.765 39bennyCarter_SweetLorraine 2.603 -0.682 3 0.794 40pepperAdams_YoudBeSoNiceToComeHomeTo 1.215 -0.062 3 0.805 41herbieHancock_OneFingerSnap 2.634 0.367 3 0.805 42steveTurre_DatDere 1.255 0.134 3 0.810 43kennyKirkland_TonalityOfAtonement 1.309 -0.587 3 0.832 44billEvans_PerisScope 1.181 -0.086 3 0.837 45bobBerg_YouAndTheNightAndTheMusic 1.446 0.501 3 0.864 46wayneShorter_Footprints 1.143 -0.252 3 0.878 47cannonballAdderley_SoWhat 2.401 0.661 3 0.896 48charlieParker_EmbraceableYou 2.912 -0.027 3 0.905 49cannonballAdderley_WorkSong 1.183 -0.514 3 0.909 50pepperAdams_HowHighTheMoon 2.756 0.379 3 0.910 51miltJackson_AllTheThingsYouAre 1.118 0.039 3 0.916 52chickCorea_Pannonica 1.462 0.588 3 0.921 53bobBerg_SecondSight 2.377 -1.004 3 0.929 54herbieHancock_EyeOfTheHurrican 1.534 -0.956 3 0.940 55mulgrewMiller_JustSqueezeMe 2.939 0.030 3 0.941 56chrisPotter_InASentimentalMood 1.229 -0.665 3 0.941 57joeLovano_BodyAndSoul2 2.106 0.798 3 0.951 58philWoods_BeMyLove 1.042 -0.166 3 0.973 59redGarland_MyFunnyValentine 2.993 -0.054 3 0.982 60leeKonitz_AllTheThingsYouAre 1.098 -0.576 3 1.012 61hankMobley_SoulStation 1.211 0.466 3 1.012 62benWebster_MyIdeal 1.053 -0.484 3 1.019 63georgeColeman_MaidenVoyage 1.139 0.380 3 1.023 64charlieParker_KCBlues 1.003 -0.321 3 1.027 65mulgrewMiller_GettingToKnowYou 1.830 -1.173 3 1.042 66joshuaRedman_IGotYou 0.996 -0.384 3 1.046 67donByas_InfideleCry 1.076 0.320 3 1.050 68johnColtrane_BlueTrain 2.368 0.869 3 1.077 69kennyKirkland_BlankNile 1.101 0.426 3 1.079 70davidLiebman_BeginTheBeguine 1.077 -0.684 3 1.081 71cliffordBrown_IllRememberApril 1.588 -1.142 3 1.082 72chrisPotter_Arjuna 1.118 -0.782 3 1.098 73miltJackson_WhatsNew 1.663 0.893 3 1.100 74herbieHancock_OliloquiValley 1.250 -0.947 3 1.106 75theloniousMonk_trinkleTinkle 3.015 0.325 3 1.107 76pepperAdams_JustOneOfThoseThings 1.187 -0.894 3 1.114 77

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bixBeiderbecke_RoyalGardenBlues 0.906 -0.258 3 1.115 78michaelBrecker_NakedSoul 1.111 -0.838 3 1.137 79cliffordBrown_StompinAtTheSavoy 1.234 0.705 3 1.157 80johnColtrane_MyFavoriteThings1 0.942 0.284 3 1.157 81leeKonitz_IllRememberApril 0.849 0.157 3 1.206 82theloniousMonk_wellYouNeednt 0.928 -0.687 3 1.213 83artPepper_Stardust1 0.815 0.036 3 1.214 84mulgrewMiller_TonyWilliams 1.949 -1.362 3 1.216 85fatsNavarro_GoodBait_AlternateTake 1.724 -1.334 3 1.221 86ericDolphy_OnGreenDolphinStreet 3.167 0.273 3 1.227 87leeKonitz_Crosscurrent 0.948 -0.801 3 1.251 88chickCorea_ItCouldHappenToYou 0.962 -0.824 3 1.252 89theloniousMonk_weSee 2.070 1.109 3 1.259 90colemanHawkins_SophisticatedLady 3.243 -0.574 3 1.299 91bennyCarter_LongAgoAndFarAway2 0.910 0.595 3 1.332 92fatsNavarro_DoubleTalk 1.192 -1.212 3 1.345 93redGarland_BluesByFive 2.707 1.026 3 1.363 94colemanHawkins_BodyAndSould 1.819 1.209 3 1.371 95joshuaRedman_TearsInHeaven 3.364 0.141 3 1.379 96dizzyGillespie_BeBop 1.291 -1.333 3 1.388 97woodyShaw_DatDere 1.109 -1.207 3 1.393 98bennyCarter_IGotItBad 1.958 1.258 3 1.407 99charlieParker_StarEyes 1.080 0.918 3 1.418 100horaceSilver_Doodlin 1.691 -1.532 3 1.422 101ayneShorter_Juju 0.781 0.599 3 1.443 102cliffordBrown_Jordu 1.810 -1.596 3 1.462 103joeLovano_CentralParkWest 0.952 -1.182 3 1.483 104steveColeman_CrossFade2 2.495 1.293 3 1.519 105charlieParker_BilliesBounce 1.192 1.143 3 1.531 106colemanHawkins_MyBlueHeaven 1.314 1.213 3 1.531 107charlieParker_MyLittleSuedeShoes 0.777 -1.070 3 1.543 108theloniousMonk_blueMonk 2.519 1.333 3 1.564 109cliffordBrown_GeorgesDilemma 0.529 0.486 3 1.616 110mulgrewMiller_OnGreenDolphinStreet 3.701 -0.363 3 1.699 111theloniousMonk_iShouldCare 3.268 -1.304 3 1.704 112redGarland_ItCouldHappenToYou 3.485 0.749 3 1.721 113bennyCarter_ItsAWonderfulWorld1 1.620 1.527 3 1.722 114artPepper_Desafinado 0.664 -1.231 3 1.731 115georgeColeman_DolphinDance 3.296 1.059 3 1.760 116pepperAdams_ANightInTunisia 3.261 -1.407 3 1.771 117miltJackson_Bag'sGroove 0.624 -1.269 3 1.787 118theloniousMonk_monksDream 2.624 1.539 3 1.793 119

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kennyDorham_LadyBird 1.108 -1.724 3 1.818 120donByas_OutOfNowhere 3.814 -0.460 3 1.826 121davidMurray_BluesForTwo2 0.266 -0.781 3 1.861 122charlieParker_Steeplechase 2.372 1.777 3 1.958 123horaceSilver_TheStVitusDance 2.715 1.767 3 2.039 124redGarland_Four 3.800 0.839 3 2.040 125louisArmstrong_SavoyBlues 1.149 1.743 3 2.080 126theloniousMonk_roundMidnight 3.717 1.160 3 2.146 127jJJohnson_Yesterdays 0.857 -1.956 3 2.147 128lionelHampton_MemoriesOfYou 0.976 1.808 3 2.215 129theloniousMonk_reflections 4.175 0.556 3 2.272 130charlieParker_HowDeepIsTheOcean 0.965 -2.165 3 2.274 131johnColtrane_Nutty 4.271 -0.539 3 2.289 132natKingCole_BodyAndSoul 2.760 2.062 3 2.333 133johnColtrane_SoWhat 0.790 -2.156 3 2.352 134herbieHancock_YoureMyEverything 3.870 -1.618 3 2.366 135dexterGordon_Dextivity 3.118 1.949 3 2.369 136redGarland_ICouldWriteABook 4.001 1.461 3 2.556 137wyntonKelly_IfIShouldLoseYou 2.234 2.417 3 2.574 138artPepper_Startdust2 3.925 -1.907 3 2.596 139leeMorgan_BlueTrain 2.693 -2.876 3 2.811 140theloniousMonk_dinah 4.783 0.441 3 2.830 141michaelBrecker_NeverAlone 3.992 -2.190 3 2.841 142kennyBarron_IShouldCare 4.802 -0.924 3 2.893 143sonnyStitt_BlueMode 5.066 -0.083 3 3.052 144theloniousMonk_everythingHappensToMe 4.843 1.225 3 3.144 145redGarland_WhenLightsAreLow 2.201 3.138 3 3.291 146theloniousMonk_rubyMyDear 5.129 1.019 3 3.325 147chickCorea_ArmandosTango 3.271 -3.260 3 3.356 148woodyShaw_Imagination 0.552 -3.427 3 3.591 149sonnyStitt_Teapot 5.269 1.989 3 3.893 150kennyWheeler_PassItOn 1.346 -4.270 3 4.176 151theloniousMonk_crepusculeWithNellie 1.584 -4.354 3 4.228 152

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Vita Connor Davis received his Bachelor’s of Music degree in Music Theory from the University

of Arkansas in 2013. Upon graduation, he began his graduate studies at Michigan State University

where he earned a Master’s of Music degree in Music Theory Research and Pedagogy in 2015. His

master’s thesis, “Three Theories of Polymetric Perception,” was completed under the advisement of

Dr. Leigh VanHandel. Following completion of this degree, Connor earned a Master’s of Art in

Instrumental Performance (jazz piano) from Eastern Illinois University, studying the Prof. Paul

Johnston. Besides music theory, Connor is interested in philosophies of music, particularly questions

surrounding objective aesthetics.

Davis’ publications and presentations explore what musical prototypicality is from a

philosophical perspective, and—from that foundation—what it means to define something as

prototypical in music via various computational, cognitive, and music theoretical perspectives. He

has presented broadly on this topic at regional, national, and international conferences.