rhythm in jazz

8/20/2019 Rhythm in Jazz

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On Phrase Rhythm in Jazz

by

Stefan Love

Submitted in Partial Fulfillment

of the

Requirements for the Degree

Doctor of Philosophy

Supervised by

Professor Robert Wason

Department of Music Theory

Eastman School of Music

University of Rochester

Rochester, New York

2011


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Curriculum Vitae

Stefan Love was born in Newport, Rhode Island on April 23, 1984. He attended Brown

University from 2002 to 2006, where he was awarded the Buxtehude Premium, given to

exceptional music students, and the Mitch Baker award, given to noteworthy jazz pianists. He

graduated Magna cum laude with a Bachelor of Arts degree in music, conferred with Honors.

Upon graduation, he was admitted into the Phi Beta Kappa honors society. He began his

graduate studies in music theory (MA/PhD) at the Eastman School of Music in 2007, and was

awarded the Sproull Fellowship for his study there. Working with advisor Robert Wason, in

2010, he earned the Master of Arts degree in music theory.


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Acknowledgments

This project would not have been possible without the help of my committee of readers. First, I

thank Bob Wason, my advisor. The concept for this dissertation emerged from an independent

study I undertook with him in the fall of 2009. His steadfast encouragement and keen eye for

the dissertation’s final shape guided its development. His expertise in jazz, as both a theorist

and a musician, made him an invaluable resource. I also thank Davy Temperley, my second

reader and phrase rhythm specialist. He immersed himself in my approach and critiqued it

from within, greatly improving the final product. Finally, Dariusz Terefenko brought an

unparalleled knowledge of jazz repertoire and performance practice to the project. I knew that

if the dissertation resonated with him, I must be on the right track.

I also thank Babe O. for her constant love and support.


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Abstract

Phrase rhythm is the interaction of grouping structure and metrical structure. In jazz

improvisation, these structures behave in ways that theories of phrase rhythm designed for

classical music cannot accommodate. Specifically, jazz improvisation involves the

superimposition of a highly flexible grouping structure on a pre-determined and predictable

metrical-harmonic scheme. In this context, theories of phrase rhythm that depend on voice-

leading or harmony neglect the subtleties of grouping structure.

In this dissertation, I present a new method for the analysis of jazz phrase rhythm. I

classify each phrase based on its relationship to the metrical hierarchy, as manifested in two

characteristics: 1) the pattern of metrical accents it overlaps (prosody), and 2) its occupation of

metrical units, from one to eight measures in length. For example, a 4-phrase occupies a four-bar

hypermeasure, and may be beginning-, end-, un-, or double-accented. The basic phrase-types

may be combined and altered in various ways.

I include detailed analyses of fifteen solos on several different forms, including AABA,

ABAC, and twelve-bar blues. Throughout an improvised solo, phrase rhythm fluctuates

between states of consonance and dissonance, as the grouping structure variously supports or

contradicts the metrical structure. Phrase rhythm thus contributes immensely to this music’s

aesthetic value.


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v

Table of Contents

Part I: Theory

Introduction: What is Jazz? What is Phrase Rhythm? p. 1

Chapter 1: Meter and Grouping in Jazz 10

Chapter 2: The Analytical Method 36

Part II: Applications

Introduction to Part II 80

Chapter 3: Thirty-Two-Bar Schemes in AABA Form 83

Chapter 4: Thirty-Two-Bar Schemes in ABAC Form 109

Chapter 5: The Twelve-Bar Blues 143

Chapter 6: Metrically Atypical Schemes 165

Chapter 7: Some Pedagogical and Analytical Extensions 192

Works Cited 214

Index of Recordings and Transcriptions 220

Appendix A: Glossary of Terms and Notations 222

Appendix B: Complete Transcriptions and Analyses 226


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vi

List of Figures

Introduction

I–1. Parker, “Dewey Square”: Grouping structure of mm. 1–16. p. 8

Chapter 1

1–1. A metrical grid in 4/4. 13

1–2. Metrical projection. 16

1–3. A projective hierarchy. 17

1–4. Hypermetrical analysis of Haydn's Symphony no. 104/I. 22

1–5. A metrical mistake. 22

1–6. Motive vs. hypermeter. 29

1–7. One phrase or two? 31

1–8. What are the second level groups? 31

1–9. Voice-leading vs. grouping. 34

Chapter 2

2–1. Segmentation factor 1: IOI. 38

2–2. Segmentation factor 2: strong beat. 39

2–3. Segmentation factor 4: motive. 41

2–4. A formula, not a motive. 42

2–5. A formula becomes a motive through repetition. 43

2–6. Conflicts among grouping factors. 44

2–7. The short form of prosodic notation. 47

2–8. Accent borrowing. 47

2–9. Effects characteristic of swing articulation of 8 th-notes. 48

2–10. No borrowed accent. 49

2–11. Metrical time-spans and associated phrase-types. 49


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2–12. The beginning-accented 4-phrase. 50

2–13. The end-accented 4-phrase. 52

2–14. Not a 4-phrase. 52

2–15. Where to place 4-phrase brackets: solid v. dotted. 53

2–16. Some un-accented 4-phrases. 54

2–17. The double-accented 4-phrase. 55

2–18. Comparison of 4-phrase types. 56

2–19. The 2-phrase. 56

2–20. Where to place 2-phrase brackets: solid v. dotted. 57

2–21. Asymmetrical 2-phrase division. 58

2–22. A challenging case. 59

2–23. The 1-phrase. 60

2–24. Sentence-structure, 1/1/2. 61

2–25. No overlapped downbeats. 62

2–26. The beginning-accented 8-phrase. 62

2–27. An 8-phrase made from four 2-phrases 63

2–28. Davis, “Oleo,” mm. 1–32. 64

2–29. A prefix. 67

2–30. Phrase overlap. 69

2–31. Grouping structure in a phrase overlap. 69

2–32. A 2+4 combined phrase. 70

2–33. Grouping structure, figure 2–34. 70

2–34. Rhyme. 72

2–35. A common source of ambiguity. 74

2–36. Combination or end-accentuation? 74


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2–37. End-accentuation that resembles combination. 76

2–38. Ambiguous phrase rhythm. 77

2–39. Phrase division without pause. 78

Chapter 3

3–1. An idealized AABA form. 83

3–2 through 3–6. Davis, “Oleo” 87–90

3–7, 3–8. Parker, “Moose the Mooche.” 92–93

3–9 through 3–12. Parker, “Yardbird Suite.” 96–99

3–13, 3–14. Parker, “Dewey Square.” 100

3–15 through 3–19. Powell, “Wail.” 101–107

Chapter 4

4–1. “Pennies From Heaven” (Johnston): Metrical-harmonic scheme. 110

4–2 through 4–12. Getz, “Pennies From Heaven.” 112–122

4–13. “Ornithology” (Parker): Metrical-harmonic scheme. 123

4–14 through 4–25. Parker, “Ornithology.” 124–131

4–26 through 4–35. Evans, “My Romance.” 133–141

Chapter 5

5–1. Metrical-harmonic scheme of twelve-bar blues in C. 143

5–2 through 5–6. Parker, “Chi Chi.” 146–148

5–7. 6/6 chorus-level phrase rhythm. 149

5–8, 5–9. Parker, “Chi Chi.” 150–151

5–10 through 5–14. Adderley, “Freddie Freeloader.” 153–157

5–15 through 5–20. Rollins, “Tenor Madness.” 159–163


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Chapter 6

6–1. “Airegin” (Rollins): Metrical-harmonic scheme. 167

6–2 through 6–9. Rollins, “Airegin.” 168–174

6–10. Midpoint of “The Touch of Your Lips” (Noble) 175

6–11. Recomposition of “Airegin,” section B. 176

6–12. Rollins, “Airegin.” 176

6–13. “Witchcraft” (Coleman): Metrical-harmonic scheme. 178

6–14 through 6–20. Evans, “Witchcraft.” 180–184

6–21. “I’ll Remember April” (Johnston): Metrical-harmonic scheme. 185

6–22 through 6–25. Brown, “I’ll Remember April.” 186–191

Chapter 7

7–1. Eight graduated exercises for practicing phrase rhythm. 194

7–2. The pedagogical program. 195

7–3. Exercise 1: 2-phrases. 196

7–4. Exercise 2: 1-phrases. 197

7–5. 4-phrases, switching types at every phrase. 199

7–6. A twelve-measure phrase plan, repeated cyclically. 200

7–7. A sentence structure, to introduce the 8-phrase level (exercise 5). 201

7–8. Phrase overlap, in 2/2O2/2 structure (exercise 6). 202

7–9. Phrase combination, in 2/2+2/2 structure (exercise 7). 202

7–10. Imitation of noteworthy solos (exercise 8). 203

7–11. Tactus shifting. 204

7–12 through 7–16. Coltrane, “My Favorite Things.” 208–212


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A Note on the Transcriptions and Recordings

Excerpts from transcribed jazz performances appear throughout this dissertation. Many of these

are based on published sources, while I transcribed several others myself. Rather than cite these

sources throughout the text, I provide a complete “Index of Recordings and Transcriptions” on

page 221. Each recording/transcription pair has a unique number. In the caption of all musical

excerpts, a recording/transcription index number appears in curly brackets (e.g., {14}).

I edited the published sources for accuracy and readability, typeset them with four

measures per line, and, when necessary, transposed them to concert pitch. I omitted many

ornaments—grace notes, “scoops” into notes, and so forth—as these had no affect on my

analyses. I advise the reader to consult the recordings if possible: these are the only

authoritative sources for this music.

For simplicity, I depart from conventional lead-sheet harmonic notation in two ways: 1) I

do not list chordal extensions beyond the chordal seventh; 2) for tonic-function harmonies, I

list only the root: “C” replaces “Cmaj7”, “C6/9”, and so forth; “C-” replaces “C-maj7”, “C-6”,

and so forth.


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1

P ART I: THEORY

Introduction: What is Jazz? What is Phrase Rhythm?

What is Jazz?

Since its origins in the early 20th century, the term “jazz” has been applied to an incredible

range of music. No definition could capture the myriad uses of the term, nor satisfy all of jazz’s

devotees. I focus on a significant subset of jazz, roughly coextensive with bebop and its close

descendants. This style predominated in the ‘40s and ‘50s, and centered on small ensembles

and improvised solos. In this dissertation, “jazz” refers to this subset only. The characteristics

enumerated in this section limit my theory’s domain: any music that does not possess these

characteristics is not within my purview.

An important and distinctive aspect of jazz is its formal structure. The form of the jazz

performance has been compared to a “theme and variations,” with the themes drawn from a

collection of well-known pieces or “standards.” Paul Berliner (1994) describes the typical

performance: “It has become the convention for musicians to perform the melody and its

accompaniment at the opening and closing of a piece’s performance. In between, they take

turns improvising solos within the piece’s cyclical rhythmic form” (63). The repetitions of the

theme, or choruses, follow one another without pause. Frank Tirro (1967) explicitly compares

this procedure to continuous variation in classical music: after the opening chorus, musicians

maintain the “structure of the piece…in chaconne fashion” during the middle choruses (317).

Similarly, Steve Larson (1993) says that both “modern jazz variations” and “classical variation

sets” are “based on…the ‘structure’ of a theme,” which has “rhythmic, harmonic, melodic, and

contrapuntal aspects. Variations may preserve any of these aspects at any level” (300).

I understand jazz variation procedure to consist of two elements: a scheme and a realization.

(“Scheme” is my word for Larson’s and Tirro’s “structure.”) The scheme outlines the elements

of a single chorus. In isolation, it is an abstract entity, existing most vividly in the mind of the


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Introduction: What is Jazz? What is Phrase Rhythm? 2

player or listener. (In geometry, the “perfect circle” is also such an entity.) The realization is one

concrete performance of the scheme.

The arrangement of a jazz performance comprises the discrete parts of the realization and

their ordering. I use the following terms for the parts of a typical arrangement:

1. The opening theme: one cycle of the scheme, including the composed melody (if

present);

2.

The variations: a number of choruses that adhere less closely to the scheme: the

schematic melody may be varied or ignored and the schematic harmony may be altered

slightly, but the highest levels of the meter will be strictly maintained;

3. The closing theme: A closing cycle of the scheme, including the composed melody.

Arrangements sometimes include an introduction, coda, or interludes between choruses. These

sections make themselves known through texture and harmony, and are easily distinguished

from the familiar portions of the scheme.1

The Scheme and Realization in Jazz

In the words of Charles Mingus, “You can’t improvise on nothin’…you gotta improvise on

somethin’.”2 The scheme is the “something” on which one improvises. It is a sequence of

harmonies occupying a fixed number of measures, which often includes a melody. The mostfamiliar depiction of the scheme is a lead sheet, showing a melody and chord symbols within a

metrical framework. In this section, I discuss the nature of the jazz scheme and its relationship

with the realization.

Many schemes are from a repertory known informally as the “Great American Songbook,”

a collection of popular songs written for the stage, screen, or home from roughly 1920 to 1960.

This collection has been the subject of at least two detailed theoretical studies (Forte 1995,

Terefenko 2004). While a scheme can be made concrete through notation (a lead sheet or

original score) and performance, in the absence of these, a scheme is best understood as a

1 These elements—introduction, coda, etc.—can themselves become schematic through

repetition in multiple performances. Consider, for example, the introduction to “Take the A

Train” (Strayhorn), which has become an expected part of the performance.2 Quoted in Kernfeld 1995 (119).


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mental representation of abstract features like meter and voice-leading. A listener or performer

arrives at an understanding of the scheme through the experience of many different

realizations. Knowledge of the scheme generates expectations and provides a basis for

comparison. Each realization is measured against the scheme while simultaneously modifying

it. As Henry Martin describes it, the scheme provides an anchor for musical expression: “Since

the progression of the changes can be easily internalized, and the symmetry and regularity of

the strophes [choruses] ‘felt’ without too much conscious attention, the player can focus on

developing the melodic and expressive essence of a solo with these ‘built-in’ features taken for

granted” (1996: 13). The scheme is what the player has “internalized,” the “built-in” features.

The interaction between scheme and realization is jazz’s defining feature. (Arguably, it is

the defining feature of all variation procedure.) The focus of this dissertation is the interaction

between the schematic meter, which is rigidly maintained, and the realization’s flexible phrase

structure. While realization often entails improvisation, I downplay this feature, because the

process of analysis works in the same way, regardless of whether the realization is improvised or

entirely composed in advance.3

The opening theme, the first instantiation of the scheme in a particular performance, can

establish certain modifications that are retained in subsequent choruses. These can include

reharmonization or metric modulation at fixed points in the scheme—for example, the bridge

of each chorus might be in 3/4, the remainder in 4/4. In this way, certain modifications to thescheme become schematic for a particular performance. In total, then, realization consists of

three distinct layers: the unmodified scheme (present only in the mind), the version of the

scheme presented in the opening theme (whose modifications to the original may be retained

throughout the performance), and the one-off elements appearing in any chorus. 4 I distinguish

these three layers here only for the sake of precision. My theory’s focus on meter, the most rigid

feature of the scheme, allows me to downplay these subtleties when analyzing phrase-rhythm.

The variation choruses may modify the scheme in many ways. Typically, the melody

undergoes the greatest modification, the harmony undergoes subtler changes, and the meter is

3 Larson (1998 and 2005) similarly argues that the line between improvisation and composition

is blurry, and of little practical consequence.4 Complicating matters further, sometimes the variations follow a slightly different scheme

from the opening and closing themes—usually, a simplified harmonic progression. In that case,

the first variation chorus can establish a modified scheme for subsequent variation choruses.


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strictly maintained.5 The melody in the variation choruses may relate to the scheme in many

different ways. In “paraphrase improvisation,” the realized melody more or less follows the

schematic melody, adding elaborations, inserting “fills” between phrases, or omitting notes

(Kernfeld 1995: 131–151). But in other cases, the realized melody may bear no obvious relation

to the schematic melody, and follows only the schematic harmony. For example, “formulaic

improvisation” is the combination of pre-learned melodic fragments into longer phrases based

only on harmonic context, and “motivic improvisation” is the systematic development of short

motives, which may have no relation to the scheme ( ibid.).6 All of these types can appear within

a single solo, but only in the case of paraphrase improvisation does the improvised melody refer

to the theme.

In jazz pedagogy, perhaps the most common method of teaching melodic improvisation is

“chord-scale theory.” The improviser draws melodic material from scales that are appropriate

for each type of chord.7 For example, one might employ a minor scale with flat seventh and

natural sixth (“Dorian”) over a minor-seventh chord. Melodies constructed through this process

need not have any connection to the schematic melody, only the schematic harmony. To

counteract this tendency, students may be told to imagine the schematic melody as they play;

but it is certainly possible to produce satisfying jazz melodies that relate only to the schematic

harmony, not the melody.

Schenkerian analysis presents a richer picture of jazz melody. Analyses peel away surfacediminutions to reveal how the improvised melody preserves both melodic and harmonic

aspects of the scheme, especially the underlying voice-leading.8 The intricacy of this analytical

method highlights the distance between the realized melody and the schematic melody: if the

melody always related to the scheme’s original melody in an obvious way, such methods would

not be necessary. And the resulting connections between the improvised melody and the theme

are sometimes obscure (not to say dubious); the clearest consistent relationship remains that

5 Chapter 3 of Berliner 1994 discusses in depth the many methods by which musicians alter

the scheme, from subtle variation of the schematic melody to the invention of entirely new

melodies.6 Owens 1974 and Kenny 1999 exemplify formulaic analysis, while Schuller 1958 includes

paraphrase and motivic analysis.7 Two examples of this approach are Mehegan 1959 and Reeves 1989.8 See, for example, Martin (1996), or anything by Larson.


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between the improvised melody and the schematic harmony, specifically, the voice-leading

strands implied by the harmony. Therefore, it appears that the variation choruses are under no

obligation to preserve the scheme’s melody.

Schematic harmony may be modified in the realization (“reharmonization”) but is seldom

disregarded altogether. There are two common types of modification: substitution and

interpolation.9 In substitution, one harmony replaces another of the same function. For

example, in tritone substitution, a chord, usually a dominant-seventh chord, is replaced with

the chord whose root is a tritone away.10(E.g., D-7—G7—C becomes D-7—Db7—C.) In

interpolation, an extra chord or group of chords increases the harmonic rhythm without

changing the harmonic middleground. For example, one can precede any dominant-seventh

chord with its ii7 chord, “borrowing” metrical time from the dominant chord (so that there are

no extra beats). The bridge of “I Got Rhythm” (Gershwin) normally features two measures each

of D7, G7, C7, and F7. By the preceding method, the following progression may be

substituted, with one chord per measure: A-7—D7—D-7—G7—G-7—C7—C-7—F7. Such

modifications may be planned in advance, or applied spontaneously by the soloist or rhythm

section. (Both of these examples involve modification of unstable harmonies, not functional

tonics. This is typical.)

In contrast with melody and harmony, the realization must strictly follow the schematic

meter. Descriptions of the scheme-realization relationship tend to focus on melody andharmony and ignore meter. Berliner (1994) observes that “composed pieces or tunes, consisting

of a melody and an accompanying harmonic progression, have provided the structure of

improvisations throughout most of the history of jazz” (63). Similarly, Tirro (1974) describes

improvisation as the “simultaneous acts of composition and performance of a new work based

on a traditionally established schema—a chordal framework known as the ‘changes’” (286–287).

These authors ignore meter not because it is unimportant, but because it is rigid and taken for

granted.

9 Strunk (1979) and Terefenko (2008) describe many modifications in detail.10 Tritone substitution is based on the “functional” tritone held in common between tritone-

related dominant chords (in equal temperament). For example, the tritone in both G7 and

Db7 is between B/Cb and F.


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I refine this description in chapter 1. For now, to illustrate the profound rigidity of jazz

meter, I offer a hypothetical example. Assume a thirty-two-bar scheme: after a 96–measure

(three-chorus) drum solo, in which the drummer employs wild syncopations and cross-rhythms,

the remainder of the ensemble, tacet for the duration of the solo, will enter in unison on the

downbeat of the 97th measure. If someone enters a beat or bar early or late, a savvy listener

recognizes this as a mistake.

According to David Temperley (2001), “Relative freedom in one [musical] rule…tends to

be balanced by relative strictness in another” (296). Jazz’s melodic freedom and metrical

strictness help define the style. Jazz musicians have great freedom to modify or replace the

schematic melody and harmony, but they must maintain the meter. This serves a practical

purpose. As Tirro puts it, “The educated and sensitive listener is at all times oriented with

regard to the temporal progress of the piece” (1974: 287). It similarly aids the performer:

according to Martin, “Since the two-, four-, and eight-bar subdivisions are easily internalized,

the soloist is free to create complexities that play off against the large-scale regularity of the

form” (1996: 41). The meter’s consistency allows the musicians and listeners to stay together in

an environment of unplanned melodies and harmonies.

What is Phrase Rhythm?

Phrase rhythm is the interaction of two musical structures: grouping and meter. Temperley

describes these structures’ conceptual independence: “Meter is a hierarchical framework of

beats…which in itself implies no segmentation. Grouping is a hierarchical structure of

segments, which in itself implies no accentuation. In principle…meter and grouping are

independent structures, which may be aligned with one another in a variety of different ways”

(2003: 125). In the next two chapters, I explain that although these structures are conceptually

independent, they are not independent in practice.

Grouping structure is the hierarchical organization of melody into motives, sub-phrases,

phrases, and sections on the basis of such features as rests, rhythm, harmony, and repetition. A

complete solo consists of many groups, in which still smaller groups are embedded. Fred

Lerdahl and Ray Jackendoff call grouping structure “the most basic component of musical

understanding” (1983: 13). According to one view, grouping structure arises in the listener’s


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mind through the unconscious application of rules to the musical surface, rules based on the

features listed above (see especially Lerdahl and Jackendoff 1983 and Temperley 2001). Maury

Yeston (1974) lists several criteria by which musical events may be grouped together. These

include temporal proximity of attack point, timbre, dynamics, event density, and pattern

recurrence (pp. 52–68). Yeston views the grouping process as pre-metrical. That is, if the analyst

begins with as few assumptions as possible, grouping criteria are the best means for

immediately organizing the musical surface, before determining metrical structure.

Meter is a regular pattern of strong and weak beats, superimposed on the musical surface

by the listener on the basis of informed expectation. It is often depicted as a hierarchy of beats

at various levels. Hypermeter refers to metrical levels above the notated measure; a hypermeasure

contains some whole number of measures, usually between two and four. 11 (I allow larger

hypermeasures as well.) “Meter” refers to the entire metrical hierarchy, including any

hypermetrical levels.

In jazz, the contrast between meter’s inflexibility and grouping structure’s freedom makes

it easy to perceive their relationship. Figure I–1 shows the first sixteen measures of Charlie

Parker’s solo on “Dewey Square.” At one level, the grouping structure is clear. Rests in

measures 3, 7, 9–10, and 13–14 suggest division into the segments A, B, C, D, and E. But

other levels of grouping structure are not so obvious. Do these segments combine to form

larger groups? B and C might be grouped together because of their temporal proximity. Thesmall melodic interval between the end of C and the beginning of D might suggest a

connection between these segments. It is even harder to determine sub-groups within each

segment. Within segment A, the tied eighth notes in measure 2 might suggest an internal

division, but there is a clear voice-leading strand across this point from the Cb to the Bb on

beat 4. Indeed, clear points of division are hard to find within any of the segments.

On the other hand, the metrical structure of figure I–1 is entirely obvious. Measures 1 and

9 begin eight-bar hypermeasures, 5 and 13 begin four-bar hypermeasures, and 3, 7, 11, and 15

begin two-bar hypermeasures. Notice how the five segments relate to the downbeats. Segments

C and D both end a little after strong downbeats—they are end-accented. Segment E has a

metrically weak ending in the fourth bar of a hypermeasure, the only such phrase in the

11 The term first appears in Cone 1968: 79.


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example. At the one-measure level, every segment begins during the first two beats of a

measure. Only segment A ends on a downbeat.

Figure I–1. Parker, “Dewey Square”: Grouping structure of mm. 1–16 {21}

It should be clear from figure I–1 that melodic groups can stand in many relationships to

the schematic meter and to each other. Other jazz theorists seem aware of these issues, but have

never tackled them directly. For example, Martin (1996), who applies Schenkerian techniques

to the music of Charlie Parker, offers some suggestive generalizations, but no analytical

method:

Parker’s [melodic] line is further enhanced through irregular phrasing and through

its large-scale syncopation with respect to the eight-bar symmetries and customary

harmonic rhythms of the song forms. His phrasing and accents will sometimes cut

across these symmetries, but as often as not, he is content to conform to the song

form by generally not phrasing across sectional divisions. (112)

This description appears in the final chapter, on non-Schenkerian aspects of Parker’s style. No

doubt Martin makes this assessment based on deep knowledge of Parker’s work, but the lack of

empirical support contrasts with the rest of the book’s rigor. Keith Waters also appreciates

these issues (1996). He even invokes the concept of hypermeter and its unconscious

A B

C

D

E


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internalization by performers: “The notion [of hypermeter] represents clearly the larger formal

divisions within the thirty-two-bar standard tune form and the twelve-bar blues. It is also a

principle intuited by improvisers who articulate longer musical spans by providing a release

point which gives stronger metrical weight to the larger divisions of the formal structure” (23).

Even more suggestively, he observes, “While jazz pedagogy and the critical literature normally

focus upon the harmonic dimension—often harmonic substitution—perhaps equally crucial for

extended improvisations are the rhythmic techniques that obscure the barline, as well as four-

bar, eight-bar, and other formal divisions” (19). The striking contrast between metrical rigidity

and melodic freedom—especially the freedom to create diverse grouping structures—invites

deeper exploration.

Why Phrase Rhythm Matters

By definition, phrase rhythm is a part of every jazz solo, whether or not the performer or

audience is aware of it. This is because every solo necessarily involves the superimposition of a

grouping structure on a metrical structure. One goal of this dissertation is to shed light on this

under-recognized aspect of jazz.

Phrase rhythm also contributes a great deal to the aesthetic value of many jazz solos. In the

following chapters, I explain how grouping structure can support or contradict meter, creatinga state of phrase rhythm consonance or dissonance. Pure consonance and dissonance occupy

opposing ends of a spectrum, within which the two components of phrase rhythm may agree or

disagree in various ways. For the sensitive listener, the fluctuation of these states throughout a

solo creates powerful sensations of tension and resolution. Phrase rhythm shares this power

with every other aspect of music to which theorists devote attention. Therefore, the other goal

of this dissertation is to awaken our sensitivity to these fluctuations.

In chapter 1, I describe the two components of phrase rhythm in more detail, with special

attention to their behavior in jazz. In chapter 2, I present my method of phrase-rhythm analysis.

In Part II, I apply the method to performances by a variety of musicians, in schemes of various

types. Performances in chapter 3 follow thirty-two-bar AABA form; in chapter 4, thirty-two-bar

ABAC form; in chapter 5, twelve-bar blues; chapter 6 covers some schemes that depart from

these norms.


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10

Chapter 1: Meter and Grouping in Jazz

In jazz, even more so than in classical music, meter and grouping coexist in a state of “creative

tension” (Rothstein 1989: 28). The meter presents a predictable background on which diverse

grouping structures may be superimposed. Meter consists of a hierarchy of temporal units—the

choruses and their constituent hypermeasures—that the grouping structure can never alter.

Grouping structure is free to imply its own hierarchy, whose units may or may not be

coextensive with metrical units. In this chapter, I explore meter and grouping in detail.

Meter

I approach meter from two angles. Chiefly, I consider it as an abstract hierarchy, based on a

view of meter that dominated until the 1990s. Secondarily, I consider how recent theories of

meter grounded in perception temper the hierarchical perspective.

The metrical hierarchy is a collection of embedded layers or levels of regular rhythmic

activity. Clear antecedents of this modern concept emerged in the late 18 th century.12 Johann

Kirnberger’s starting point for meter is a stream of “undifferentiated tones” (Mirka 2009: 4).

From this stream, “for meter to arise, a second-order regularity must be superimposed on the

otherwise undifferentiated beats,” in the form of accents ( ibid.). Heinrich Christoph Koch

espouses a similar view. Kirnberger is equivocal with regard to whether or not the meter-

defining accents are phenomenal—dependent on features of the music—or generated in the

mind of the listener—the modern concept of the “metrical accent” (Mirka 2009: 5). In fact,

both phenomenal and metrical accent are involved in metrical perception, as I explain below.

Koch extends the hierarchy in both directions. Taktteile (beats) group together into Takte

(measures), and may be divided into Taktglieder (beat divisions), which may be further divided

into Taktnoten (subdivisions) (Mirka 2009: 8). Koch considers all layers in relation to the streamof pulses: “The eighteenth-century metrical hierarchy is centered around the level of Taktteile”

(ibid.). The level of Taktteile is thus similar to the modern concept of the tactus, discussed

below. Kirnberger anticipates modern theory by positing three classes of accent, which roughly

12 In the following summary I rely on Caplin 2002 and chapter 1 of Mirka 2009.


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correspond to the modern concepts of metrical accent, phenomenal accent, and dynamic stress

(Caplin 2002: 670). So-called Akzenttheorie became somewhat jumbled in the 19 th century, with

Marx notoriously suggesting that the performer apply stress to notes falling on the strong beats

of the measure (1854). Nevertheless, two components of late 18 th-century metrical theory—a

hierarchy based on the Taktteil and distinct types of accent—anticipate modern views.

Almost two hundred years later, Grosvenor Cooper and Leonard Meyer presented a

“new” theory of meter (1960). Though they do not refer to 18th-century theory, their

description of meter as “architectonic” resembles earlier views: meter is the “measurement of

pulses between more or less regularly occurring accents” (4). 18th-century theorists emphasize

notation, especially bar lines and the time signature. Cooper and Meyer recognize that these

markings depict only two or three levels of the metrical hierarchy, observing that architectonic

organization continues above and below these levels. Their theory falls short in its description

of accent: they apply accents not only to events but also entire groups, and they do not classify

accents into distinct types, although they do offer the memorable (but vague) definition of

accent as a “stimulus which is marked for consciousness in some way” (8).

Edward Cone’s Musical Form and Musical Performance (1968) discusses the metrical aspects

of the Baroque, Classical, and Romantic styles, and vividly juxtaposes each style’s treatment of

the metrical hierarchy (chapter 3). According to Cone, each style-period focuses on a different

level: in the Baroque, the beat is primary, in the Classical, the measure, and in the Romantic,the four-bar “hypermeasure” (79). This demonstrates his awareness that meter, understood

broadly, goes beyond notation. His description of Baroque meter also points towards the

concept of the metrical accent: “The beats seem to form a pre-existing framework that is

independent of the musical events that it controls” (70). This should sound familiar based on my

preliminary description of the schematic meter in jazz. In jazz, the “pre-existing framework”

goes much deeper than in Baroque music.

Arthur Komar (1971) describes the metrical hierarchy in more precise terms. To him, each

level of the hierarchy has the same properties, further minimizing the role of notation. He

writes, “‘Strong’ beats at a given metrical level are those that coincide with beats at a higher

metrical level” (53). In other words, the property of strength within a level is nothing more

than the presence of a beat at the next highest level. While Koch formulated the hierarchy in

terms of accents on the level of Taktteile, Komar argues that the very existence of regular accents


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within a metrical level depends on the presence of a higher level. The difference is in causal

orientation: for Koch, the accents on the level of Taktteile create the level of Takte; for Komar,

one level of beats creates the accents in the level below, a top-down view heavily influenced by

the late work of Heinrich Schenker. He believes the entire metrical hierarchy flows from its

highest level: “The interrelations of strong and weak beats at higher metrical levels carry down

into lower metrical levels, so that in the foreground, beats are typically both strong and weak

relative to different time-spans” (53). Though Komar’s top-down perspective on meter has not

been taken up by others, his conception of the metrical hierarchy has been influential.

Maury Yeston (1974) approaches the hierarchy from the other end—the lowest levels—but

arrives at a similar formalism to Komar. He writes, “The fundamental logical requirement for

meter is…that there be a constant rate within a constant rate—at least two rates of events of

which one is faster and another is slower” (90). In other words, like Komar, he explains regular

accents within a level as originating in a higher level. He says that meter “appears” on neither

the faster nor the slower level alone: “There is apparently, then, no such thing as a level of

meter or a level on which meter may appear; but rather, meter is an outgrowth of the

interaction of two levels” (90). Like Komar, Yeston develops his metrical theory on

Schenkerian lines, equating the different levels of the metrical hierarchy with different levels of

tonal events. He also uses his theory of rhythmic strata to model metrical consonance and

dissonance, in a manner adapted by Harald Krebs (1999).Building on Yeston, Fred Lerdahl and Ray Jackendoff present the clearest picture of the

metrical hierarchy (1983). For them, it is the “interaction of different levels of beats (or the

regular alternation of strong and weak beats) that produces the sensation of meter” (68). In

other words, they equate regular accents on a single level with the presence of multiple levels:

these are simply two ways of looking at the same thing. Following Yeston, they note that all

strong beats at one level carry over to the next-higher level, and that beats at any given level are

strong beats at all smaller levels (19–20). They also develop the familiar “dot” notation for the

metrical hierarchy. Figure 1–1 shows a hypothetical “metrical grid” using dots. Metrical levels

are labeled on the left, and a dot indicates the presence and location of a beat on that level.


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Figure 1–1. A metrical grid in 4/4.

# # # # # # # # # # #

$

#

#

#

#

#

#

% # # #

2–Bar # #

4–Bar #

Lerdahl and Jackendoff’s greatest innovation is in their presentation of the metrical

hierarchy as a perceptual entity: a model of how listeners comprehend meter. They distinguish

three types of accent: 1) phenomenal, resulting from “any event at the musical surface that gives

emphasis or stress to a moment in the musical flow” (something “marked for consciousness”);

2) structural, “caused by the melodic/harmonic points of gravity”; and 3) metrical, “any beat

that is relatively strong in its metrical context” (17). Of these types, the first, phenomenal

accent, acts as a “perceptual input” to meter ( ibid.). The listener unconsciously applies a series

of rules to determine the most logical meter based on the music’s attributes (72–101). These

rules capture our intuitions about meter. For example, their fifth Metrical Preference Rule

(MPR5) expresses the intuition that relatively long rhythmic values tend to occur on relatively

strong beats (80–87). “Beats” in the hierarchy represent “metrical accents,” which are inferred

from the unconscious processing of phenomenal accents. Their theory represents the “final

state” of listeners’ understanding. Though their explanation of the metrical hierarchy moves

beyond previous theories, Danuta Mirka observes that it is unrepresentative of real-time

metrical processing (2009: 16 ff). Below, I present her refinement of their theory. For now, I

pursue the concept of the metrical hierarchy a bit more deeply. Justin London writes, “One may characterize meters in terms of their hierarchic depth”

(2004: 25). Jazz’s metrical hierarchy is extremely deep. In a medium-tempo thirty-two-bar

scheme, it includes a quarter-note, half-note, measure, two-measure, four-measure, eight-


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measure, sixteen-measure, and thirty-two-measure level. Carl Schachter provides a vivid account

of metrical accent, germane to this account of jazz’s metrical hierarchy:

Once the listener becomes aware of recurrent durational units—beats, measures, and

larger periodicities—that awareness, in and of itself, adds another layer of

accentuation to the musical image. The accents thus produced are true metrical

accents—metrical because they arise directly out of the listener’s awareness of the equal

divisions of time that measure the music’s flow. (1987: 5)

In jazz, these “recurrent durational units” are determined by the scheme and known in advance

by the performer, and by any listener familiar with the particular scheme. When hearing a

performance, a listener sensitive to the metrical hierarchy has an entirely different experience

from a naïve listener. The savvy listener anticipates each passing beat, from the lowest to the

highest levels.

Performance conventions also highlight the scheme’s largest metrical units. Transitions

between soloists nearly always occur within a measure or two of the boundary between

choruses—the chorus being the largest metrical unit. This transition can also occur at the

midpoint of each chorus, highlighting the second-largest metrical unit. Consider also the

common practice of “trading fours,” in which soloists take turns improvising during four-bar

hypermeasures, and the related practices of “trading eights” and “trading twos.” (No one ever

“trades threes,” only metrical time-spans.) Jazz’s treatment of the lowest metrical level is also distinctive. The tactus is a primary

metrical level, the “level of beats that is conducted and with which one most naturally

coordinates foot-tapping and dance steps” (Lerdahl and Jackendoff 1983: 71). The standard jazz

tactus is the quarter-note; at very fast tempos, the half-note takes over. While the tactus is often

almost metronomic, establishing a groove, division of the tactus is characteristically loose.

(Consider the incredible variety in “swing” articulation of eighth-notes.) Duple, triple, and even

quadruple division of the tactus are all common, and may be freely mixed and inflected.

London (2004) details the perceptual limitations on the tactus. He claims that the range of

ideal tacti—those judged by a listener to be neither too long nor too short—is between 80 and

120 beats per minute (bpm). Beat frequencies below 30 bpm or above 240 bpm are too slow or

fast to be heard as tacti (29–30). Jazz’s characteristic treatment of the tactus as the fastest regular

level of beats combines with this wide perceptual range to explain the phenomenon of tactus-


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shifting , commonly called “double-time” or “double-time feel.” This occurs at tempos in the

lower end of London’s range, at which the tactus’s frequency can double without exceeding the

possible range. (For example, a tactus-tempo of 60 bpm can double to 120 bpm while

remaining within the ideal range.) In this situation, the perceived tactus shifts from the quarter-

note to the eighth-note. Kernfeld describes the effect: “Double-time involves a doubling of

tempo in the rhythm section, a doubling of the general speed of the melody line, or both"

(1995: 8). This description (and the term “double-time”) is misleading, however, because the

tempo only seems to double as a result of a shift in tactus. Under such a shift, the number of

tacti per chorus doubles; each chorus contains twice as many tactus-beats, but the same amount

of quarter-note beats as before. Because the listener is inclined to interpret the lowest regular

level as the tactus, musicians bring about the tactus-shift simply by playing the eighth-note level

strictly, and “swinging” the eighth-note divisions in the same way that eighth-notes are normally

swung. At times, one member of an ensemble may imply a shifted tactus while others do not,

creating tension between competing interpretations.

Refining this View: Metrical Projection and Perception

Christopher Hasty (1997) challenges the hierarchical view of meter described above. His theory

attempts to model the real-time experience of meter. It is based on the notion of projection intime. According to Hasty, “Projective potential is the potential for a present event’s duration to

be reproduced for a successor. This potential is realized if and when there is a new beginning

whose durational potential is determined by the now past first event” (84). Example 1–2 shows

the projective process. The labels A and B respectively designate an “event”—a sounding note,

for example—and the silence that follows. The onset of a second event, A´, demarcates the end

of the first “duration,” C, comprising the event A and silence B. At the onset of A´, the “actual

duration” C creates the “potential duration” C´, which is not yet past. The solid arrow

indicates a completed duration, while the dotted line indicates only a “potential duration,” yet

to be realized. In simple terms, the experience of the duration C creates an expectation of

parallelism for the duration of C'.


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Figure 1–2. Metrical projection. (Hasty 1997: fig. 7.1, p. 84)

C C´

A B A´ B´

Hasty’s theory influences the recent work of Danuta Mirka (2009), which combines

projective theory with Lerdahl and Jackendoff’s hierarchical view. Echoing London (2004),

Mirka divides the act of metrical perception into “finding” and “monitoring” meter. She uses

projection to depict the initial determination of meter and the negotiation of metrically

challenging passages, and uses the metrical grid to depict an established meter. On this basis,

she claims, “All of the analyses presented in [Hasty 1997] are designed to reveal intermediarystages of [metrical] processing by bringing to light the projections of which it consists” (29; my

emphasis).13

In other words, Hasty shows only one portion of the act of metrical processing:

finding, not monitoring meter.

Based on a synthesis of research into metrical cognition, London also argues for dividing

metrical processing into two stages (2004). He depicts the perception of meter as a process of

“entrainment.” Meter is the “anticipatory schema that is the result of our inherent abilities to

entrain to periodic stimuli in our environment” (12). Listeners have an innate sensitivity to

regularity, and learn to anticipate future events on the basis of past regularity. The second

phase of metrical processing, monitoring meter, is marked by the perception of metrical

accents, a consequence of entrained anticipation: “A metrical accent occurs when a metrically

entrained listener projects a sense of both temporal location and relatively greater salience onto

a musical event” (London: 23). The expectation of accent creates an accent in the listener’s

mind, no matter the event that ultimately coincides with the accent—a self-fulfilling prophecy.

This is why metrical accents can fall on rests. Metrical accents arise only in the phase of

monitoring meter, the phase that London, like Mirka, thinks Hasty overlooks. This view

accounts for the perception of metrical accent even on the first hearing of a piece, going

beyond Lerdahl and Jackendoff’s claims (1983).

13 This echoes an earlier critique in London 1999: “Hasty’s analyses…can be readily understood

as fine-grained explanations of metric recognition,” i.e. the early part of processing meter (265–

266).


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According to Mirka, the initial events of a piece enter a “parallel multiple-choice

processor,” which unconsciously compares possible interpretations of the meter.14

A potential

metrical analysis enters consciousness only after it has passed a certain threshold of regularity,

which varies depending on the context (19). The end result is a “projective hierarchy,” as

reproduced in figure 1–3, and the comparatively easy task of monitoring meter, in which

metrical accents arise from the expectation of continued confirmation of projections ( ibid.).

Figure 1–3 combines aspects of figures 1–1 and 1–2. When meter departs from expectations,

the parallel processor “wake[s] up” and compares possible analyses once again (23).

Figure 1–3. A projective hierarchy. (Mirka 2009: fig. 1.12, p. 19)

The experienced jazz listener assumes a priori that a fixed metrical hierarchy, up to the level

of the chorus, will persist throughout a performance. The first chorus establishes this structure.

Metrical processing then involves the weighing of perceptual input against prior knowledge of

jazz metrical convention.

15

This knowledge operates at two levels: familiarity with specificschemes and scheme-types, and familiarity with the broader demand of metrical regularity. All

performances will fall into one of the following categories (listed in order of increasing

cognitive demand):

1. A familiar scheme, realized…

a. …without additions (intro, interludes, etc.) or revisions;

b. …with additions, but no revisions;

c.

…with revisions, which are introduced in the opening theme and retained in

the variations;

14 Mirka 17–18; the “parallel multiple-analysis model” is first posited in Jackendoff 1991.15 Knowledge of metrical convention informs the perception of many styles besides jazz; but the

conventions of jazz meter are unusually powerful.


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d. …with two metrical schemes, one for the theme and one for the variations,

requiring that the listener use the first variation chorus as a metrical scheme

for the others;

2.

An unfamiliar scheme…

a. …with the same scheme in theme and variations, and no additions;

b.

…with the same scheme in theme and variations, and additions;

c.

…with a different scheme in theme and variations (see 1d).

The cognitive demands of an unfamiliar scheme are significantly lower if it conforms to a

common form, like thirty-two-bar AABA or ABAC (or its common variants), or twelve-bar

blues. Experienced listeners recognize these easily.

Consideration of metrical perception refines the account of jazz’s highest metrical levels. I

have grouped the chorus-level in the same category as other metrical levels: the chorus is a

recurring temporal unit, as are the sixteen- and eight-bar hypermeasures of thirty-two-bar

schemes. But cognitive limits on beat perception suggest that meter is not perceived in the

same way at all levels: as metrical units grow larger, meter blurs into form. According to

London, “Metric entrainment can only occur with respect to periodicities in a range from

about 100 ms to about 5 or 6 seconds” (2004: 46). At a tempo of 120 beats per minute, a four-

bar hypermeasure lasts eight seconds. I speculate that one perceives the regularity of large time-

spans through the unconscious accumulation of smaller spans, a learned skill.

16

Metricalaccents at higher levels still feel stronger than those at lower levels; however, the eight-bar

downbeat (the first quarter-note beat of an eight-bar unit) receives its metrical accent not via a

projection originating from the previous eight-bar downbeat, but from the aggregation of lower-

level beats and foreknowledge of the scheme.

16 Gridley (2006) writes, “Each musician is silently counting the beats and thinking of the

chords that are progressing while he is not playing” (14). This may describe the experience of

beginning players, but experienced musicians only bother to count consciously when realizing a

scheme with an unusual meter; for most schemes one simply feels the hypermetrical units.


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Challenges to the Meter

I divide meter-disturbing events into three categories: expressive variation, dissonance, and

alteration. London defines expressive variation as “subtle nuances involving compressions and

extensions of otherwise deadpan rhythms” (2004: 28); it is as much a part of jazz as classical

music. Benadon (2009) interprets jazz soloists’ microrhythmic accelerations, decelerations, and

fluctuations as “transformations” of underlying rhythms, by tracking how certain passages

depart from regularity. These variations challenge the metrical hierarchy “from the outside”:

they involve clock time and could not be shown on a conventional metrical grid (see fig. 1–1

above).

Yeston 1974 contains the first detailed discussion of metrical dissonance (chapter 4),

which arises from a conflict among metrical levels. Harald Krebs (1999) divides dissonances

into “grouping” and “displacement.” Hemiola exemplifies the former, persistent syncopation

the latter. In a jazz context, metrical dissonance might be considered the superimposition on

the schematic meter of any conflicting, regular layer of accents. For example, in a 4/4 scheme, a

pianist might play accompanying chords on every third quarter-note beat, creating a layer of

regular rhythmic activity that contradicts the scheme. The schematic meter need not be literally

present in the realization for metrical dissonance to take place. “Subliminal dissonance”

describes a dissonance that takes place against an implied metrical layer (Krebs 1999: 46).Subliminal dissonance is very common in jazz, aided by the power of metrical convention to

bolster the memory of the schematic meter during extended digressions.

The prevalence of metrical dissonance in jazz has made it a popular topic of theoretical

research (recently, Downs 2000/2001, Folio 1995, Hodson & Buehrer 2004, Larson 1997 &

2006, and Waters 1996). Each author uses a slightly different set of terms, but their collective

focus is on dissonances at or near the tactus-level. Steve Larson and Keith Waters devote some

attention to hypermeter. Larson suggests that episodes of grouping dissonance often begin and

end on hypermetrical downbeats (2006: 117). Waters (1996) defines a dissonant effect called a

“2-shift”: a phrase that begins in the second measure of a four-bar hypermeasure. Hodson and

Buehrer (2004) even apply Krebs’s methodology to jazz. In general, these articles adapt classical

theory to the jazz repertoire, rather than introducing approaches uniquely suited to jazz.


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Metrical alteration is the replacement of one metrical level with another. I already

mentioned that a realization can incorporate into every chorus certain pre-planned alterations

to a familiar scheme. For example, there might be metrical modulations at certain points in

each chorus, or the addition of beats or measures. Such alterations become part of the scheme

for that performance, even if known in advance only to the performers. I distinguish these

cases from spontaneous metrical alterations, those that occur with no prior planning or

discussion, and that require only non-verbal communication to coordinate.17

All spontaneous metrical alterations must be comprehensible as subliminal grouping

dissonances that preserve some higher metrical level. Typical examples involve the replacement

of duple with triple division at some level, with the next-highest level held constant.18

Consider

a measure-preserving metrical modulation from 4/4 to 6/8 ($ = .).19

This replaces duple

division of the half-measure with triple division. But the flow of half-measures and measures

continues uninterrupted through the modulation, as do all higher levels; no matter how long

the modulation persists, it could be understood and heard as a subliminal dissonance against

the schematic 4/4.20

To suggest this alteration to the rhythm section, a soloist only need

persistently employ triple division of the half-measure; a skilled rhythm section will quickly

recognize the change. Even if they do not acknowledge the change, or if several measures pass

before they perceive it, the ensemble will continue their parallel progress through the scheme,

due to the synchronization of higher metrical levels between the original and altered meter.

Compare this with an invalid alternative, tactus-preserving modulation from 4/4 to 3/4 (

= ). After this modulation, each chorus will last 96 quarter-notes, not 128, but each quarter

17 Dunn (2009) discusses how musicians suggest metrical dissonances and alterations to one

another through musical cues alone.18 Mirka (2009) discusses how all grouping dissonances can all be understood relative to both a

lower and a higher level (156 ff). The latter orientation is more useful here.19 Waters (1996) distinguishes measure-preserving from tactus-preserving polymeter, based on

whether the downbeat-level or the tactus-level is common to both of the dissonant metrical

layers. The same distinction may be made between metrical modulations, based on the note

value that is held constant.20 Fred Hersch oscillates between 4/4 and 6/8 in just this manner throughout his performance

of “Con Alma” from the album Songs Without Words (2001).


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note will last the same amount of time. This cannot be understood as the re-division of a

metrical level, and it would be absurd to treat this as subliminal grouping dissonance at some

higher level.21

Furthermore, if a soloist attempted to make this alteration unilaterally, without

prior planning, the rhythm section would probably mistake the alteration for a superimposed

polymeter, and retain the 4/4 scheme. Unless the rhythm section instantaneously responded to

the soloist, the two parts would “decouple,” drifting further and further apart in their progress

through the scheme.

For this reason, though hypermetrical alteration is ubiquitous in common-practice music,

it is impossible in jazz, since it cannot be understood as re-division of a higher metrical level.

Figure 1–4 shows a “metrical reinterpretation.” In measure 16, the regular alternation of strong

and weak downbeats is interrupted by an unexpected strong downbeat, arising from the forte

entrance of the orchestra on a new phrase and tonic harmony. The two-measure level and any

potential four-measure level are disrupted by the unexpected strong downbeat in measure 16.

There is consistency only at the next-lowest metrical level, the downbeat-level.

Alterations that violate this rule may safely be interpreted as mistakes. Consider figure 1–

5. Here, the Bill Evans Trio inserts an extra beat in a 3/4 context, resulting in a measure of

4/4. Just before measure 7, as marked with an “X,” Evans continues the harmony D7, implying

that D7 continues through the downbeat of bar 7. This is a distortion of a rhythmic cliché in

which the left-hand anticipates downbeat harmonies by an eighth-note. The late arrival ofEbmaj7, on beat one-and of measure 7, implies that beat two is a downbeat (since the pianist

would typically play a new harmony just before the downbeat). In consequence, the rhythm

section inserts an extra beat in the following measure. The bassist and drummer erroneously

believed that Evans had (accidentally) inserted an extra beat, and they attempted to

compensate.22

21 The 3/4 scheme and the 4/4 scheme will only align every 384 beats: three choruses of 4/4

and four choruses of 3/4.22 A skilled rhythm section is highly sensitive to potential errors on the part of the soloist, in

order to minimize the audible consequences. In this case, they were too sensitive. Errors can

and do occur at every metrical level: the addition or subtraction of a beat is perhaps most

common, but measures and even sections may be accidentally added or subtracted.


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Figure 1–4. Hypermetrical analysis of Haydn's Symphony no. 104/I, Allegro.

(Temperley 2008: fig. 1, p. 307)

Figure 1–5: A metrical mistake. (Evans, "Someday My Prince Will Come,” beginning

of 2nd chorus) {9}

How do I know figure 1–5 shows a mistake and not an intentional alteration of the

scheme? Because the additional beat does not appear at any other point in the performance. Its

appearance in other choruses, especially an appearance at the same place in each, would suggest

that the performance followed model 1c above—a familiar scheme with revisions in the

realization. It is inconceivable that the group would deliberately insert a single extra beat only

once in the performance.


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The top-down rigidity of jazz meter has a precedent in classical variation procedure.

Variations, except in the freer variation style of the late nineteenth century, preserve the

metrical scheme established by the theme (Nelson 1949: 6). Jazz develops this procedure in two

ways. First, it combines the metrical continuity of ostinato variations with the greater thematic

length of discrete variations (those performed with an intervening pause). (Consider Tirro’s

comparison of jazz variation procedure with a “chaconne,” quoted in the introduction.)

Second, it liberates grouping structure from the scheme, which is maintained through meter

and harmony alone.

Grouping

Meter in jazz is not only rigid, it is also highly independent, requiring a minimum of

reinforcement from other musical features once it has been established. This is true not only of

lower metrical levels, but also of the highest metrical levels. In contrast, hypermeter in classical

music remains closely tied to phrase-level grouping structure and tonal structure. Specifically,

hypermeter, when present, depends on tonal structure and phrase structure. (The distinction

between “phrase structure” and “grouping structure” is vague. I use the terms more or less

interchangeably. The term “phrase” has received a range of definitions—based on length,

motivic content, essential voice-leading, and so forth—but all imply that a phrase is a kind ofgroup, and so it seems appropriate to mix the two.)

The conceptual separation of grouping and meter clarifies thought; but in practice, the

two structures are mutually dependent, and theorists recognize this. Of course, grouping and

meter are often in a state of slight misalignment—“out of phase,” in Lerdahl and Jackendoff’s

terms—but this is a long way from true independence. I quoted David Temperley in chapter 1,

writing that “in principle…meter and grouping are independent” (2003: 125). But elsewhere,

he acknowledges: “It appears that grouping and meter both affect one another” (2001: 70–71).

Indeed, it is impossible for a composer to establish hypermeter without the help of grouping

structure or tonal structure.

Given the close link between hypermeter and phrase structure in musical practice, it is

unsurprising that 18th-century theorists treated them as a single concept. Joseph Riepel’s mid-

century treatise on composition defines the units of phrasing in terms of their metrical length,


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a practice continued sometimes even to this day (as in Caplin 1998, quoted below, and in my

analytical method, presented in chapter 2). Melodic and harmonic features delineate Riepel’s

Zweyer , Dreyer , and Vierer —phrases two, three, and four measures in length (Eckert 2000: 106–

110). Riepel writes that minuets employ only Zweyer and Vierer , reflecting a preference for

duple hypermeter derived from dance practice (Eckert 2000: 108).

Heinrich Koch’s “mechanical rules of melody,” written in the 1780s, develops Riepel’s

ideas into a more systematic study. Koch defines the basic phrase (enger Satz) in terms of

metrical length—four measures of duple or triple meter, or two compound-duple (4/4)

measures. A melodic segment of this length “is complete when it can be understood or felt as a

self-sufficient section of the whole, without a preceding or succeeding incomplete segment

fortuitously connected to it” (Koch 1983: 6–7). Phrases of other lengths arise through

extension or combination of basic phrases (41 ff). Koch also classifies these modified phrases by

their metrical length.

Koch recognizes the phenomenon of phrase overlap, in which the ending of a phrase

coincides with the beginning of the next phrase. Modern theorists believe that this happens in

two distinct ways. Sometimes, it results in a “missing” measure, as in figure 1–4, measure 16.

But sometimes, phrases can overlap without disturbing the hypermeter (Rothstein 1989: 44).23

This distinction depends on the conceptual separation of grouping and meter, so Koch cannot

make it. He thinks all phrase overlaps result from the “stifling or suppression of a measure”(1983: 54–65).

Koch shares Riepel’s preference for duple and quadruple hypermeter. His Einschnitt, or

sub-phrase, is typically two measures long. Not only is the four-bar phrase “basic,” it is also

ideal: “Most common, and also, on the whole, most useful and most pleasing for our feelings

are those basic phrases which are completed in the fourth measure of simple meters” (11).

Anton Reicha extends this duple preference to the next metrical level (1818). He bases his

theory of melody on the eight-measure period, divided into four-measure “rhythms” or

“members,” which are further divided into two-measure “figures” (Reicha 2000). Like Koch,

Reicha permits various modifications to these units of phrasing, including “supposition,” his

term for overlap (26–27). These modifications can change the metrical length of the basic units

23 For a critique of this view of phrase overlaps, see Lester 1986: 187–192.


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but not their underlying status. Going beyond his predecessors, Reicha observes the effect of

tempo on the units of phrasing: “The slower the movement [tempo], the shorter the members

should be [in metrical length]” (36). Shortening the metrical length of phrases at slower tempos

has the effect of equalizing the “clock length” of phrases at all tempos. Reicha’s advice

demonstrates his intuitive awareness of the cognitive limits on perceiving periodicity.

For these three theorists, hypermeter does not exist as a concept outside of grouping

structure. They all express a preference for melodic periodicity, which inevitably creates

hypermetrical periodicity. Reicha even insists that the three-measure sub-phrase “always

requires a companion” (2000: 29). Thus, Reicha associates three-measure sub-phrases with

three-bar hypermeter, which would require repetition of this unit.

Over a century after Reicha, Cone (1968) similarly blends hypermeter and phrase

structure in his belief that the “four-bar phrase” does not need to be four bars long (75, quoted

above). The characteristic “rhythm” of these phrases arises through patterns of harmonic and

melodic tension rather than metrical length. Though Lerdahl and Jackendoff separate grouping

and meter conceptually, they also recognize their close links in musical practice. For them,

meter exerts its organizational power at a local level, while grouping takes care of the highest

levels—entire sections and movements. But “in between lies a transitional zone in which

grouping gradually takes over responsibility from metrical structure. It is in this zone…that

metrical ambiguities occur in tonal music” (99 ff). This zone corresponds to the units ofphrasing classified by Riepel, Koch, and Reicha. In classical music, meter does not exist beyond

this zone.

Though meter and grouping are intermixed, meter depends on grouping in a way that

grouping does not depend on meter. Lerdahl and Jackendoff’s second “metrical preference

rule” explicitly accounts for the influence of grouping on meter.24 Elsewhere, they write:

“Parallelism among groups of irregular length often forces metrical structures into irregularity

above the measure level” (99). It is irregular groups that cause irregular metrical structures, not

the other way around. Example 1–4, discussed earlier, showed how harmony and grouping

structure can override an established hypermetrical level. Rothstein (1989) also endorses the

24 “MPR 2 (Strong Beat Early) Weakly prefer a metrical structure in which the strongest beat

in a group appears relatively early in the group” (1983: 76). This rule takes grouping structure

as a given, and assumes the listener uses it to help determine metrical structure.


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conceptual separation of grouping and meter, while deriving hypermeter from grouping

structure: “If two or more non-duple phrases, each of the same length, follow each other in

direct succession, a feeling of regularly recurring accents is likely to be created, and with it a

feeling of hypermeter” (37).

William Caplin (1998) defines phrases through melodic content and metrical length. He

echoes 18th-century thought in his definition of the phrase as “minimally, a four-measure unit,

often, but not, necessarily, containing two ideas” (256). Caplin’s phrases are of many types, and

need not end with a cadence: for example, the “presentation phrase” is a four-measure unit that

prolongs tonic harmony, as might begin a larger group (45, 256). Thus, Caplin explicitly

defines the “phrase” through a combination of meter, thematic structure, and tonal structure.

Historically, other theorists have also linked grouping structure to tonal structure as well

as hypermeter. Riepel and Koch define the phrase through its degree of tonal closure. Both

theorists recognize half and full cadences, and cadences “on different degrees” (modulations),

as means of ending a phrase. Lerdahl and Jackendoff believe tonally self-contained groups are

most easily perceived (1983: 52). Rothstein’s theory of phrase rhythm augments the historic

view of the phrase with the insight of Schenkerian analysis. Rothstein defines the phrase as

“directed motion from one tonal entity to another” (1989: 5). This definition places a lower

limit on phrase length, but not an upper limit: Rothstein claims that “large phrases may

contain smaller ones” (10). To determine phrase structure, Rothstein believes that “the bestavailable means…is the Schenkerian method, because that approach reveals underlying tonal

motions most precisely” (13). Schachter also uses Schenkerian analysis to clarify hypermeter

(1980, 1987). Like Rothstein, he believes that some phrases of irregular length derive from

regular prototypes, and that tonal structure reveals phrase structure. His process of “durational

reduction,” a combination of Schenkerian and metrical reduction, “shows a ‘higher-level’

metrical organization of measures” (1980: 198).

Theories of classical music assume a close relationship between phrase structure,

hypermeter, and tonal structure. To wit: at the phrase level, tonal structure determines

grouping structure, and both structures work together to create hypermeter. Jazz upsets these

relationships. In jazz, the scheme determines both metrical structure and middleground tonal

structure; grouping structure has been emancipated.


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Distinctive Features of Jazz Phrase Structure

Although the grouping structure of improvised jazz melodies is unencumbered by the scheme,

jazz themes, by and large, preserve the conventional alignment of phrase structure, meter, and

tonal structure that is found in common-practice music. Allen Forte (1995) analyzes schemes by

the “big six” composers of the Great American Songbook: Harold Arlen, Irving Berlin, Jerome

Kern, George Gershwin, Cole Porter, and Richard Rodgers. Their work may be taken as

representative of the style. Forte writes,

In the American popular song the four-bar length of the phrase is canonical, so much

so that “phrase” used with respect to form means “four-bar phrase.” The musical

markers that delimit the phrase engage melody, rhythm, harmony, and often, but not

always, the lyric. (37)

Forte says that phrases are often divided into two-bar “groups,” and combined into eight-

measure “periods.” Periods combine into songs, so that all of these units “manifest a

hierarchical arrangement” (37). While Reicha and company also describe the units of phrasing

as duple and hierarchical, they acknowledge that composers modify these units; but in jazz

standards, non-duple groups are almost unheard of.25

Forte’s approach is Schenkerian. He highlights some instances in which tonal structure

cuts across melodic grouping structure:In general, it is important to recognize that the components of the template form—in

particular, the two-bar group and the four-bar phrase—do not delimit motions of

larger span, such as long lines and harmonic progressions. In fact, more often than

not, harmonic progressions override those surface groupings. (41)

In many examples, tonal resolution only occurs at the ends of periods, pairs of periods, or even

entire songs (see especially Forte’s chapter 8 on Jerome Kern). But these large tonal motions

still tend to coincide with large metrical groups—eight- and sixteen-measures hypermeasures.

25 One might speculate that this regularity arose from the practical needs of accompanying

social dancing, as in the metrical conventions of Baroque dance movements. But popular

dance steps of the day, such as the foxtrot or various styles of swing dancing, only required

predictibility at the measure level or below—certainly not through four- and eight-bar levels.

(Indeed, the “basic” step in West-coast swing lasts six beats, which is consonant at the half-note

level, but creates metrical dissonance with the measure-level!)


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Smaller groups, indicated by rests and longer notes, more or less follow the two- and four-bar

levels of the meter.

Terefenko (2004) also examines a large repertoire of standards from a Schenkerian

perspective. He concludes, “In the case of standard tunes, there appear to be a finite number of

typical phrase models, each with its own distinctive melodic structure, essential jazz

counterpoint, and supporting harmonies” (3). At no point does Terefenko discuss hypermeter—

perhaps because it is so consistent as to be taken for granted—but his conclusion reflects the

formulaic quality of phrasing in the standard repertoire.

The formulaic quality of standard schemes alters the relationship between grouping, tonal

structure, and hypermeter. No longer can grouping and tonal structure be said to determine

hypermeter, as they do in classical music. Rather, a composer might set out from the start to

write a thirty-two-bar song in eight-bar sections, or intuitively follow this model, and then craft

the tonal and grouping structure to fit the hypermeter.26 There are many examples in classical

music where tonal structure overrides any “preference” for duple groups, demonstrating its

primacy (indeed, the “preference” for duple hypermeter is not uncontroversial); such is seldom

the case in jazz.

After the opening thematic statement, the melody in the variation choruses freely departs

from the grouping structure of the theme. Many authors have recognized the resulting tension

between schematic meter and melodic grouping, but their work does not go far enough. Owens1974 is the first large-scale formulaic analysis of improvised melody, devoted entirely to Charlie

Parker. Like Henry Martin, quoted in the Introduction, Owens mentions Parker’s phrase

rhythm in an aside. He describes Parker’s varied phrase lengths and their relationship to the

hypermeter:

Larger aspects of [Parker’s] phrasing are observable in any of the transcriptions. A

glance through these solos reveals a great variety of phrase lengths, from two- or three-

note groups lasting only one or two beats, to single sustained notes, to elaborate

musical sentences of ten or twelve measures. Parker tended to construct his phrases

26 There are certainly schemes that deviate from the thirty-two-bar models, and these deviations

are brought about by tonal and grouping structure. But the most common modifications take

the form of two- or four-bar extensions, which preserve the flow of two-bar downbeats. In

chapter 6 I discuss several solos on metrically atypical schemes.


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to coincide with the phrase structure of the piece being performed. Thus, his solos in

32-measure, *aaba* pieces generally show endings in the seventh or eighth measures

of each section of each chorus. But deviations from this procedure abound, adding to

the unpredictability and freshness of his performances. (14)

Owens does not elaborate on Parker’s “deviations from this procedure,” nor how these

contribute to the performances. The imprecision of his claims is typical of writing on this

subject.

Keith Waters (1996) analyzes rhythmic displacement in a solo by Herbie Hancock. He

notes that in two places in Hancock’s solo, “Pitch and motive connections cut across the

twelve-bar formal divisions and serve to blur the largest hypermetric divisions” (30). Figure 1–6

shows one instance of this. The motive in question is shown with brackets.

Figure 1–6. Motive vs. hypermeter. (Hancock, “The Eye of the Hurricane,” mm. 69–76,

from Waters 1996)

It is certainly true that at this point in the solo, a motive cuts across the hypermetrical

division on the downbeat of measure 73, and that this connection unifies the solo. But I think

Waters overstates the case by saying the hypermetrical division is “blurred.” The grouping

structure of the solo reinforces the hypermetrical division: the final measure of the chorus (72)

is entirely empty, and Hancock begins his next chorus on the chorus-level downbeat. As I

explain in the next chapter, both motive and rests play a role in determining grouping

structure; but here, the long rest trumps the motivic continuity and prevents any real conflict

between grouping structure and hypermeter that the motive might create. In later chapters, I

present several examples in which grouping structure and motive contradict hypermetrical

divisions, and for which “blurring” seems a more appropriate description.


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Of all jazz theorists, Steve Larson confronts the subject of phrase rhythm most directly

(1996A, 1999). He recognizes the misalignment between schematic meter and melodic

grouping structure: “Since [Charlie] Parker’s ‘phrases’ do not coincide with the 8-measure

phrases of the original melody, I call these 8-measure units ‘sections’ rather than ‘phrases’”

(1996A: 154). Larson describes a 4+2+2 grouping structure as a “reverse sentence,” saying that

after the longer unit, “the two shorter units press forward” (ibid.). (This sort of description of

grouping structure through measure counting appears as early as Reicha 1818 and Marx 1854.)

Larson refers to sentential structure twice more in the article (158, 159). He describes phrase

rhythm’s interaction with listener expectations: “The bridge begins as if its first half will be a

1+1+2 sentence”; when the third phrase is three measures instead of two, it surprises the

listener (158). Elsewhere, Larson says that progressively lengthening phrases in an Oscar

Peterson solo increase energy, and he even presents a chart of the phrase rhythm (1999: 298–

99). But these discussions play a supporting role to the main point of these articles,

Schenkerian analysis. Larson’s treatment of phrase rhythm does not go much beyond what I

have quoted here.

One obstacle to developing a theory of jazz phrase rhythm is the lack of a definition for

“phrase.” Clive Downs also notes this problem: “Phrasing is a term that tends to be used

loosely by critics, and musical dictionaries often fail to give a precise definition” (2001: 42). He

attempts to correct this situation with his own definition, supposedly “precise enough that acomputer program could be written to autom

rhythm in jazz

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