Rhythm in Jazz

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    On Phrase Rhythm in Jazz 


    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


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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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    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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    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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    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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    List of Figures


    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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    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



    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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    Introduction: What is Jazz? What is Phrase Rhythm? 3

    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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    Introduction: What is Jazz? What is Phrase Rhythm? 4

    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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    Introduction: What is Jazz? What is Phrase Rhythm? 5

    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


    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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    Introduction: What is Jazz? What is Phrase Rhythm? 6

    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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    Introduction: What is Jazz? What is Phrase Rhythm? 7

    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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    Introduction: What is Jazz? What is Phrase Rhythm? 8

    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


    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




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    Introduction: What is Jazz? What is Phrase Rhythm? 9

    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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    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.


    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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    Chapter 1: Meter and Grouping in Jazz 11

    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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    Chapter 1: Meter and Grouping in Jazz 12

     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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    Chapter 1: Meter and Grouping in Jazz 13

    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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    Chapter 1: Meter and Grouping in Jazz 14

    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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    Chapter 1: Meter and Grouping in Jazz 15

    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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    Chapter 1: Meter and Grouping in Jazz 16

    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


     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–


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    Chapter 1: Meter and Grouping in Jazz 17

     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.


     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;


    …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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    Chapter 1: Meter and Grouping in Jazz 18

    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;


     An unfamiliar scheme…

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


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


    …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.


     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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    Chapter 1: Meter and Grouping in Jazz 19

    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


     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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    Chapter 1: Meter and Grouping in Jazz 20

    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


    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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    Chapter 1: Meter and Grouping in Jazz 21

    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



    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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    Chapter 1: Meter and Grouping in Jazz 22

    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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    Chapter 1: Meter and Grouping in Jazz 23

    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.


    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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    Chapter 1: Meter and Grouping in Jazz 24

    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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    Chapter 1: Meter and Grouping in Jazz 25

    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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    Chapter 1: Meter and Grouping in Jazz 26

    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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    Chapter 1: Meter and Grouping in Jazz 27

    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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    Chapter 1: Meter and Grouping in Jazz 28

    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


    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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    Chapter 1: Meter and Grouping in Jazz 29

    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


    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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    Chapter 1: Meter and Grouping in Jazz 30

    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