Changes Over Time:

Theory The theoretical modeling, analysis and redeployment of jazz improvisational,

and time-feel, mechanisms

Milton Mermikides

Submitted in partial fulfillment of the

requirements for the degree

Doctor of Philosophy in Composition

Supervised by Dr Stephen Goss, Reader in Composition

Department of Music and Sound Recording

University of Surrey

2010

Contents

Overview 3

1. M-Space and Expressive Contours 6

1.1 Introduction 6

1.2 Background 8

1.3 Chains of Thought and Musical Refractions 11

1.4 Limitation and Variation of Musical Topics 17

1.5 Improvisation as Musical Mutation: M-Space Modelling 25

1.6 Changes and Time: Expressive Contours 56

1.7 Applications of M-Space and Expressive Contours 69

1.8 Reflection 79

2. Time-feel 82

2.1 Sub-notational Rhythmic Expression 82

2.2 Relevant Research 86

2.3 SLW Model of Time-feel 89

2.4 Where’s the Beat? Determining the Master Time-Line 100

2.5 Defining Swing: Offbeat Asymmetry 106

2.6 Ensemble Swing and Swing Friction 108

2.7 Latency 110

2.8 Weighting 112

2.9 Time-Feel Matrix 113

2.10 Relationships between Swing, Latency and Weighting 116

2.11 SLW-Coach : A Computer Application for Time-feel Analysis 121

2.12 Real World Time-feel Analysis 125

3. Case Studies 130

3.1 59% Swing on Swing '42 131

3.2 A Little Drag 134

3.3 Constant Friction 139

3.4 Swing Blocks 142

3.5 Push-Pull 146

3.6 Temporal Plasticity 149

4. Coda 168

4.1 Ongoing Theoretical Research 168

4.2 Presentations 170

4.3 Glossary 172

4.4 References 176  

3

Overview

This collection of writings contains two theoretical papers and a compilation of case

studies. The first paper, M-Space and Expressive Contours offers a consolidated theoretical

model of jazz improvisation. This draws together a range of pedagogical sources and

improvisational theories, and provides a framework in which to appreciate the unifying

concepts behind the diverse compositional portfolio (Changes Over Time: Practice). It also

serves as a necessary foundation for the second paper (Time-feel), which presents a model

of expressive micro-timing and forms the central theoretical contribution in the thesis.

Finally, a collection of analyses (Case Studies) drawn from a varied repertoire, and

employing time-feel, M-Space and expressive contour methodologies, demonstrates the

real world relevance and utility of these concepts.

Throughout the thesis, the term jazz improvisation is used repeatedly, so it’s advisable

at the outset to clarify this terminology. The area of research in this submission focuses

upon the popular genres of African-American born instrumental music including jazz,

blues, funk, soul and rock; but also extends to the variously related genres including

reggae, ska, fusion, hard rock and metal (with various levels of density) and the hip-hop,

rap, R&B and electronic dance styles. However, the musical mechanisms at work are

broadly applicable to all groove-based, quasi-metronomic, variably improvisatory and

technological genres. Any one word would be too broad, or too narrow, for satisfaction,

but references will be made where appropriate and the moniker ‘jazz’ used as a

placeholder. The expected breadth in theoretical knowledge, stylistic understanding and

technological awareness of the serious contemporary jazz student is some vindication of

the use of this shorthand convenience. Improvisation presents another potential

terminological pitfall: it may be argued that a distinction should be drawn between the

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practice of free improvisation within a wider musical community – sometimes conducted

with little special training - and the enormously skilled discipline of the jazz heritage with

its demands on form, rhythmic accuracy, aural skills, ensemble techniques and evolved

language, on which this thesis focuses primarily. However, the techniques presented in

this thesis are found in, and are applicable to, all skilled improvisational scenarios from

traditional ‘standards’ improvisation to ‘free jazz’. It is telling that Hal Crook, an eminent

jazz instructor, released six instructional volumes on every nuance of improvisational

technique before addressing ‘free’ jazz (Crook, 2006). These various forms, although

somewhat amenable to categorization, exist on a continuum of flexibility, and rigidity, of

various musical components (solo forms, melody, harmony, vocabulary, structure etc.),

rather than entirely different skill-sets.1 Terminology from the jazz idiom, which often

has little consensus on precise meaning, is used in this thesis and somewhat refined, and

some new terms have also been coined. A glossary of such terms is included in Section

4.3 (p 172).

The theoretical models in this thesis have been developed through years of jazz

training, performance, composition, teaching and audio production, and are informed

primarily by creative practice. However a feedback cycle has emerged whereby

theoretical concepts are refined and continually reintroduced into the creative process

with varying degrees of premeditation and intuition. A critical reflection of the results

helps refine and develop these theories for further deployment. During this cyclical

process, music technology has provided an invaluable tool with which to analyse the

repertoire, test and employ theoretical models, and enhance significantly creative

opportunities in both performance and composition.

In the graphical representation of music in this submission, standard notation is

sometimes employed, but these examples should always be accompanied with the 1 A comprehensive and instructive survey of ‘free jazz’ is provided in Northern Sun, Summer Moon: Europe’s Reinvention of Jazz (Heffley 2005).

5

reminder of the important limitations inherent in this system. Standard notation is not

without value, however due to its impoverished and discontinuous treatment of pitch,

timbre and rhythm, it should always be seen as a convenient approximate guide (masking

all manner of tacit stylistic implications), and not a definitive account of the deep

complexity of music that exists in the artist’s creative intention, the captured sound wave

or the listener’s experience. Annotated standard notation, sonograms and diagrammatic

representations are all employed where appropriate to the concepts discussed.

Throughout these theoretical writings, references to the creative portfolio Changes

Over Time: Practice are made, these may be explored as the examiner is compelled,

however the presentation of concepts in the theoretical writings has been made so that a

complete reading forms a framework and terminology with which to best approach the

portfolio.

All audio examples cited in the theoretical writings appears on CD1: Audio Examples

(where for example, CD1.3 identifies the third track of the CD). Some of these audio

examples are short and require attentive listening, so the ability to loop a track, and the

use of quality headphones (or monitors) is recommended.

.

6

1. M-Space and Expressive Contours The modeling and reapplication of jazz improvisational technique

Abstract

This paper presents, from a practitioner’s perspective, a consolidated model of jazz improvisation. This is

drawn from a range of theoretical and pedagogical sources, as well as the author’s own heuristic inquiry.

In this model, a musical object is seen as possessing an array of properties available for modification, and

existing at a point in multi-dimensional musical space (M-Space). Improvisation is represented as the

artful carving of trajectories through M-Space via corresponding gestural manipulations of consynchronous

musical parameters (expressive contours), which may form larger scale musical structures. This view of

improvisation offers practical applications for performance, as well as a framework in which to analyse

and appreciate the repertoire. Music technology is of great value in the facilitation of this model’s

employment in analysis, performance and composition. Also presented is the heterogeneous adoption and

reapplication of these concepts throughout a portfolio of stylistically diverse collaborative electroacoustic

works: ‘Changes Over Time: Practice’.

1.1 Introduction

This paper outlines an improvisational and compositional methodology enabled by a

heuristic understanding, theoretical modeling and technological redeployment of jazz

technique. This approach demonstrates how the musical mechanisms found in the

heritage of improvisational practice may be reemployed in composition and performance

beyond their presumed stylistic and practical restraints (Berio 2000, p 82-84). The

author’s experience as a jazz practitioner allows a deconstruction of the improvisational

process from ‘behind the lines’, and an informed level of analysis. Furthermore, extensive

experience with music technology has enabled the design and employment of tools to

understand better the improvisational mechanisms in question, and to reapply these to an

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extent beyond the limitations of traditional practice. These resources provide an

opportunity to extend the creative reach of the improviser and, at the furthest extreme,

compose quasi-improvisational electronic pieces that once established, require little or no

creative input from the composer, rather deferring musical decisions to various external

physical patterns.

This thesis serves to identify and demonstrate the utilisation of jazz improvisational

technique into a wider stylistic and theoretical context. This binding of a heuristic

understanding of improvisation, analytical models and the judicious employment of

music technology can inform the compositional process and improvisational practice in a

range of styles.

The model of jazz improvisation presented here, drawn together from diverse

theoretical and pedagogical concepts, has wide opportunities for application, and these

are outlined with reference to the Changes Over Time: Practice portfolio.

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1.2 Background

The analysis and pedagogical focus of the jazz idiom before the 1980s was largely

limited to those musical features most easily described within the standard notational

system. Standard transcription, scale choices, harmonic extensions, melodic material and

formal structures took precedence over hugely important stylistic features such as

improvisational practice, rhythmic feel, timbral modulation, horizontal vs. vertical

consideration and melodic interpretation. Improvising Jazz (Coker 1987) first published in

1964, represents a typical approach of its time: A comprehensive study of useful scales,

progression and chords, but ‘swing’ is incompletely defined (Coker 1987, p 45-9) and a

welcome mention of contour is frustratingly fleeting (Coker 1987, p 54-5). With some

notable exceptions2, jazz practitioners sided with the analysts’ bias, touting ever more

complex harmonic and scalar systems while largely ignoring all other salient stylistic

features.3 This can be attributed to the difficulty in analyzing certain idiomatic practices,

but may also the result of the incentive of jazz analysts and performers to achieve a sense

of academic parity with ‘classical’ music within the established analytical framework. It is

not that these other unarticulated aspects of improvisation were considered unimportant

by practitioners; rather they were generally considered to be only transferrable though

listening and absorption, and not direct instruction. Jamie Aebersold’s introduction to a

popular Charlie Parker transcription, the Charlie Parker Omnibook, illustrates this:

2 Charlie Mingus’ 1962 lecture discussing the beat ellipsis (Mingus, cited in Berliner, 1994, p 151), solo structuring in Clifford Brown’s playing (Stewart 1973), and Gunther Schuller’s 1968 (Schuller 1986, p 58) linking of jazz improvisation with seed-pattern variations in African music (Jones 1959) are salient and unusual analytical approaches for the time.

3 The jazz community’s adoption of such texts as Nicholas Slonimsky’s Thesaurus of Scales and Melodic Patterns (Ratliff 2008 and Slonimsky 1999), George Russell’s Lydian Chromatic Concept of Tonal Organization (Russell 2008) and The Schillinger System of Musical Composition (Schillinger 1978) illustrate the bias of scalar and harmonic devices over other important mechanisms.

9

Only a minimum of articulations have been put in this book.

We feel that jazz, being an aural art form, is often times best

imitated by listening over and over, and then playing the notes

the way you hear it on the record. This might seem like the

long way to do it, but experience has proven reliable. After all,

who would object to listening anyway? Listening is what

music is all about.

Aebersold & Slone, 1978, p iv

Ironically, many of the tools and vocabulary helpful to the academic understanding

and development of the jazz idiom were already underway in other genres4. The lack of

adoption of these tools by authoritative jazz practitioners of the time was a loss to all

genres concerned. Meanwhile, non-pedagogical research into the jazz idiom was confined

to the areas of harmonic observation, cultural history and heuristic enquiry, with little

attention to the mechanisms addressed in this thesis: phenomenological and sociological

rather than more analytical musical perspectives.5 Other research into improvisation (in

the general sense) has addressed relevant issues but is often divorced from the stylistic

practice within the jazz idiom, and largely from a non-jazz practitioner’s perspective.6

However, the advents of digital audio analysis, computer-based modeling systems and a

fresh, stylistically relevant approach have started to demystify and illuminate the

mechanics of jazz improvisation.7

4 Folk music research, (in the areas of cantometrics (Lomax 1968) and melodic contour typology (Adams 1976)), semiotic analysis (Cook 1994, p 151-82) and the field of notes inégales (Fuller 1980) were all readily amenable to the study of jazz improvisation. The lack of adoption into jazz research of the concepts in electroacoustic music particularly with a timbral, non-score based concept of the musical object, such as (Erickson 1975), was also a missed opportunity.

5 There exists a wealth of valuable cultural and phenomenological research from the 1970s including (Nketia 1971), (Roberts 1972), (Wang 1973), (Titon 1973), (Nettl 1974), (Tirro 1977) (Sudnow 1978), (White 1978) and (Sickler 1979).

6 The concept of generative improvisation (Clarke, 1988), aspects of timing (Gabrielsson 1988), tonal theories (Lerdahl & Jackendoff 1983) and mechanisms of score interpretation (Sundberg 1988) are all relevant improvisational research but were not immediately adopted in relation to jazz.

7 Valuable and welcome research have emerged in such fields as Markov chain analysis of Coltrane solos (Franz 1998) and broad improvisational processes and ensemble interaction theories (Hall 1992), (Larson

10

The emergence since the late 1980s of jazz improvisation writings from practitioners

of great authority8 - born of pedagogical, rather than academic, incentive - is a significant

landmark in the dissemination of jazz methodology, and in opportunities to explore

these mechanisms beyond the immediate stylistic context. This paper combines the

practitioner-based pedagogical perspective of Crook, Jerry Bergonzi et al., with broader

theoretical concepts (found in the writings of Jeff Pressing, Eric Clarke, Trevor Wishart

et al.), including ‘non-musical’ ideas in biology and mathematics, to provide a more

complete model of jazz improvisation virtuosity. These musical mechanisms (with

particular emphasis on the crucial field of expressive micro-timing in time-feel) are, with

the use of music technology, sharpened and re-employed as supporting devices to

compositional practice. Wherever possible, references and analytical examples in the

recorded repertoire are limited to the author’s chosen instrument, the guitar. However it

should be clear that the concepts presented are relevant to all instruments, and indeed, a

wide range of musical styles.

1998), (Monson 1991, 1994, 1996) and (Sawyer 1992). The hugely important and burgeoning field of research in expressive micro-timing is explored and developed in Time-feel in this submission.

8 The new role of the jazz performer/educator/writer, usually associated with an institution such as Berklee College of Music, offers a valuable insight to the jazz student and researcher. Key texts from top-level practitioners who also have the ability to communicate clearly their concepts should not be ignored by the research. See (Bergonzi 1992, 1994, 1996, 1998, 2000, 2002, 2004), (Crook, 1991, 1992a, 1992b, 1992c, 1995, 1999, 2006), (Goodrick 1987), (Hall 1991) and (Liebman 1991, 2000) for an introduction.

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1.3 Chains of Thought and Musical Refractions

The author’s formative musical background in jazz performance has instilled a

particular bias and interest in all subsequent creative endeavours. Although there are clear

limitations within improvised music, the challenges imposed have, by necessity,

encouraged a particular set of skills to develop. An approach to improvisation, in which

the author is found in good company9 is to conceive of every musical object as

containing a set of properties, each individually open to modification in future phrases:

New material is created by altering a selected set of musical parameters from previous

fragments. In other words, improvisation is the construction of a musical train of

thought where every subsequent phrase relates to a preceding one in terms of a changing

set of variable parameters. In Acknowledgement (Coltrane 1965), to pick one of countless

examples from the repertoire, a simple phrase is manipulated in terms of chromatic

transposition, metric placement and rhythmic subdivision (CD1.1). As is always the case

there are many important musical parameters - such as timbre, articulation and micro-

timing - present in the performance that elude the limitations of standard musical

notation.

Figure 1.3.1 (p 12) comprises one simple phrase that is transformed in terms of

easily visualised discrete pitches and rhythms. Phrases 2-34 can all be described as

variations of Phrase 1 in terms of chromatic transposition, metric placement and

rhythmic subdivision, with the exception of Phrase 30, which does not hold strictly the

same intervallic structure.

9 See, for example, (Damian 2001, p 12-20), (Crook 1995, p 8-31) and The More Ways you Have of Thinking (Berliner 1994, p 146-69)

12

Figure 1.3.1 Improvisation as transformation of coexisting musical parameters:

Phrase 1 is repeated with independent modifications of 3 parameters: Chromatic transposition, metric

placement and rhythmic subdivision (CD1.1).

Occasionally, phrases merge; for example, the last note of Phrase 5 is the first of

Phrase 6. This passage provides a clear, and easily notated example but this concept of

improvisation as differential manipulation of consynchronous10 musical parameters holds

analytical power in a far wider range of complex examples. The following excerpt from

Swish (Mermikides 2008) illustrates the kind of conceptual process adopted in a more

complex manner (CD1.2). Figure 1.3.2 (p 13) presents a portion of the improvised solo,

notated and analysed.

10 The term consynchronous is coined here, to describe multiple parameters that co-exist simultaneously and continually along a time-line.

13

Figure 1.3.2 An illustration of the chains-of-thought improvisation methodology (CD1.2).

In this analysis, phrases are generally identified as being related to a previously

occurring phrase, and may themselves combine into larger, or break off into smaller,

phrases, and are labelled accordingly. The types of relationships between each phrase are

described by sets of transformational processes in boxed text.

This improvisational methodology thereby involves the selecting of a particular

subset of musical properties of a phrase, or melodic fragment of the tune. This subset of

properties is then either fixed, or modified by varying amounts in the subsequent phrase,

to form a series of interlinking chains. Some points for consideration:

1) There may be many valid analyses of an improvisation, and the performer’s

conception, and listener’s interpretation of the solo may differ.

2) A single phrase may form the impetus for any number of subsequent phrases,

along any number of transformational processes.

3) Phrases may be hierarchical (e.g. B.1 contains phrases A.1.2, A.1.3 and A.1.4)

Figure 1.3.2 (p 13) offers one of several reasonable analyses. Small, or larger-

scale phrase structures are all open to modification.

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4) Sufficient transformation may result in the formation of a new phrase unit for

further modification.

5) This analysis purposefully omits the complex interactions between performers in

an ensemble, whereby musical material created by one player may influence

the improvisations of any number of other players. The interaction between

players follows a similar methodology as described here, whereby musical

material is shared within a common ideas pool and modified between members

of the ensemble.11

6) A particular solo, performer’s identity or musical style may be described not just

by their melodic, harmonic and rhythmic vocabulary, but also by the types of

transformational processes and extent of variations employed.

7) Phrases G.1 and G.2 provide a glimpse of how technology may be employed as

part of the improvisational process, and how it may offer otherwise

unavailable transformational dimensions.

8) The precise demarcation of musical material into units for transformation, which

are called ‘phrases’ here, is a subjective exercise. Furthermore the definition

of a phrase unit may change in relation to the transformational process

employed. For example, a set of five notes might be considered a complete

phrase for a sequencing process, but a timbral modulation may also be

applied through those five notes, implying a smaller conceptual subdivision. It

is tempting (and sometimes useful) to describe musical fragments as cells,

which are combined into hierarchical phrases. But it soon becomes clear in

analysis that a cell’s autonomy is temporary, there are no uniformly indivisible

musical units; even a single note can be subject to all manners of

transformation and recombination, and parameters such as timbre do not

allow for such a convenient atomistic perspective12.

9) This example mainly presents a traditional improvisation where phrases occur in

a strict series. Contrapuntal mechanisms, ensemble interactions and the

smearing of a phrase (through electronics) allow phrases to coexist, and their

relationships to be parallel, rather than strictly serial.

11 See (Sawyer 1992) and (Berliner 1991, p 647-51) for theoretical, and transcription analyses of ensemble motivic interactions respectively.

12 See Curtis Road’s Microsound (Roads 2004) for an exploration of ‘sound particles’ - lasting less than 100ms - and their role in the creation of line, pulse and texture.

15

10) There is a differing amount of variation from one phrase to the next; so a solo

may be characterised by the extent of relatedness (and how this measure

changes) between phrases. This concept of proximity, is discussed in Section

1.5 (p 25).

We may employ the above methodology, both as a form of retrospective analysis and in

terms of real-time improvisational choices. Figure 1.3.3 shows how a phrase offers the

performer a set of options for the continuation of an improvisation based upon various

transformational processes.

Figure 1.3.3 An illustration of musical refractions. In the course of an improvisation, a phrase is manipulated by the selection of one of many transformational process (1-8 present a few of countless possibilities). The

resulting phrase is in turn open to further modifications. Improvisation is seen as the realization of a pathway through the multitude of refracting musical possibilities.

Since there are a non-trivial number of precise transformational processes (let alone

combinations thereof), the above diagram shows but the briefest glimpse into the

refracting pathway of an improvisation, but it should also provide an imaginative approach

to a process which hints at the wealth of musical possibilities available. Phrase-based

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improvisation may be seen as the artful carving of a pathway through this mesh of

musical possibilities. Indeed a particular solo, or style of playing, may be described in

terms of which transformational processes are selected. Acknowledgement (CD1.1) favours

chromatic transposition, rhythmic displacement and subdivision. A section of John

Scofield’s Chank (Scofield 1998, CD1.3) on the other hand uses timbral modulation as an

expressive mechanism. Examples of expressive shifts in rhythmic density appear in Allan

Holdsworth’s playing (see Figure 1.6.1, p 56 and CD1.11), while Time-feel and Case Studies

(Sections 2 and 3) provide numerous examples of the virtuosic control of micro-

rhythms.

This chains-of-thought perspective runs the danger of narrowing the concept of

improvisation into exclusively linear, serial and causal relationships between phrases, with

no acknowledgement of the important role of spontaneous, novel inspiration. However,

as this model is developed through this paper, it will be shown that these ‘pristine’

moments may in fact be accommodated into a theoretical model with the introduction of

the concepts of multi-dimensional musical space, ensemble interaction, proximity and

surprise (p 25-55).

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1.4 Limitation and Variation of Musical Topics

In the author’s own playing, the improvisational methodology outlined above grew

in sophistication, with increased experience and formal jazz training. Although

instrumental proficiency, jazz harmonic devices and vocabulary were developed, the core

approach, and considerable challenge, of applying this knowledge in improvisational

practice remained essentially the same.

Some external validation for this approach is received from both the pedagogical

and theoretical literature. Studies for a Bachelor’s degree at Berklee College of Music

(Boston, USA) introduced an approach to developing improvisational skill that went

beyond the typical ‘Learn your scales, transcribe and good luck’ advice. Instructors such

as Ed Tomassi, Jon Damian and Hal Crook would set particular challenges for students

such as:

1) Improvise through the tune using only chord-tones of the harmonic progression.

2) Improvise a short phrase. Rest. Improvise a short phrase. Rest. Improvise a long

phrase. Rest and repeat.

3) Improvise a phrase that starts with the concluding material of the previous

phrase. Rest. Repeat.

4) Improvise a solo with a prescribed dynamic pattern.

5) Improvise a phrase with a particular intervallic structure, adjusting accidentals to

negotiate the harmony.

Improvising with such types of limitations is a surprisingly challenging yet effective

exercise in forcing new ideas and avenues of exploration. Often the ensuing

improvisations are more successful than prior ‘free’ attempts, and the strictures of the

exercise rarely inhibit the potential musicality. Indeed, the educational benefit of

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practicing improvisation within a carefully selected set of limitations is a central theme of

the work of jazz educators Crook, Tomassi, Jerry Bergonzi and Mick Goodrick. One

might think of this type of approach as the training of a particular type of skill: The

independent and artful modification, or maintenance, of coexisting musical parameters.

Developing proficiency in this area fosters a truly creative improvisation when the

limitations are relinquished during performance, allowing the improviser to create

authentically chosen material rather than pat phrases at the moment of improvisation:

“There is no freedom without structure” (Crook 1991, p 55). This improvisational

technique of variation within self-imposed limits may also be employed compositionally

(See 1.8 Reflection, p 79 and the submitted portfolio).

In addition to the support from jazz pedagogical material, further validation, this

time from an academic theoretical standpoint, was offered by the paper Improvisation:

Methods and models (Pressing 1988) in which Jeff Pressing puts forward a model of

improvisation as the variegated attention paid to various parameters and transformational

processes. Values of various musical parameters and types of transformation of a phrase

are defined. Alongside this set of variables, the amount of attention paid to each of these

variables is described by the currency of cognitive strength; this is unlikely to be more than

conjecture, and it is challenging to imagine how it could be measured: personal and

anecdotal reports on improvising seem to suggest that at any particular moment, the

creative improviser is thinking actively about one or two musical goals at the most

(Werner 1996, Nachmanovitch 2000 and Solstad 1991). Pressing’s model taken alone is

not immediately stylistic relevant nor authoritative to jazz improvisation research.

Nonetheless by defining this multi-level vision of music in which the improviser may

navigate, Pressing provides a very powerful conceptual vocabulary. Despite the difficulty

in proposed distributed cognitive strengths, the independent defining of attention to, and

values of, particular musical parameters and processes is illuminating. The staggering

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developments in music technology now allow us to adopt this type of model in a

practical way in terms of composition and real-time performance, as well as computer-

based generative improvisation systems.13

It is the marrying of wide-ranging theoretical concepts and practical application that

best informs the work in this submission. Bringing these theoretical concepts back to a

practical demonstration, here follows an example of the process. Here, a simple phrase

(Figure 1.4.1) is used as the starting point (a seed) for various subsequent improvised

phrases, which were then transcribed, within the limitations of standard notation.

Figure 1.4.1 Phrase α, a starting point for improvisation (a seed phrase).

Despite its simplicity, this phrase could be described in innumerable ways and levels

of detail such as: (i) a phrase starting on beat ‘4 and’. (ii) a three note rhythmic pattern

with no particular rhythmic placement, (iii) a melodic gesture, (iv) a broken chord

implying part of a Cmin9 or Ebmaj7 chord, (v) a phrase with a particular harmonic altitude

relative to the harmonic context, or (vi) or a particular pattern of timbral characteristics

and envelope represented as amplitude over time (Figure 1.4.2, p 20).

13 See Bäckman, K. & Dahlstedt P. (2008) for a recent significant development in this field.

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Figure 1.4.2 Coexisting interpretations of Phrase α.

In this way, the phrase can be conceived as possessing many sets and subsets of

properties, variably simple or complex, or to adopt Pressing’s language, an object existing

in a particular point in multidimensional conceptual space. It becomes clear how an

improvisation might develop with this concept in mind. Any number of the subsets of

musical characteristics may be used as a reference point for ensuing phrases. For

example, the starting beat may be fixed for a new phrase, the rhythmic pattern preserved

with new notes, or the melodic contour maintained but transposed and so on. Not only

can the concept of isorhytmos (fixed rhythmic structure) be explored but also isomelos (fixed

sequence of melodic pitches) (Persichetti 1961), isotimbre (fixed timbre), isopaesi (fixed

intensity), isomodos (fixed scale implication), isokinetos (fixed gesture) and isologos (a fixed

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concept or pattern applicable across multiple parameters)14. From a jazz practitioner’s

perspective; by limiting certain parameters one is more able to explore “otherwhere”

(Pate, cited in Berliner 1994, p 385). A language naturally evolves from here to describe a

musical relationship defined by the significant variation of a particular parameter

(displacement, distimbre etc.) Here follows some improvisations, each starting with Phrase α,

and with little preconception of what was to be played, other than the intent to vary the

type of transformational process used (Figure 1.4.3, CD1.4).

Figure 1.4.3 Improvised continuations of Phrase α (CD1.4). Instances of Phrase α, and its close relations,

are labeled with solid and dashed outlines respectively.

Phrase 1 takes the rhythmic structure and general melodic shape of α as a constant,

and uses diatonic transposition and rhythmic displacement as transformational processes.

The increased swing of the second phrase introduces us to the concept of expressive

micro-timing, an important focus of this submission, with its own dedicated paper

(Section 2 Time-feel, p 82-129).

14 For clear examples of the compositional application of isokinetos and isologos see Primal Sound and Omnia 5:58 in the submitted portfolio.

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Phrase 2 uses the strict intervallic structure of α and employs chromatic

transposition and rhythmic displacement to create an angular, dissonant line.

In Phrase 3, the melodic structure and ordering of notes of α is kept strictly

constant, but the placement of each note and articulation of the repeating melody is

altered for rhythmic interest.

In Phrase 4: The three-note rhythm of α is repeated without a rest to create

rhythmic displacement and a simple polymetric implication. A shape on the fretboard is used

as a parameter of musical expression. The left hand shape is kept constant but played on

a progressively descending set of three strings.

Phrase 5 continues by adopting a scalar implication of Phrase α, the Eb, G and C

are seen as belonging to a larger set of notes, C jazz melodic minor. The introduction of

B-natural is a slight variation on the harmonic context and alters the ‘colour’ and harmonic

altitude of the solo.

In Phrase 6, the rhythmic information of Phrase α is removed and the phrase is

collapsed into a three-note harmonic structure that is repeated and transposed with

timbral modulation. A volume pedal is used to lengthen the natural attack time of the guitar

and create expressive interest through simple technological employment.

Phrase 7 is an example of interruption in an improvisation. Phrase α is abandoned

and interrupted with a phrase of contrasting rhythmic and melodic content, albeit with a

lingering stylistic timbral and harmonic relationship.

The initial phrase α is refracted through a few of many possible musical pathways, it

acts as a potential seed to future branches of musical growth. The trajectory is

characterised as much by which parameters are held constant as by which are altered.

Figure 1.4.4 (p 23) illustrates how the particular musical topics, guide the ensuing

improvisation.

23

Figure 1.4.4 An illustration of how the fixing and variation of musical topics may forge improvisational continuations from Phrase α.

The importance of considering a host of available topics for modification is reflected

in the ever-growing jazz pedagogical material of the last two decades. Some pedagogical

texts give an overview of many transformational topics within one book15, while other

writers choose to create a series of volumes addressing each topic separately, of which

Bergonzi’s Inside Improvisation Series is a clear example.16 A contemporary bibliography of

jazz pedagogical material has started to resemble a library of chess books with stacks of

general principle texts alongside titles dedicated to every conceivable opening, variation

of opening and style of end game. The study of these differentiated skills, as in both

15 See Crook (1991, 1995) and Damian & Feist (2001) for examples of improvisational meta-views.

16 To date, Bergonzi has written 7 volumes of the Inside Improvisation Series, each focusing on a different topic. (Bergonzi 1992, 1994, 1996, 1998, 2000, 2002 and 2004) In fact these can be seen as studies in the fixing of these featured topics (e.g. a particular melodic cell) and thereby exploring deeply other variables (e.g. permutation, harmonic altitude, segmentation etc.)

24

chess and jazz improvisation, aims to offer the player informed options and intuition at

the moment of performance.

The process of limitation and variation may be deliberate or unconscious17, regardless

there will inevitably be associated parameters that alter, or have to maintain constant, as a

consequence of any given improvisational choice. For example the ascending chromatic

transposition in Phrase 2 causes a corresponding non-linear response in dissonance.

(These types of relationships are categorized in 1.6 Changes and Time: Expressive Contours p

56). The consequential effects of any particular musical choice may also be harnessed

musically18.

This section has introduced and given some examples of the concept of

improvisation as a mutation of preceding phrases, whereby a phrase is modified

according to various parameters and wanders from its starting origin, while remaining

comprehensible to the listener – The musical object is progressively transformed along a

varying set of dimensions. The next section will look more deeply into this idea of

trajectories through multi-dimensional musical space (M-Space), an approach employed

extensively in Changes Over Time: Practice. This concept is refined through analysis, linked

with a broad time component (Expressive Contours 1.6 p 56), bolstered with important

stylistic mechanisms (such as time-feel, harmonic pathways and melodic shadowing) and always

applied practically.

17 Psychological models of improvisation are explored in such texts as (Solstad 1991), (Juslin & Sloboda 1991), (Hall 1992), (Monson 1996), (Gustavsen 1999), (Rothenberg 2002), (Reason 2004) and (London 2004)

18 In String Theory and Event Horizon from the submitted portfolio, the natural bowing technique associated with playing certain passages is picked up by the electronics of the Hyperbow, which in turn modulates the electronic effects of other consynchronous musical layers.

25

1.5 Improvisation as Musical Mutation: M-Space Modelling

The improviser, given a starting phrase, is presented with a range of choices for

continuation depending on the differential attention to a host of musical subsets. Beyond

the theoretical interest, this concept may be applied pedagogically and in performance to

guide improvisational practice.

Returning to Coltrane’s Acknowledgement (CD1.1), a simple melodic fragment is

transformed in terms of three parameters, chromatic transposition, metric placement and

note separation. The values of these parameters are notated in Figure 1.5.1.

Figure 1.5.1 An analysis of Coltrane’s Acknowledgement in terms of the values of 3 parameters: metric placement, rhythmic separation and chromatic transposition (CD1.1).

Although the transformations in the improvisation occur in a time series, it is

possible to visualize all mutations of Phrase 1 in the same conceptual space. Figure 1.5.2

(p 26) shows a three-dimensional space that represents all the possible variations of the

phrase, in terms of the three specific parameters. The individually numbered phrases in

26

the solo are plotted in reference to the individual phrases in the solo. With the caveat

that important articulation, dynamic and timbral elements are set aside for now,

Coltrane’s solo may be seen as constituting a small subsection of this clearly demarcated

musical space.19

Figure 1.5.2 Coltrane’s cube: The phrases of Coltrane’s Acknowledgement plotted in the three-dimensional musical space of metric placement, rhythmic separation and chromatic transposition, with a few co-

ordinates illustrated with standard notation.

19 The phrases’ positions in three-dimensional space has been derived here from a standard notation transcription. However, this multi-dimensional graphical and conceptual vision can accommodate readily a continuous – rather than discrete - range of values in all three parameters including sub-notational, yet perceptible and musically relevant, elements of micro-timing and intonation. In this way it is liberated from the “finitistic” limitations of Wishart’s lattice (see 2.1 p 85).

27

Figure 1.5.3 Raup’s cube: An illustration of shells existing in genetic space. Three genes (spire, flare and verm) contribute to the shape of the shell. The shaded area of the cube represents the shells existing as a

product of natural selection (Illustration from Raup, cited in Dawkins 1996, p 192).

Immediately a reference may be made with the language of evolutionary biology.

Figure 1.5.3 (Raup, cited in Dawkins, 1996, p 192) shows Raup’s cube; an illustration

where three genes contributing to the shape of a shell (spire, flare and verm) are laid out in

three dimensions. Every possible expression of these genes is laid out in multi-

dimensional space and the evolutionary pathway, through genetic variation, of a species

may be drawn. The shaded area represents the shells that have been found in nature as a

product of natural selection, and a subset of all possible species.20 Similarly, the phrases

in Coltrane’s solo represent the ‘naturally-occurring’ subset of all possible phrases within

a defined musical space.

Figure 1.5.2 (p 26) used a simply arranged set of transformed phrases however the

exact layout of phrases within that musical space is debatable. One could make a good

case that potential phrases existing along a particular dimension may not always have an

easily described continuum of proximity: A semiquaver displacement may actually be a

more radical mutation than a minim displacement; an octave transposition is perhaps less

20 For an overview of current research in the use of evolutionary mechanisms in music composition, see Evolutionary Computer Music (Miranda & Biles 2007).

28

extreme than a semitone, and a semitone less extreme than a quarter-tone for that

matter.21

This problem of defining proximity may be approached carefully. For example,

Phrase α (Figure 1.4.1 p 19) may be imagined as existing at a particular point on an axis

of rhythmic placement within the concept of a cyclical bar (Figure 1.5.4 p 29). Because of

the pattern of strong and weak beats, a minim displacement is to be considered the

‘nearest’ displacement (despite it being the furthest in terms of beat placement). A

crotchet displacement is more distant, the D for example would now fall on beats 2 or 4,

rather than 1 or 3, a more significant change in character. Any quaver displacement alters

the phrases yet more extremely, removing the upbeat and interfering with any swing

quaver characteristics that may exist. Semiquaver shifts, and yet finer rational

subdivisions (if appreciable), alter the phrase still more radically.22

This particular axis is represented here and usually conceived as a series of discrete

points along an axis representing integer divisions of the beat. In Section 2 (Time-feel p

82-129), this notion is challenged with the conception of this axis as a continuum rather

than a fixed grid, albeit with weighted nodal points.

21 This non-linear nature of musical proximity is noted in On Sonic Art in reference to the relationship between frequency and consonance (Wishart 1996, p 71-73).

22 The layout of these phrases is not static, once a rhythmic displacement has been made, phrases are reordered in terms of proximity. For example if Phrase α is displaced by a crotchet, its ‘nearest’ neighbour is now a minim away.

29

Figure 1.5.4 An illustration of Phrase α existing within a range of proximate phrases, the ordering of which is determined by the extent of their musical transformation.

With this concept of musical proximity in mind, more dimensions may be added and

a new musical space may be constructed for exploration. Orthogonal to this rhythmic

placement axis (Figure 1.5.4), a note separation axis may also be postulated, representing the

progressive elongation and contraction of Phrase α, with wider note separation in one

direction, and shorter in the other.23 In Figure 1.5.5 this axis is arranged with the

23 It is useful to differentiate the concepts of note separation and note length. Note separation describes the rhythmic distance between adjacent notes as opposed to their individual durations. This allows, for

30

emphatic top D used as a rhythmic anchor about which the outer two notes are stretched

or compressed. The individual notes may compress until they form a chord and then

extend beyond that point to form a retrograde transformation of Phrase α.

Figure 1.5.5 Phrase α with some of its musical neighbours arranged in terms of increasing and decreasing note separation.

In addition to rhythmic placement and note separation another axis may be added that

represents all possible diatonic transpositions of a phrase (diatonic to the key of C

example, some measure of sparsity to be made as well as the concept of a phrase compressing to form a chord of any duration, which has practical improvisational implications.

31

Dorian, as opposed to the chromatic transposition in Figure 1.5.1 p 25), higher in one

direction and lower in the other. Chromatic transposition within a tonal harmony creates

a non-linear pattern of musical distance. However within a modal setting, from which

Phrase α is derived, the hierarchical nature of scale degrees is less clear. The subjective

decision has therefore been made to arrange the proximity in terms of diatonic

transposition very simply, so that proximity in this dimension is equivalent to similarity

of melodic register (Figure 1.5.6).

Figure 1.5.6 Phrase α transformed through diatonic transposition in the key of C Dorian. Given the definition of these parameters, variations of Phrase α exist in three

dimensions, with potential mutations of the phrase existing side by side in conceptual

32

space. A sense of musical proximity within these constraints may also be perceived

(Figure 1.5.7).

Figure 1.5.7 Phrase α existing at the centre of a three-dimensional musical space with variously proximate neighbouring phrases. Phrase α is indicated in red and the musical distance between it and various close

neighbours is shown in green. The boundary of the orange sphere describes a boundary of equal proximity, and contains phrases within this musical distance. The lower part of Figure 1.5.7 shows an impression of

Phrase α existing at a point within this musical space. Now that the concept of proximity has been established, one might also imagine

additional transformational dimensions emerging from the Phrase α, including a

chromatic transposition dimension, axes of various timbral characteristics (including

33

those only achievable through electronic manipulations), points of symmetry, intonation,

segmentations and so on. An impression of how a musical phrase exists in multiple

simultaneous dimensions of transformation, here termed M-Space, is shown in Figure

1.5.8.

Figure 1.5.8 An impression of M-space: Phrase α (circled in red) sits at the centre of many simultaneous dimensions of musical transformation. Twelve of these are represented in four three-dimensional subsets

(some of which are continuous rather than discrete values) with some proximate phrases indicated. A phrase may move along any number of such transformational axes during the course of improvisation. In

the top right of the diagram a phrase (circled in blue) shows the result of a small move in all of these subsets simultaneously (the modification is marked as a blue disc in each transformational subset).

It becomes clear that most jazz analysis limits itself to variation of only a few

dimensions such as harmonic altitude, standard-notational rhythmic placement and

simple vocabulary choice while ignoring characteristics less easily notated, such as

rhythms and pitches that fall between the cracks of standard notation, timbral gestures

and many forms of motivic transformations.

The co-existence of these multiple dimensions is possible to conceive, but difficult

to illustrate precisely in one diagram (Figure 1.5.8 is an illustrative attempt using two and

three-dimensional subsets for clarity). Similarly, the representation of three genes (or

34

musical transformations) with linear expressions is easy, but once we add several more,

particularly with more complex transformations a clear visual illustration is problematic.

A conceptual model, whose precise demarcation can be delegated to a computer, may

serve better than two-dimensional illustrations24. Regardless a logical visualization of a

phrase existing within a radiated sphere of closely related musical material may readily be

adopted and, as will be demonstrated, a concept of relative musical proximity is

intuitively accessible, despite the mathematical complexity on which it is constructed.

As more axes of transformation are added, an idea is built of any particular musical

object living at a particular point in a conceptual space of all its possible variations. A

point within a grand Musical Library of Babel 25 from which the improviser may explore in

any direction, or to use saxophonist Evan Parker’s description of improvisation, take a

note for a walk (Parker, cited in Borgo 2005, p 36).

Proximity is simply distance in M-Space. These fields, grouping related phrases

together, are shown later as cloud-like structures, but the actual shape is harder to grasp.

Since we are conceiving this boundary as a multi-dimensional object of a particular

radius, its shape cannot be conceived as a simple three-dimensional sphere. An n-sphere

(or M-Sphere here), a multi-dimensional sphere, exists in many dimensions and has a

conceptually challenging shape to consider. It may extend far along a few axes if stable in 24 Research by the author, beyond the scope of this thesis, is currently underway in the production of M-Space computer modeling and real-time computer improvisations. The musical distance between phrases Px and Py is calculated using Euclidean geometry over m musical dimensions, thus:

!

d(Px,Py) = (xi " yi)2i=1

m

#

25 See the Library of Babel, (Borges 2000). In this short story, Jorge Luis Borges describes a library of similar length books, housing every possible permutation of the alphabet and a short list of punctuation marks. So the library contains mainly nonsensical books, among all versions of the Bible, Great Expectations and On the Origin of Species – all with every imaginable alteration of plot, protagonists, obscenity, profundity and editing. It is alarming that books could span clearly labeled volumes, and alternative encyclopedias could exist. Stranger still, despite the awesome size of the library, it would have to be finite, encompassing the limits of our imaginations. In lectures at the Royal Academy of Music, the author has postulated an (also finite) CD library of Babel, whereby every permutation of the bits of a 16-bit 44.1kHz stereo information within a CD capacity are housed. These include all one’s favorite – and least favorite - records, arranged for every conceivable ensemble, standard of playing, and nuance of performance – amongst of course a catalog of inconceivable noise and extremities of expression. Students were invited to contemplate which few of this vast number of CDs they wished to recreate during their recording careers.

35

others, and if many parameters change then they are relatively constrained. This concept

is illustrated in Figure 1.5.9 (p 36), three M-Spheres of different radii are illustrated, each

with Phrase α at their centres. The surface of each sphere represents phrases of equal

musical proximity (from Phrase α). Since these are multi-dimensional shapes, proximity

and distance may be distributed unevenly across many dimensions. For example the

boundary of M-Sphere A may be seen as one small change in one dimension, while B

may represent one moderate alteration or a few small changes. The surface of M-Sphere

C includes phrases with for instance, radical changes on one dimension, moderate

alterations on several and small changes on many. A phrase exists within this complex

radiated sphere of proximate musical material, and once a selection has been made,

another sphere congregates around this newly created phrase.

36

Figure 1.5.9 Phrase α illustrated in the centre of three M-Spheres of differing radii. The surface of

each sphere links phrases of equal musical proximity. Each sphere represents distance across multiple

musical dimensions, and musical proximity does not have to be distributed evenly across all dimensions.

Multi-dimensional musical proximity would imply that the exact repetition of a

phrase, with a major alteration in a single dimension, such as a huge timbral modification,

may be equally proximate as a repetition of the phrase with many slight alterations.

Techno (and associated electronic dance music styles) illustrates this idea clearly, a

continuously repeated phrase may be subjected to extraordinary timbral manipulations

while remaining an intelligible relationship to the original phrase (For one of numerous

examples of this, see extract Flaphead (Aphex Twin 1992) with an audio extract on

CD1.5). Funk, with its relatively immobile chord structure and repetitive hypnotic nature

allows a highly sophisticated ensemble-interactive and dynamic expression of time-feel.26

On the other hand, jazz, for the unaccustomed ear, may vary too much from one phrase

to the next, becoming unintelligible. “Without certain musical glues, it all sounded like

noodles” (The Real Frank Zappa Show 1989). A stability of many parameters may often be

uninteresting, but can also engender a greater sensitivity to subtle musical changes, as

26 In-depth multidimensional ensemble time-feel analyses of James Brown’s rhythm section performances have been conducted (Mermikides 2005), and in samba music (Naveda et. al. 2010).

37

may be said of the minimalist movement. This interrelationship of parameters and the

concept of slack theory, the relaxation of parameters to allow expansion in others, is

discussed in terms of expressive contours later in this paper.

Reintroducing the improvisational process from section 1.3, Phrase A.1 (Figure 1.3.2

p 13) may be seen as existing at a point in the multidimensional space of all possible

mutations. The labeling of the relationship between continuing phrases now makes sense

in terms of M-Spheres or fields of proximity, for example A.1, A.1.1, A.1.2, A.1.3, A.2 and

A.3 all exist within the same field: they are sufficiently closer to be recognized as similar.

In this case the relationship can be seen through standard notation, but the definition of

M-Space includes a host of musical parameters that escape easy notation, which

nonetheless contribute to musical proximity (Figure 1.5.10 p 37).

Every executed phrase implies a field of related phrases – along many dimensions of

transformation. The precise demarcation of these fields is subjective and may cross-fade,

as illustrated. The coherence of any new phrase in an improvisation depends on which

phrases have occurred in the past and a measure of relative proximity.

38

Figure 1.5.10 An M-Space representational analysis of the Swish solo (CD1.2) Phrases exist in fields of

proximity, which may overlap, and the improvisation is conceived as an exploration of multi-dimensional

musical space.

Given a particular starting phrase, one may imagine a field existing of appreciable

‘natural’ continuations of the phrase. The language of evolutionary biology returns, just

as Raup describes evolution as a walk through this multi-dimensional space of genetic

mutation, the improviser artificially selects (whether consciously or not) subsequent

39

phrases from a radiated sphere of proximity.27 These fields contract over time as the

memory of a phrase dwindles; an exact repetition of a phrase may be appreciable to the

listener for some duration, whereas more extreme mutations would have to occur

relatively soon to maintain an intelligible relationship28. This concept of genetic drift in

biology is useful, but not entirely analogous to the process described here. In this model

phrases do not have to reference the immediately previous phrase, we may skip generations,

any phrase in the past is fair game (as if from a storehouse of recessive genes), and the

performer is allowed to restart a pathway from any point in M-Space at will. We can

thereby imagine a cumulative proximity caused by the repeated referencing, along varying

transformational dimensions, of a starting motif. One implication of this time-based

model is that the repetition of similar phrases will expand the field of proximity, meaning

that a new phrase has to be relatively more different to maintain a similar level of

novelty. For example, a one-note solo would require a high level of rhythmic and/or

timbral activity to maintain a level of novelty; an example of slack theory in action29.

A contour of proximity over time may be described through a solo as the distance

traveled in M-Space from one phrase to the next. The itinerary of this ‘flight path’ is

shown in Figure 1.5.11 (p 40).

27 Unlike the evolutionary process, the improviser is not constrained by the inconveniences of reproduction or limits of genetic viability, she is free to skip to the ‘hopeful monster’ (Goldschmidt cited in Dawkins, 1996, p 87-88) at any point in the performance.

28 Incorporating a time function into a mathematical calculation of a distance:

!

d(Px,Py) = f T (Px,Py)( )( )2 * (xi " yi)2i=1

m

#

Where T(Px,Py) is the time difference between phrase events Px and Py, and f is a (linear or non-linear) function simulating memory response.

29 For a humorous illustration of this type of principle in a compositional context, see CD1.6, Johnny One-Note (Keneally 2007).

40

Figure 1.5.11 The Swish solo (CD1.2) illustrated as a trajectory through M-Space.

The musical distance of each leap in M-Space can be measured and tracked over

time. Close repetitions of phrases would appear on a flat line while radically changing

material would be represented by consistently high peaks. Figure 1.5.12 illustrates an

impression of the improvisation as a proximity contour.

Figure 1.5.12 An impression of a proximity contour, tracking the novelty of each new phrase in Swish.

The height of the contour represents the distance travelled in M-Space, a high flat contour would for

example represent a steady fast velocity through musical space, while upward and downward countours

would correspond to M-Space acceleration and decelleration respectively.

41

This raises a question of the existence of an optimal ‘musical’ distance in M-Space

from one phrase to the next. The skill-set of the proficient improviser includes the ability

to control musical proximity for artistic effect. In The Sound of Surprise (Balliett 1959),

Balliett’s “aural elixir” is the result of perfectly selected surprises and, as Borgo notes

(Borgo 2005), effective improvisation is not a random stumble through musical space,

nor is it always a dainty, careful and predictable movement through it.

Randomness does not produce a sense of surprise, but rather

confusion, dismay, or disinterest. And small departures from

an orderly progression, if insufficiently interesting or

dramatic, will pass without much notice. Surprises are by

definition unexpected, and yet those that most capture our

interest or delight have a feeling of sureness about them once

experienced.

Borgo 2005, p 1

Some approaches to finding this ideal middle-ground between predictability and

randomness are addressed later in this thesis. Regardless, the concept of proximity allows

an awareness of a rarely identified expressive contour: Irrespective of the specific

vocabulary, a series of phrases with only subtle changes creates a different musical effect

than a series of wildly disparate phrases.30 In other words, M-Space distance and velocity are

in themselves, avenues of expression, as is acceleration, the rate with which proximity

between phrases alters.

Rather than improvisation as a meandering drunken walk through this M-Space, large

scale improvisational strategies are possible, and occur often in the hands of skilled

30 For an example of an unbounded improvisation refer to an extract from Derek Bailey’s Sheffield Phantoms (Bailey 1975) on CD1.9.

42

practitioners. Listening to Jimmy Smith’s solo on The Sermon (Smith 1958) (Figure 1.5.13

and CD1.7) with the M-Space model in mind, it is easy to hear the separation of phrase

fields.

Figure 1.5.13 A standard notation transcription of an extract of Jimmy Smith’s solo on The Sermon

(CD1.7) with some salient time-feel features notated.

A first listen sorts these phrases into five main fields (A-E) with 2-5 phrases in each

(A1-3, B1-4 etc.) These phrases and fields are labeled and coloured respectively in Figure

1.5.14.

43

Figure 1.5.14 The phrases and fields of Jimmy Smith’s solo on The Sermon (CD1.7) labelled.

There are common features within each group that form a strong gravitational force

(or ‘Zappa’s glue’) between the phrases. This proximity means that they can tolerate and

44

indeed draw attention to any subtle transformations including editing of notes and

detailed variations of time-feel and inflection. The creation of proximate phrases fixes

groups of musical dimensions and thereby frees up other musical dimensions for

effective expression. Note also that exact repetitions of phrases in terms of notes still

include alterations in harmonic altitude, given their context, and small but effective

rhythmic and micro-timing variations. Figures 1.5.15-19 (p 45-49) illustrate the grouping

of these phrases within fields, with descriptions and illustrations of salient differences

between members of the same field. The diagrams to the right of each figure give an

impression of the musical proximity between component phrases of each field.

45

Figure 1.5.15 Phrase field A: Phrase A1-3 share a very similar melodic structure and vary in terms of

placement of component notes, time-feel and harmonic altitude. An impression of relative distance in M-

Space is shown in the lower diagram.

46

Figure 1.5.16 Phrase field B: Phrase B3 differs from B1, B2 and B3 in its use of diatonic

transposition, yet, in its relationship to the anticipated Bb7 chord, maintains a harmonic altitude proximity

with B2 and B4 hence its illustrated position in the lower diagram.

47

Figure 1.5.17 Phrase field C and its component phrases. Phrase C3 is illustrated slightly closer to C1,

than C2 due to the dotted crotchet, as opposed to quaver, rhythmic displacement of the first 3 notes.

48

Figure 1.5.18 In Phrase field D the core G, D, G motif is kept constant but a changing upbeat

phrase, rhythmic placement, time-feel, harmonic altitude and articulation separate its component phrases.

49

Figure 1.5.19 Phrase E1 and E2 are loosely linked by a general melodic shape, use of chromatic

approach notes and expressive mechanism of falling behind the beat. The length of Phrase E2 and use of

transformations of similar low-level motives lends itself to further separation into smaller phrase units. The

proximal relationship of Phrase E2.1-E2.11 are represented in the right-hand diagram and provide the

vision of hierarchical structures in M-Space.

50

The most loosely connected group is Field E, the two members of which share

the same contour, use of ornaments and rhythmic expression derived from a progressive

falling behind the beat. Phrase E2 is also distantly linked to fields A and C with the use of

the double chromatic approach to a held note.

Just as there is a particular configuration between phrases within a field, it becomes

apparent that fields themselves exist in a nexus of proximal relationships with each other.

As was shown in reference to E2, phrases may also be conceived as housing similar

constructions. This multi-level hierarchical structure of phrases and fields in M-Space is

illustrated in Figure 1.5.20 (p 51). Fields A-E co-exist as part of the same solo, but their

relative proximity is also due to registral, timbral as well as temporal considerations. Not

shown in Figure 1.5.20 is the yet more complex interaction of fields and phrases between

other performers and musical objects. This is explored variously in Section 3 and Scores

and Notes.

Although Figure 1.5.20 is illustrated in two dimensions, one must be reminded that

the relative distances between fields, and between their constituent phrases, is the

cumulative result of their relative positions in multi-dimensional space (i.e. variations of

many co-existing musical parameters). Once the concept of M-Space structures and their

relative positions has been grasped, the listening and analytical process becomes far

clearer. From the straight-ahead to the most avant-garde contexts, it becomes possible to

untangle Zappa’s noodles.

51

Figure 1.5.20 A multi-level depiction of The Sermon. Improvisation is seen as a configuration of fields

at varying distances and trajectories in M-Space, with each field containing a constellation of phrases.

Phrases, in turn, may be broken down into a nexus of smaller phrase units as is shown in reference to E2.

Phrase E2 has been placed closer to Fields A and C than B and D, to reflect features of E2.1 as discussed

on page 49. Fields themselves are linked together in terms of timbral, registral and temporal components

and may co-exist in a yet greater nexus of relationships with other performers or musical objects.

One can hear, for example, in Wes Montgomery’s solo on No Blues (Montgomery

1965, CD1.8), one very narrow phrase field being used repeatedly as a pivot to other

fields in a ‘call-and-response’ manner. In Figure 1.5.21 (p 52), fields grouping similar

phrases are coloured accordingly and a pivoting pattern emerges so quickly and clearly

that the ensemble are compelled to share the motif. The pattern settles into a two-field

(blue and green) interplay before relinquishing the structure. The repetition of the blue

phrase field is so clearly defined that the other ensemble members are compelled to mark

it with their own musical material, in other words, the soloists M-Space structures has

infiltrated those of the accompanists, as should occur in any responsive ensemble

environment.

52

Figure 1.5.21 A field illustration of an extract of Wes Montgomery’s solo on No Blues. (CD1.8)

Various phrases pivot around one very tight field (labelled in blue) and settle into a two-field exchange

(Notation transcription by Jeremy Poparad).

Coltrane’s Acknowledgement (CD1.1) on the other hand displays the strategy of

identifying a narrow field and then furtively exploring that space for extended periods

before moving to a new locale and repeating the process. Pat Metheny’s approach on

Unquity Road (Metheny 1976) (Extract on CD1.9) is less clearly delineated: Phrase fields

exist, but the transitions between them are often blurred, and referenced interchangeably

(Figure 1.5.22 p 53).

53

Figure 1.5.22 Pat Metheny’s solo on Unquity Road (CD1.8) merges and switches between phrase fields

fluidly. Fields have been identified by colour and smooth transitions illustrated by a cross-fade between the

relevant colours.

(Notation transcription by Jeremy Poparad)

As analyses of improvised solos are gleaned, it becomes possible to sort constituent

passages into broad categories. These are grouped in terms of the relationships between

the phrases rather than the vocabulary itself. A pictorial comparison of five

improvisational strategies is presented in Figure 1.5.23 (p 54): nuclear, field series, pivot,

merged and unbounded of which Acknowledgement (CD1.1), The Sermon (CD1.7), No Blues

(CD1.8), Unquity Road (CD1.9) and Sheffield Phantoms (Bailey 1975) (CD1.10) are

54

respective examples. The categorisation of these strategies involves some subjectivity

(one man’s nuclear, may be another man’s unbounded improvisation) and there may be

borderline cases, but a clear terminology and framework in which to analyse, compare

and contrast a range of improvisations regardless of style is presented.

Figure 1.5.23 Five improvisational structures: 1) Nuclear: phrases, with only occasional small

anomalies, fall within one close field with only minor variances (CD1.1) 2) Field Series: close phrases are

played a few times with variances before repeating the process at a different point in M-Space (CD1.7) 3)

Pivot: one particular narrow field is played often, acting as a springboard to various satellite fields (CD1.8)

4) Merged: fields are merged by the use of a transitional phrase of otherwise distinct phrase fields (CD1.9) and

5) Unbounded a series of phrases with little proximity of one phrase to any other (CD1.10).

Identifying improvisational strategies such as these informs a practical approach to

improvisational performance and ‘guided’ score instructions as well as creating a broad

analytical foundation. However, an appreciation of M-Space structures may act readily as

a supporting mechanism to compositional practice and employment of electronics. M-

Space architecture, the computer-assisted formation of structures, often with live

interaction with human performers, is explored extensively in the Changes Over Time

portfolio.

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Through a practice-based and pedagogical exploration of jazz improvisational

method this section has crossed paths with an elaboration of Pressing’s event-cluster model

(Pressing 1988). This meta-view of improvisation is made more powerful with the

support of a practical stylistic understanding of the jazz idiom, which provides an

appreciation of time-feel, harmonic altitude and the extrapolation of the concepts of

proximity and velocity. The implications of a time element applied to this model is

examined in the next section, followed by a survey of the broad compositional

reapplication of these theoretical concepts.

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1.6 Changes and Time: Expressive Contours

The previous section identified how subsequent phrases might develop in the course of

an improvisation in terms of selecting from a vast library of variously related material.

This holds analytical and practical power in many contexts, but there are some

limitations. M-Space modeling does not provide the clearest picture of how particular

parameters evolve over time, both within a phrase and through multiple phrases, nor

does it most readily show the interactions between parameters. Furthermore, as can be

seen in a transcription of the Un-merry Go-round (Holdsworth 1985, CD1.11) in Figure

1.6.1 (p 57), M-Space analysis can break down when phrase boundaries become too

merged or ambiguous. The phrases in the first seven bars may be seen as the toying

between two fields, a long note with a semiquaver offbeat kick and a diatonic descending

phrase. They are linked by a fragile timbre, made more ethereal with a subtle whammy-

bar vibrato. From bar 7 onwards however, the rhythmic density and phrase length

increases, jeopardising clear identification phrase boundaries.

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Figure 1.6.1 Transcription of Holdsworth’s solo on The Un-merry Go-round (CD1.11) with harmonic context.

There are however valuable expressive mechanisms at work in this passage that

should not escape analysis. It is clear that the expression inherent in this section does not

come from proximal relationships between clearly defined phrases, but from the

continuous control of co-existing parameters. Most importantly, there is an interplay of

varying rhythmic density and melodic register that, together with an arresting tone,

combine with remarkable effect. Figure 1.6.2 (p 58) tracks melodic register (in red) and

rhythmic density (in green with a measure of notes per beat in the vertical axis) against

time. This analysis gives insight, which may escape conscious perception, into the

emotive power of the phrase. Melodic register tends to be positively correlated with

rhythmic density; however, this correlation is broken in bars 5, 11 and 14 where the line

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lingers on medium-high register notes, and the expressive contours separate. Of

particular interest is bar 11 where the density plummets to reveal a slow microtonal glide

in melodic register. Despite its brevity, this passage lays the foundation for extensive

practical research in the effect of various linear and non-linear correlations, and

interrupted patterns of these two parameters.

Figure 1.6.2 Holdsworth’s Un-merry Go-Round bars 5-14 (CD1.11): Melodic register and rhythmic density

(measured in notes per beat) tracked over time. Breaks in the generally positive correlation between the

two parameters occurs in Bars 5, 11 and 14.

This approach, of mapping particular parameters against time, can allow a vision of

the overall shape of a solo, or composition to emerge, as well as draw attention to the

interaction between parameters. It also lends itself readily to pedagogic practice, real-time

electronic manipulation, compositional techniques and analysis where clear delineation

between phrases becomes impractical. This analysis can be seen as slicing M-Space into

individual dimensions, and tracking motion across these component layers over time as is

illustrated in Figure 1.6.3 (p 59).

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Figure 1.6.3 Illustration of a multi-dimensional M-Space view of an improvisation collapsed into its

multiple component parameters tracked over time.

In order to dig deeper still into the complex interplay between musical parameters,

an extensive analysis of a short active phrase is required. Phrase β (CD1.12) taken from

Standard Deviations (Mermikides 2008) is transcribed in Figure 1.6.4. Though short, this

passage is analysed in considerable detail in this section as a demonstration of the many

complex and interactive contours available for expressive manipulation and analytical

consideration. Not all of these approaches will be relevant in every context, but an in-

depth analysis is taken to present a survey of the contours, and the subsequently derived

meta-contours.

Figure 1.6.4 Phrase β from Standard Deviations (CD1.12).

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Section 1.5 (p 25-55) put forward a conceptual model of grouped phrases within

overlapping phrase fields. A possible analysis of Phrase β is given below. This layout gives

an impression of how core motivic material, at times overlapping, is introduced and

revisited with modification over the course of the improvisation (Figure 1.6.5).

Figure 1.6.5 Phrase field analysis of Phrase β (CD1.12).

Observing one particular parameter, for example the pitch height (a lattice approach is

taken: ignoring microtones and micro-rhythms), and tracking it over time, presents a

particular contour (Figure 1.6.6).

Figure 1.6.6 Pitch contour analysis of Phrase β (CD1.12).

This type of analysis with respect to melody has been researched in the field of jazz,

and other styles.31 In respect to jazz solos, the term tension and release curve is often used to

describe the shape of a particular parameter over time (Berliner 1993, p 57). Since the

perception of tension and release is rather subjective, or occasionally inappropriate for

some parameters, the author suggests the term expressive contour to describe the

31 See melodic contours of jazz phrases (Coker 1987, p 57-61), jazz melodies (Goldstein 1993, p 13-14) and folk music melodic contour typology (Adams 1976). The reversal of this relationship, whereby prescribed contours (often derived from non-musical sources) are attached to musical parameters, is explored in Changes Over Time (See Primal Sound, Head Music and Blood Lines), and with a historical precedent (See Villa Lobos’ New York Skyline Melody (Frey 2010)).

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modulation of a particular musical characteristic over time32. Opportunities for musical

expression exist along many parameters, and combinations thereof. For example,

tracking the intonation of the phrase, relative to an equal temperament, creates another

expressive contour. Note how this contour captures vibrato and bends and is

represented as a cyclical scale, wraps around vertically as a note passes the midway point

between semi-tones (Figure 1.6.7).

Figure 1.6.7 Intonation contour analysis of Phrase β (CD1.12).

The dynamic contour, representing the volume (of each onset) of an improvisation

over time, is illustrated in Figure 1.6.8.

Figure 1.6.8 Dynamic contour analysis of Phrase β (CD1.12).

32 Wishart’s gestural contours represent a similar idea of parameter control in the context of electronic music (Wishart 1996, p 109-125).

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Rhythmic density, the rhythmic distance between attack points may also be tracked

as before. It becomes clear that an expressive gesture may be formed by the change of a

parameter, as much as its absolute value. In other words, movement, as much as

position, in M-Space may create a musical effect (Figure 1.6.9).

Figure 1.6.9 Rhythmic density analysis of Phrase β (CD1.12).

Harmonic altitude may be defined as the chromaticism of the phrase relative to the

harmonic context. This is a complex field, with hosts of interacting factors (Liebman

1991). In this illustration, a simple measure is employed relative to the G7 context, this

runs from chord tones (CTs) (root, 3rd, 5th, minor 7th), to harmonic extensions (HEs) (9th,

11th, 13th) to common non-harmonic extensions (CNEs) (#9, #11) and the uncommon

non-harmonic extensions (UNEs) (b9, b13, major 7) (Figure 1.6.10).

Figure 1.6.10 Harmonic altitude analysis of Phrase β (CD1.12).

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A medium of expression is also possible in the varied employment of intervals.

Taking a measure of absolute intervals gives an idea of the predominant intervallic leaps

and changes in this field (Figure 1.6.11).

Figure 1.6.11 Intervallic contour analysis of Phrase β (CD1.12).

Another perspective, covered extensively in the previous section, is taken in the

observation of a proximity contour - the extent to which a phrase is altered through the

solo. An impression is given in Figure 1.6.12 of how far one phrase moves to another in

M-Space. As new motivic material is introduced the contour rises and falls as this

material is transformed by smaller degrees. This analytical approach gives a general

impression of how the novelty of an improvisation changes over time.

Figure 1.6.12 M-Space proximity analysis of Phrase β (CD1.11).

These contours do not function entirely independently but exist in various correlations.

These relationships fall into three general categories: 1) Independent: contours that may

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move freely against one another with no cross-effect (e.g. rhythmic density and harmonic

altitude) 2) A direct linear relationship, positive or negative, between contours (e.g.

dynamics and intensity) 3) An exponential relationship (positive or negative) (e.g. interval

and melodic range) 4) A non-linear relationship between contours (e.g. melodic contour

and harmonic altitude) (Figure 1.6.13).

Figure 1.6.13 Four types of relationship between contours: 1) independent 2) linear 3) exponential 4) non-

linear.

So by tracking individual parameters of the same improvisation from several musical

perspectives, a multi-dimensional image of an improvisation is built. This vision allows

the effect of multiple parameter changes to be understood more clearly, and in turn,

applied practically in improvisational practice or compositional construction.

There exists a complex resultant musical effect of these many consychronous expressive

contours. In search of this, a meta-contour formed by the summative effects of several

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contours may be conjectured. Examples of meta-contours might include 1) Activity: derived

from a combined measure of the contours of rhythmic density, intervallic change (a first

order differential of interval with respect to time) and proximity. 2) Intensity: determined

by amplitude, melodic range and harmonic altitude. Assuming an additive function of

these meta-contours, an impression of these may be calculated (Figures 1.6.14 and 1.6.15,

p 65-66).

Figure 1.6.14 Activity contour, derived from an additive function of rhythmic density,

intervallic and M-Space proximity contours.

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Figure 1.6.14 Intensity contour, derived from an additive function of dynamic, pitch and harmonic altitude.

In Hal Crook’s How To Improvise (Crook 1991, p143-5) some “solo curves” are

prescribed as improvisational exercises. The educational aim is to improvise a solo while

following a particular curve, either in terms of register, dynamics or “excitement level”.

The latter is presumably a form of meta-contour, but how it is to be derived is open to

interpretation. However, if an additive function is assumed, there is an important musical

implication: given a specific level of a meta-contour, any increase in one expressive

contour must be compensated by a relative decrease in the other component expressive

contours. So at a constant meta-contour level of, for example, intensity, a drop in one

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expressive contour (e.g. dynamics) must be compensated for by a total increase in

melodic contour and harmonic altitude. This concept of compensatory musical

parameters, is given attention in the submitted portfolio and referred to as slack theory.33 A

meta-contour of significant interest and research potential, developed by Rolf Bader and

David Borgo (Borgo 2005, p 92-121), is the “fractal correlation dimension”, which is a

composite measure of the complexity of harmonic overtone components, inharmonic

frequencies and amplitude modulations. This hugely involved analytical process, taking

weeks of computer processing for each piece and including up to eighty transformative

dimensions is rendered into a two-dimensional representation of complexity over time,

and aligns quite convincingly with the subjective listening process. However clever, no

one contour can capture the pluralistic structures of music, but directed attention to a

salient set of contours can help explain the emotive effect of mechanism specific to each

musical context.

Although musical gestures occur at small time-scales, such as intonation or time-feel

inflections, a full understanding of expressive contours allows for the appreciation of

how a series of seemingly meandering phrases can create larger scale musical structures

or gestures, the shape of a solo. These larger scale structures are certainly appreciable to a

tuned-in audience, and the candid practitioner34, but without the vocabulary of expressive

contours, they remain largely unspoken.

Expressive contours in general are employed in the author’s works in a number of

ways:

1) The development of the practical skill to independently control expressive contours,

2) the musical effects of particular contour types, drawn from eclectic sources, on

parameters, 3) the effect of contrasting and complementing contours on overall music

33 The observation of expressive contours is also found in the dramatic arts including script-writing (McKee 1999) and Zeami’s theory of Jo-ha-kuy in Japanese Noh theatre (Rimer & Yamazaki 1984).

34 See Composing in the Moment (Berliner 1993, p 192-220).

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experience, 4) the construction of meta-contours by the manipulation of individual musical

parameters, 5) the real-time control of expressive contours in live performance, and in

studio composition and 6) the exploration of slack theory in the differentiated control of

interdependent expressive contours.

Expressive contours may be seen simply as the introduction of the time component

into M-Space modeling35, but they also serve to bypass the difficulties in subjectively

identifying the proximity, and the demarcation, of phrases in general. Phrase demarcation

is by its very nature a form of post-hoc analysis; one must wait for a phrase end in order

to understand its position in M-Space, or to put it more precisely, a phrase’s position in

M-Space moves during its execution. This is certainly the case for the listener and is

often true for the improviser.36 It is important to remember that, as is the case with all

good musical analysis, there is no one-model-fits-all approach. With increased

experience, as both a performer and listener, one becomes more skilled at choosing the

most useful approach in any given situation, for example, an M-Space model is particular

illuminating in The Sermon (Figure 1.5.14, p 43 and CD1.7) but is inferior to a study of

contours in the case of the Un-merry Go-round (Figure 1.6.1, p 57 and CD1.11).

Discernment is also required within a particular analytical approach, when selecting

which of the many features deserve the most attention, and which are the most salient in

terms of our musical experience. As ever, good analysis should serve to illuminate, rather

than replace, the visceral experience of performing and appreciating music.

35 One could add time occurrence as just another dimension to M-Space, but the results are somewhat unintuitive, difficult to visualize and implement.

36 The relationship between M-Space and expressive contours is illustrated in Figure 1.7.2 (p 73).

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1.7 Applications of M-Space and Expressive Contours

The view of improvisation as a variegated walk through M-Space with

corresponding modulations of consynchronous music parameters is manifestly employed

in the author’s work in a variety of ways. These concepts have been developed through a

continuing cyclical pattern of practice, reflection, analysis, theory and reapplication and

are grouped here into general categories.

Improvisational Strategies

The meta-view of improvisation outlined in this paper provides a wealth of options

for performance. The training and skill in order to control effectively this walk through

M-Space (via the limiting, and focusing of dimensions) is considerable and a never-

ending pursuit. In the model of improvisation given above jazz skill can be seen as the

ability to manipulate a stockpile of prepared material (Solstad 1991) alongside newly

created elements to create expressive gestures through certain parameters while keeping

others unaffected. ‘Making the changes’ (proficient negotiation of jazz harmony) for

example, may be seen as altering melodic and rhythmic content while maintaining

control over harmonic altitude and melodic range. Equally, a lack of improvisational

interest can be described as a lack of variation of in for example, rhythmic placement,

dynamic or harmonic control. Hence the incentive for the specific exercises of Tomassi,

Crook and Damian. This view acts as a framework not only to practice improvisation but

also a way to evaluate and appreciate the repertoire. One is given the ability to describe

cultural and individual styles as fields among various dimensions: The skills required in

the bebop heritage involves the fixing of rhythmic density (usually quavers) and a specific

realm of time-feel and timbre, while negotiating complex harmonies with mainly step-

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wise and arpeggiated lines. BB King’s skilful variation of rhythmic placing, phrase length

and vibrato, despite a limited note choice and rhythmic density, is characteristic of his

style (for example Payin’ The Cost To Be The Boss King 2006, CD1.13). Wayne Krantz’s

playing on Is Something I Don’t Understand Yet (Krantz 1995, CD1.14) may be seen as the

limiting of motivic material (intervallic structures) and creating great interest in variation

through transposition, phrase length, metric placement and time-feel control) In short,

an awareness, and ability to identify, the limitating and variation of a range of topics fuels

endless analytical and practice-based research.

Reaching Out

Music technology allows the improviser to extend her reach across several otherwise

inaccessible dimensions providing an expansion of the improvisational palette. Whereas

the traditional saxophonist has stretched to the widest extent of the instrument’s timbral

spectrum, electronic effects expand hugely the available horizon (See CD1.15, an excerpt

from Strike, for saxophone and guitar).

The use of delay tools in improvisations allow the capturing, looping and warping of

live input to form a textural background to improvisations (See CD1.16, an excerpt from

Torus (Mermikides 2008) - a solo electric guitar (and electronics) improvisation, featuring

a polymetric layering of material and triggering and manipulation of speech samples).

This can be seen as a technological smearing of motivic phrases, where a motif is frozen in

time and stretched and manipulated. Performers are no longer limited by a serial

procession of phrases, they may coexist in a parallel with newly initiated phrases and

form a quasi-ensemble relationship (See Omnia 5:58 (CD2.17) in the submitted portfolio).

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Guided Improvisation, Flight Paths and Stripping Contours

Awareness of the multiple paths by which an improvisation may travel allows for

conscious direction during performance, or in score indication. These may be simple

instructions such as ‘Explore timbre’ in String Theory (CD2.15), the harmonic pathways in

Event Horizon (CD2.16) or the modal specifications in Koshinokawa (CD2.9). Figure 1.7.1

shows an excerpt from Event Horizon where the intention is to allow the soloist to

improvise spontaneous long arching phrases. To facilitate the navigation through the

complex harmony, without having to resort to excessive preparation that might mar

spontaneity, a solution was devised. To avoid the undesirable ‘running of scales’ that

often results from improvised passages with non jazz-trained performers, harmonic

pathways are indicated in the score. The performer is allowed free reign to choose notes

from the provided scales within each harmonic context. However, when transitioning

from one chord to the next, smooth voice-leading and an unbroken line is required. To

achieve this each note is given one of three symbols to indicate whether it is sustained

into the next harmony, or altered by a semi-tone and in which direction. The technique

works extremely well, and provides a large range of paths through the chord

progressions without prescribing any particular one, and allows the soloist to form large

scale melodies without an extensive jazz training. This mechanism can be seen as the

maintaining of harmonic altitude, melodic register and phrase length through complex

harmonies.

Figure 1.7.1 Harmonic pathways in Event Horizon indicating methods for negotiating complex harmonies

while maintaining long phrases and melodic register. Symbols above each note indicate voice-leading

strategies via semitone ascent, descent or maintaining the note.

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In other works more responsibility is offered to the soloist with greater jazz

experience. In Eleventh Light (CD2.8) the performer is given key locations in M-Space to

which the improviser must travel via a field series or merged improvisational pathway; the

soloist is given an itinerary through M-Space with fixed destinations but no specified

flight path. Intentional guidance of an improviser (from various disciplines) by the use of

instructions of which parameters should be fixed, and which must be varied, appear

throughout the portfolio and allow a work to retain an authentic spontaneity while

maintaining a common curve of transformation between performances (See the Rumore

(DVD 5.5) and Rat Park Live concerts (DVD 4)).

The use of electronics can expand greatly improvisational concepts. For example, in

I is a Robot (CD9.5), electronics are used to strip pitch and timbre information from a live

improvisation, replacing them with randomised timbres and pitches. This can be seen as

the stripping apart and reattaching of expressive contours, in this case, rhythmic elements

are hijacked from an improvisation and glued to another field in M-Space. String Theory

(CD2.15), on the other hand, uses the physical gestures of the cellist’s Hyperbow and

reattaches these to musical parameters that effect the timbre of the cello as well as other

independent musical layers.

The concept of M-Space may also be employed compositionally and not in the

context of improvisation. Omnia 5:58 (CD2.17) takes an isologic approach, a particular

conceptual pattern (φ≈5/8) is applied heterogenously to a range of musical topics

including hierarchical phrase structures (as in Figure 1.5.20, p 51), spatial placement,

rhythmic elements, vertical stacking, form and time-feel. This may be seen as a

premeditated compositional ‘solo’ where one conceptual seed is manifested in a host of

M-Space dimensions.

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M-Space Modeling

The concept of a motif existing at a point of musical space, transformable along

many dimensions, offers another, more lateral improvisational process to occur. In a

standard improvisation a trajectory in M-Space is taken, so that a starting phrase (P1)

arrives at the next phrase (P2) at some variable distance. The process is then repeated

along another (varying or similar) set of parameters to arrive at the next destination (P3).

A phrase may reference any previous phrase not just the most recent (P4 may reference

P2 for instance) Consequent phrases describe a pattern of proximity relative to what

phrases have occurred in the past, albeit with a fading memory (Figure 1.7.2).

Figure 1.7.2 The relationship between M-Space, expressive contours and time.

A series of phrases over time will build up a nexus of proximal relationships - which

may interweave with the nexuses of other ensemble members - and carve differentiated

expressive contours in a host of parameters. There is a resultant complex interplay

between a newly initiated phrase and a range of previously performed material.

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In some compositions there is an effort to provide glimpses of these separate

potential pathways of a phrase and their relationship to the memory of the seed phrase.

An extreme example of this is Omnia 5:58 (CD2.17) where the various effects on each

individual string, extremely spatialized in the hall, allow the listener to experience quasi-

improvised ideas radiating from one phrase. In other words, the electronics add a

fragmented multi-dimensional ‘glow’ to the musical object (Figure 1.7.3 p 75). As the

piece progresses, the fractured glimpses of past phrases are heard, heading through

independent pitch, timbral and spatial pathways. There is flexibility in the score so that

the performer can respond to these reflected musical strands, in the manner of Figure

1.7.2 (p 75), which in turn affects the character of the ensuing sections of the work.

Shutter Speed (CD2.21) takes a similar approach where one simple phrase is, with the

use of electronics, transformed into multiple co-existing phrases creating a quasi-

ensemble performance with complex elements of micro-timing rhythmic expression

automated.

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Figure 1.7.3 Each of the five cello strings in Omnia 5:58 (CD2.17) are sent along separate trajectories in M-

Space, a graphical representation is shown above a standard notational transcription of the effect of a

single chord.

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Mapping

The Changes Over Time portfolio includes works that take the concept of an

improvisation forming particular expressive contours and structures in musical space,

and reverse engineers the process. Compositions are created from electronic systems that

use physical phenomena as source material to drive expressive contours and M-Space

positioning. The intention is to provide an aesthetic and philosophical grounding to a

work, many of which are inspired by scientific phenomena, and also to explore the

modeling of quasi-improvisational electronic systems, so that the composer delegates

many musical decisions, and can listener to his own work as an impartial listener. Three

examples are shown below. Figure 1.7.4 (p 77) shows images from Primal Sound (CD2.1),

in which a contour – derived from the coronal suture of a human skull – is mapped onto

co-existing expressive contours. Event Horizon (CD2.16) employs the use of real-time

mapping in performance; the data from the Hyperbow is linked electronically to many

consynchronous musical parameters so that the performer may purposefully, or by

consequence, sculpt the various musical layers via the seven sensors on the bow. A

technological mapping is provided in Figure 1.7.5 (p 77).

Microcosmos (DVD 2) represents a yet more complex mapping system. The

composition is created via the input of colour information, and DNA coding from

microbacterial colonies. Colour information, represented in RGB, and genetic sequences

are mapped onto three parameters subsets in M-Space to form a complex, interactive and

emergent work that responds synaesthetically with the imagery (Figure 1.7.6, p 78).

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Figure 1.7.4 Mappings in Primal Sound: the coronal suture (centre) is mapped to (clockwise from top

right) 1) amplitude against time, frequency against time in vertical (2) and horizontal (3) configurations and

as a control of event triggers and pan position.

Figure 1.7.5 Event Horizon physical gestures of the Hyperbow are linked to consynchronous musical

parameters, allowing the soloist to control various aspects of otherwise independent musical layer.

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Figure 1.7.6 Microcosmos employs the mapping of colour and DNA data to three-dimensional musical

subsets.

The works in Changes Over Time which, as briefly discussed, range from ‘standard’

informed improvisation, bionic extensions to traditional performance and large–scale M-

Space modeling and mapping, are covered in detail in Changes Over Time: Practice.

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1.8 Reflection

This paper offers a broad framework in which to practise, develop and analyse

improvisation. This more complete view of improvisational mechanics also allows the

varied and subtle direction, through score notation or rehearsal, of guided improvisation

in composition; performers may be required to explore certain parameters or keep others

fixed, allowing a more sophisticated description of ‘freedom’ in execution. This approach

stands in contrast to the familiar ‘box of notes’ instruction of contemporary score

notation, where a performer is given a set of notes with which to play – but no other

guidance in terms of gesture or modifications of parameters - also reminiscent of the

‘learn your scales and good luck’ approach of much jazz pedagogy. The concepts

discussed in this thesis are amenable to a range of stylistic contexts and help guide

effective and compelling performance without the obligation to always employ the

overtly complex harmony and rhythmic devices often associated with contemporary jazz.

Harmony and rhythmic density represent just a fraction of all potential musical

transformations, and improvisational virtuosity, and more importantly expressive depth,

is possible within the constraints of a superficially ‘simple’ context. Phrase development,

time-feel, timbre, articulation, and the interaction between these parameters are as valid,

musically effective and technically demanding as any other transformative dimensions,

even if the scale material is pentatonic, and a standard notational approximation appears

simple. The concept of M-Space and expressive contours can explain the effectiveness of

these apparently ‘simple’ improvisations, as well as detect large-scale structures that

connect seemingly fragmented phrases in more obtuse extemporisations.

The adoption of music technology in improvisation is, in this model, a natural

evolution, simply extending the limits of various parameters, allowing direct control of

multiple expressive contours and the real-time capture and manipulation of musical

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material. Music technology also allows the deployment of these improvisational

mechanisms in deliberated electronic composition and generative systems. However, if

the breadth of choice confronted by the performer during a standard improvisation is

daunting, then the meta-view of improvisation presented in this paper can be utterly

overwhelming. How is one to begin formulating and constructing pieces using the

concept of M-Space, with its Babelian complexity? The author has found a solution in

the application of a higher-level vision of the ‘limit and variation’ improvisational

technique to the compositional process. Can a piece be constructed with only one

specified expressive contour applied to many multiple parameters?37 What is the effect of

a group improvisation where electronics randomize pitch and timbral content, leaving

only rhythmic elements under the performers’ control?38 Can a satisfying chord sequence

be composed spontaneously within the constraint of fixed bassline and topline

contours?39 What is the result of mapping downward physical force of the bow to the

cello’s cut-off frequency, colour values and DNA codes to timbre, or blood cell

populations to multiple consynchronous musical parameters?40 With very little musical

material, can a systematic cycle of the topic of improvisation form the structure of the

piece? Can geometrically derived coordinates and trajectories in M-Space form musically

coherent melodies, or the expressive contour of harmonic altitude in a blues progression

form the melodic curve in a stylistically distant context? This type of targeted approach

to M-Space exploration has shown to be a useful compositional exercise, improving with

practical experience, developed intuition and critical reflection, and is the case with the

Berklee improvisational exercises (see 1.3 p 11), the strictures imposed rarely inhibit the

potential musicality.

37 See Primal Sound (CD2.1) for this use of isokinetos.

38 See I is a Robot (CD4.5) from the compositional portfolio. 39 Selfish Theme (2.7) employs a simple algorithm to derive a cyclical motion for outer two voices of a chord progression, compositional freedom is allowed only in the inner voice writing.

40 See Event Horizon (CD92.16), Microcosmos (CD2.4) and Blood Lines (CD2.3) respectively.

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The view of improvisation as transformations in multi-dimensional musical space is

so broad that it connects the mechanics and pedagogy of jazz practice with a diverse

range of compositional and analytical research. These include: 1) Xenakis’ formal

modelling (Xenakis 2001) which, with its consideration of stochastic functions over

multiple – albeit discretely valued - musical parameters, has parallels with the concept of

proximity and improvisational strategies in M-Space. 2) Wishart’s “gestures” in electronic

music (Wishart 1996) – a taxonomy of continuous sonic modifications - may be

considered analogous to expressive contours with respect to timbre. 3) The multi-

dimensionality of Pressing’s improvisation model (Pressing 1998) is, as discussed (p 18-

19, 55), related directly to M-Space. 4) Moles’ and Schaeffer’s prescient graphical

representations of l’objet sonore (Holmes 2008, p 45-48) are conceived readily in respect to

three consynchronous expressive contours, or three dimensions in M-Space. 5) Methods

within Schillinger’s compositional systems (Schillinger 1978) may be described as

employing isokinetos, isorhytmos and isologos, and 6) Dreyfus’ detailed studies of motivic

transformation in the music of J.S. Bach (Dreyfus 1996) are readily adopted in terms of a

chains-of-thought methodology. However, despite these parallels, this model’s foundation in

the intuitive and idiomatic discipline of jazz practice, allows a wide range of

compositional and analytical frameworks to be approached with confidence and a unified

creative ethic.

With an explanation of M-Space and expressive contours established, a vision of

improvisation as the virtuosic modulation and structuring of consynchronous musical

parameters has been established. At this point, the discussion turns to one particular set

of these parameters that, though hugely important, is under-represented in the literature

and rarely well understood. The next paper models various micro-rhythms that are

integral to the expression inherent in jazz, and are here collectively termed time-feel.

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2. Time-feel

Abstract

This paper presents, with reference to current pedagogical and analytical approaches, a simple,

usable model of expressive micro-timing in jazz and contemporary popular music, variously referred to as

‘swing’, ‘groove’ or ‘feel’ and here collectively termed ‘time-feel’. Central to the model is the conceptual

separation of the mechanisms of swing (offset of the second quaver) from latency (the sub-notational

rhythmic placement of an individual performance relative to a negotiated time-line). Analytical methods

are suggested that create useful comparisons of stylistic and performer-based variations, as well as how

time-feel may be dynamically controlled during an improvisation as an expressive medium in its own

right. A formal mathematical model is shown that may be employed with great flexibility in the analysis

of a performance, or as a supporting mechanism to performance, pedagogical practice and composition.

2.1 Sub-notational Rhythmic Expression

This paper is concerned with aspects of rhythmic feel in jazz, and other

contemporary musical styles (funk, soul, rock etc.). It aims to clarify salient characteristics

of rhythm that ‘fall between the cracks’ of the standard notational system and general

music terminology. From a practitioner’s perspective41 an analytical method is offered, in

an effort to enhance understanding and appreciation of this under-researched but hugely

important aspect of jazz. By way of an introduction to the field, this paper focuses much

of its attention to the ‘jazz quaver’42 and offers a method of analysis that most readily

41 Much insight has been gained from the author’s experience as a jazz performer, composer and in the production and editing of a large range of contemporary and popular music projects. 42 In the appendix of case studies, time-feel aspects of the semiquaver, the funk sixteenth note, are also explored.

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relates to the experience and skills of the contemporary performer, and the listener’s

experience.

There is a lack of clarity in the field that is likely due to no generally accepted

terminology and little consensus of opinion. Whereas the harmonic and melodic aspects

of the jazz language have been well documented and are easily accessible, specific studies

of jazz rhythm are relatively scarce and late to the body of research. Jazz musicians have

tended to only talk of the subject in vague terms, or not at all. When asked in a

masterclass at the Berklee College of Music (Boston, MA) about the influence of

Brazilian music, and the subsequent ‘straightening’ of the quavers in his music, Horace

Silver responded flatly “I don’t think about that stuff” (Silver 1994).

Yet despite disproportionately little elucidation on the subject, the importance of

rhythmic time-feel is often advocated as an important, or the most important, aspect of

jazz skill:

Rhythmic time-feel is the most basic, fundamental element

communicated by the soloist, and appreciated (or criticized) by an

audience. The greatest technique, creativity, melodic accuracy,

lyricism, sound, style, etc. matters very little if the music doesn’t feel

good rhythmically, whereas less evolved technique, ideas, melodic

choices, sound etc. can actually sound okay when executed with

rhythmic accuracy (good time-feel) and conviction.

Crook 1991, p 10

And more colourfully, from Berklee professor Ron Mahdi:

Good time-feel is like good barbeque sauce… I’d eat anything

with a good barbeque sauce. Hell! I’d eat shit if you gave me

enough sauce!

Mahdi 1994

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Indeed, it seems that with the odd exception43 the greatest practitioners and those

most qualified to explain the subject are often either unwilling or unable to do so,

preferring to encourage learning through imitation, and using qualitative rather than

clear, absolute terms.

Even some of the most articulate jazz critics and chroniclers

will avoid a penetrating discussion of swing and generally

back themselves into a corner when they are asked to engage

in one.

Coker 1964, p 45

In short, it seems that those that fully understand time-feel won’t explain it; and

those that potentially could, don’t fully understand it. Part of the issue is that time-feel

characteristics do not lend themselves to standard notation, and are thus less amenable to

academic dissemination. This notational inadequacy is described eloquently by Trevor

Wishart:

The fundamental thesis of this system (standard musical

notation) is that music is ultimately reducible to a small, finite

number of elementary constituents with a finite number of

‘parameters’, out of which all sounds possibly required in

musical praxis can be notated by combination. It must be

noted from the outset that this finitistic thesis is a

requirement of notation rather than fundamentally necessary

to conceivable musics. For a notation procedure to be of any

use it must use only a manageable (small) number of

constituents which are then permuted; notation of the

continuum is necessarily approximate.

Wishart 1996, p 22

43 See Crook (1991), Moore (1995), Mingus cited in Berliner (1996), and Govan (2010) for rare examples of useful analytical discussion of time-feel in a pedagogical context.

85

Wishart goes on to suggest that aural rhythm allows the performer the “most

intricate” and “subtle” articulations of time against a “silent backdrop of somatic

rhythm.” In contrast, the summative, ‘finistic’ and “economy” of notation loses these

subtleties (Wishart 1996, p 22-23).

Wishart’s contention, that the expressive complexities rhythm, and pitch are – at

best - approximated in notation informs his illustration of a lattice of discrete time-pitch

points. Adding the simplified dimension of discrete timbre (as each instrument), Wishart

arrives at a schematic representation (Figure 2.1.1).

Figure 2.1.1 Wishart’s lattice. The representation of standard notation’s limitation as a lattice, due to

the ‘notational economy’ of ‘finistic’ division of pitch, timbre and rhythmic subdivision (Wishart 1996, p 26).

So when jazz, and other relevant music styles are approached through standard

notation alone, we arrive at a distilled, ‘lattice-filtered’ strain that has stripped out very

important musical aspects. Wishart again:

Viewing duration through lattice notation leads some

members of the musical community to view Dave Brubeck’s

excursion into 5/4 metre as a major breakthrough in jazz

rhythm (rather than the minor excursion on the lattice which

it is), while entirely overlooking the highly articulate

development of phrase-structures against the lattice (Charlie

Parker) or placement of individual events or groups against

the lattice (the essence of ‘swing’)

Wishart, 1996, p 30

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It becomes clear that the aspects of time-feel presented here are preserved through a

heuristic exploration of the musical style in question rather than through jazz scores. It is

learnt by ear rather than by eye. The advent of digital audio technology has allowed a far

deeper exploration into this field, as timing may now be accurately measured beyond the

limits of human perception, and standard notation can be now be seen as a

representational guide of rhythm, rather an accurate account of its detail.

How might it be possible to formulate a system for measuring deviation from the

‘Wishart lattice’ in a coherent and relevant way? In the recording studio, on what basis is

it chosen which way, and how far, to nudge a particular rhythmic placement, or which of

many alternate takes make the cut? Is it possible to form some kind of system that tallies

with the feel of a performance that sits ‘in the pocket’? How can a musician who does

not play metronomically be described as having ‘good’ time? The author’s experience of

performing, listening, composing and editing jazz and popular contemporary music has

allowed the creation of a model that addresses the salient features of these ‘deviations’ in

a simple and usable manner, so that the lattice is transformed into a continuum of

expression.44 Here follows a survey of related research in this field, and how the model

presented here differs from, and adds to, other approaches to the field.

2.2 Relevant Research

The complexity of jazz rhythmic mechanisms that occur beyond the standard

notation lattice, often termed micro-timing, has inspired diverse analytical methodologies

and pedagogical approaches. Stylistically distant research into notes inégales, ritartendo,

classical ensemble asynchrony and time warping in computer music (Fuller 1980, Desain

& Honing 1990, Gabriellson 1988 and Dannenberg 1997 respectively) also hold

44 The author has also conducted research in the continuum of pitch (Mermikides 2007) and timbre (Mermikides 2006) which together with time-feel have built towards a concept of multi-dimensional continuous musical space (See 1 M-Space and Expressive Contours).

87

relevance to the nuanced field. Enquiries into jazz micro-timing may be broadly

categorized into five reasonably separate groups. 1) Musicological, anecdotal and

heuristic responses to the experience of hearing and performing jazz rhythm (Schuller

1968, Werner 1996, Sudnow 1995). 2) Pedagogical material to encourage and guide

exploration of sub-notational timing in jazz practice (Crook 1991, 1996, 1999 and Moore

1995). 3) Audio analysis, measurement and music software applications of swing 8ths (or

jazz quavers) (Cholakis 1995, Friberg & Sundström 2002 and Benadon 2006). 4) Tempo

modulation mechanisms including behind-the-beat playing, rubato and superimposition

of differing simultaneous tempi (Prögler 1995, Ashley 2002, Collier & Collier 2002, Folio

& Weisberg 2006 and Benadon 2009) and 5) Studies of ensemble synchrony, the internal

construction of grooves and rhythmic templates and statistical analysis of rhythmic

placement (Cholakis 1992, Millward 2001a, Millward 2001b, Tait 1995, Butterfield 2006,

Gouyon 2007, Hennessy 2009 and Naveda, Gouyon, Guedes & Leman 2010). Within

this context, this paper provides a model born of a practitioner’s experience, with

analytical utility and creative applicability. With the conceptual separation (and

interrelationship) of swing (displacement along a continuum of the offbeat in an

individual performer’s musical material) from latency (the relative temporal placement of

an individual’s musical material against a relatively rigid mutually negotiated master time-

line) many of the mechanisms within the existing field of research are covered within one

relatively simple framework. The inclusion of weighting in the model serves as a useful first

step into the understanding dynamics and articulation play in the experience of time-feel,

towards which much valuable research is required. Important musical mechanisms such

as ensemble swing, swing friction, swing modulation, latency curves, looseness,

hyperlatency, rhythmic superimposition, time-feel cadences, time-feel blocks and

differential elasticity, all emerge naturally from the model and are presented in 3 Case

Studies. The model has authenticity from a practitioner’s perspective and musical

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intention as well as in the visceral experience of the listener. A purpose-built software

application is also presented which serves as a real-time pedagogical and analytical tool.

The Changes Over Time portfolio demonstrates the variously intuitive and conceptual

reapplication of the time-feel model in a diverse range of improvisational and

compositional contexts.

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2.3 SLW Model of Time-feel

Traditionally, time-feel is learnt through imitation and rarely analysed critically.

However, there exist clear identifiable features of expressive microtiming that can aid

understanding, appreciation and development of the art.

The complex subject of time-feel may be approached from many angles, the model

presented here determines the salient features of time-feel as three conceptually distinct

components: swing, latency and weighting (Figure 2.3.1).

Figure 2.3.1 The Swing-Latency-Weighting (SLW) model of time-feel.

The understanding of jazz quavers amongst musicians seems to be largely divided

between two camps. One group offers the theoretical simplification of the jazz quavers

as ‘triplet quavers.’ The other group, mainly jazz musicians, are aware of the range of

subtleties in the jazz quaver, and can readily recognize and imitate deviations of quaver

placement. However, familiarity with the subtleties of time-feel has not necessarily led to

an ability or willingness to explain these features in objective terms. Rather, subjective,

loosely descriptive terms will describe particular characteristics of time-feel: ‘lazy eighths’,

‘light swing’, ‘pushing’ and so on. These terms (by no means standardised) are clearly

well-defined within the perceptions of individual experienced jazz musicians, but the

terminology is unhelpful, particularly when swing is used to describe other elements of

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time-feel such as latency, or simply as a qualitative measure. The time-feel aspect of

contemporary music is conventionally tacitly absorbed, rather than explicitly taught. Its

salient properties are inherent within the explicit melodic material of the language, and

learned through the imitation of other player’s styles. The explicit melodic and harmonic

language of jazz obfuscates and mystifies this hugely important aspect of the idiom.

Note that although swing is often used to define time-feel in general, the SLW model

describes it as only the offset of the second quaver (or relevant metric subdivision, which

will be called the offbeat). Swing values exists on a continuum that includes straight 8ths

(50%)45, the traditional notion of jazz quavers (66.6° %), dotted eighths (75%) as well as

numerous points in between. In Figure 2.3.2 (p 91), this continuum is illustrated along

with some descriptions of degrees of swing have been added, but there is no

terminological consensus of opinion for such nuance and they are unlikely to hold over

all tempi and stylistic contexts. They are included here as an indicative guide and

illustration of the continuum.

45 Swing values below 50% exist, but tend to occur via inevitable fluctuations in performance (random noise). It seems that once a swing value drops significantly and repeatedly below 50%, it is conceived as the first triplet quaver (33. 6̄ % ‘scotch snap’) or the first semi-quaver (25%). In contrast, under some conditions the concept of the quaver can still be maintained even with repeated swing values close to 75% (See 2.10 p 117).

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Figure 2.3.2 The continuum of swing points. Discrete nodes, such as triplets and

quavers are indicated with solid lines, and 5% differentials in dotted lines. The concept of jazz quavers falls

between the 50-75% range, within which some general and subjective descriptions given.

Clear elucidation of swing values is rarely seen in pedagogical context, although

there are some exceptions: Hal Crook (Crook 1995, p52) suggests an exercise of playing

a repeated quaver on one note while gradually moving from straight (50%) to triplet

(66.6%) quavers, albeit with no scenic stop off points. The drummer Stanton Moore

(Moore 1995) describes and demonstrates examples of swing levels in various drum

styles but does not assign explicit values, describing his approach as “swimming” in

between swing values (Moore 1995 23:21-35). Guthrie Govan, a virtuoso of many

electric guitar styles, speaks clearly about the concept of swing levels as a fundamental

component to groove. In response to an interview question on the development of his

playing, Govan recommends that guitarists learn by playing along to records, rather than

a metronome or drum machine, because it “has a groove, it has something of interest

going on between beat one and beat two”. In this listening process, Govan claims he was

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exposed to “all these different levels of swing”, and goes on to proficiently demonstrate

examples of straight, light swing, and hard swing playing. Swing, he says, is not an “on-

off” but a “dimmer” switch, having varying levels and is something that you can only

learn by “enjoying it first, hearing it and responding to it” (Govan 2010, 5:08 - 5:42).

Traditional standard notation has dealt with the issue of jazz quavers by a blunt

approximation. To indicate swing, a ‘fake sheet’ approach is to include an instruction that

written quavers should be performed as a crotchet triplet followed by a quaver triplet

(66.6%). On other occasions they are explicitly written as dotted quaver followed by a

sixteenth note, this is most likely due to notational economy as this hardness of swing

(75%) is unlikely to be desired in the ‘show-tune’ setting where this practice is commonly

found. (Figure 2.3.3)

In jazz pedagogical material however, these simplistic guides are rarely given, there

may be a few words in the introduction (Coker 1964, Aebersold & Slone 1978) but in

general jazz quavers are written as quavers and their stylistic execution is expected

through a tacit absorption of style.

Figure 2.3.3 Standard notation representations of swing.

The advent of MIDI, sequencing and computer notation brought the inadequacy of

rhythmic notation to light. Criticisms of the mechanical, inhuman, soul-less nature of

computer performance and quantization are not without substance, but the underlying

inadequacy is in fact with a musician’s excessive attachment to the score, and more

fundamentally, a simplistic concept of rhythm. Computers after all, only follow human

instructions. Ironically, it is this dogmatic nature of MIDI and audio sequencers,

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incapable of independent interpretation, that has encouraged a better understanding and

terminology of time-feel. Quantisation in sequencing, the ‘correcting’ of a performance

to a predefined rhythmic nodes, started with a simple lattice approach to rhythm, but has

now developed to include varying levels and subdivisions of swing, limited degrees of

correction, ‘humanizing’ functions to introduce levels of randomness, and the ability to

map a recording to a template from a database of human performances46 (Figure 2.3.4).

Figure 2.3.4 The evolution in Logic of computer quantization of swing, from none (left, Logic

Notator 2.0,1988), to discrete, but not explicitly defined, values (middle Logic Pro 6, 2004) to continuous

values and advanced options (Logic Pro 9, 2009).

This paper includes analyses on examples with either quaver swing or semiquaver

swing, but research suggests that statistically significant rhythmic nuances may occur on

different subdivisions simultaneously (Naveda et al. 2009). Analysis of this kind raises the

concept of swing telescopy; which questions whether swing ratios are maintained or altered

46 See Cholakis’s DNA project for an example of a commercial database of performer-derived groove templates (Cholakis 1992).

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between the quaver and semiquaver levels, or between normal time, half-time and

double-time phrases within a solo.47

In contrast to swing, defined here as the offset of the offbeat in an individuals

performance, latency is concerned with performance in relation to another time reference,

be it an ensemble, a click or a pre-established sense of groove in a solo performance. In

other words, latency is defined as the placement of the performer’s crotchet (onbeat)

against a negotiated time-line (defined clearly in 2.4, p 100-105), and is the component that

defines such aspects of a performance as behind-the-beat (positive latency) or rushing

(negative latency). Again, this element of time-feel exists on a continuum rather than

discrete points. Charlie Mingus described the beat as an ellipsis, rather than a fixed point

in time (Berliner 1994, p 96). Figure 2.3.5 (p 95) illustrates the SLW representation of this

continuum, in terms of objective percentage degrees and notational landmarks, as well as

subjective descriptive terms, next to an illustration of Mingus’ ellipsis. The perception of

latency depends on tempo and stylistic context, so the descriptions are only intended as

illustrative guides to underline the expressive opportunities of this parameter.

Positive latency is more common idiomatically than negative latency, and can be a

significant contribution to a player’s style. Tom Morello, guitarist from Rage Against The

Machine – a band revered for their eschewing of synthesizers and quantization in a rap-

rock context – has reported that when recording a certain track, the studio engineer

noticed that all his notes were similarly late and shunted them back into the ‘correct’

position. On hearing the results, Morello objected to the ‘fix’ (“That’s not my sound”)

and asked for the track to be reverted to its original position (Morello in Guitar

Techniques 1996).

47 See 3.4 (p 142-5) for a discussion of swing telescopy in the context of Jimi Hendrix’s Little Wing.

95

Figure 2.3.5 The latency continuum (top) illustrating behind the beat (positive) and ahead of the

beat performance (negative) latency. Descriptive terms are included as an illustration of the expressive

range available. A similar idea of a beat ‘ellipsis’ was made by Charles Mingus, who illustrated it graphically

(bottom) in masterclasses (Mingus, cited in Berliner 1994, p 96).

Furthermore, behind-the-beat playing is often encouraged pedagogically, certainly in

preference to rushing. There is more conceptual and aesthetic tolerance for positive,

rather than negative, latency:

The problem I see in a lot of students is, I think, anxiety-

related when they play and they are actually rushing

everything…If you’re not going to play like a sequencer and

be bang on the note every time, the other thing that can work

is actually playing late, listen to Miles Davis, or something like

that, or a lot of the hip-hop guys doing their thing…it’s often

preposterously late, and it never sounds like a mistake, it just

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sounds like they’re cool, they’re relaxed, they’re not in any

hurry to get to the next note, because the note they are doing

right now is so good.

Govan (2010) 4:29 – 4:52

This ‘preposterous’ lateness is, in this paper, given the term hyperlatency, to explain

musical moments where a note can under some conditions, fall near, and sometimes

beyond the semiquaver (25% latency) and still maintain the sense of being an onbeat.

Why such a hyperlatent note is not conceived, or notated as falling in its ‘proper’ place (e.g.

the second semiquaver) is due to elements of stylistic context, rhythmic preparation and

articulation.48

There is another more fundamental question still unanswered: Given a fixed tempo,

why is one player described as late, and not the other as early? The answer lies in the

concept of a hierarchy of rhythmic establishment, the idea that one performer holds

more (or all) of the authority in the definition of the time line than others. This mutually

negotiated time-line is described mathematically in Section 2.4 (p 100-5), and explains

why jazz mechanisms of falling behind the beat cannot be adequately equated with rubato,

latency is an expressive mechanism concerned with friction against a relatively rigid time

line, not the elasticity of the time-line itself. Tempo changes do of course occur in

contemporary popular music, both as rubato cadences (Ashley 2002) and as (usually

intuitive) ensemble tempo shifts between sections of a song (Millward 2001a). However

it is important to separate the idea of the master time-line trasformations (rubato,

accelerado, tempo shifts etc.) from the subtle but important art of rhythmic placement

and movement against this framework. Counter-intuitively, it is the soloist rather than the

48 See 2.10 (116-120) for a suggested explanation of this mechanism.

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accompanist, or accompanying ensemble, who has the least say in the tempo, but the

most opportunity for expression in terms of latency mechanisms.49

There are moments in the jazz (and wider) repertoire when the concept of one

master time-line can no longer be usefully maintained. The superimposition of the

soloist’s differing, or even fluctuating, tempo implications over an accompanying time

framework have been identified (Mermikides 2008 and Benadon 2009). These may occur

as short gestures or longer passages that include points in time when soloist and

ensemble synchronize at specific anchor points, before separating tempi again. At the

furthest extreme, the use of technology can easily allow the ‘Ivesian’ co-existence of

many unrelated tempi or the lifting of musical material from one musical context to

another, as in Zappa’s concept of xenochrony.50 In these cases, the notion of a single time-

line needs to be released, and analysis and appreciation should be made in reference to

multiple time-lines, which may or may not be related simply. The identification of

simultaneous tempi (Benadon 2009) and analysis of latency or note separation curves (see 3.5

Push-pull (p 146-8) and 3.6 Temporal Plasticity (p 149-67)) are useful adaptive tools in these

contexts.

Weighting is simply the strength of attack of the offbeat relative to the onbeat. In

straight-ahead jazz, the emphasis of the weaker beats occurs routinely on the crotchet

level (the hi-hat, finger-click in count-in and idiomatic walking bass-line all add weight to

beats 2 and 4, relative to beats 1 and 3)51. In addition, emphasis is commonly added, at

49 This is in direct contrast to the governance of tempo for the classical concerto soloist, where the conductor relays tempo fluctuations to the ensemble, who follow obediently. 50 Dissatisfied with the recorded sound of his electric guitar solos in the studio, Frank Zappa took to recording his guitar solos from live concerts. He would then in the studio, transplant these solos into another piece with a similar tonality but differing rhythmic context. Zappa enjoyed the transformative effect of this process, which he termed xenochrony, examples of which have become the standard solo in his recorded compositions. Dweezil Zappa, who now performs his father’s music achieves the impressive task of transcribing, memorizing and performing live, extensive xenochronous solos in his Zappa plays Zappa project (Hrab 2010). 51 In contrast, classic funk music tends to have a very strong 1st beat, strong beats 2 and 4 and a weak 3rd beat. Swing values (predominantly in the 55-63% range) occur at the semiquaver level, as well as latency components. For excellent overviews and demonstrations of funk and related drum styles see Slutsky & Silverman (1997) and Moore (2005) respectively.

98

differing amounts, at the quaver level, the ‘bop’ of bebop (Crook 1991, Crook 1994,

Berliner 1996)52. It is this element that is introduced as the third component in the time-

feel model. Weighting may be calculated objectively as simply the dB differential between

offbeat and down-beat quavers. However, to align with the listener’s subjective

experience of offbeat emphasis, this calculation may be made by more complicated

algorithms of attack, harmonic content and pitch considerations. The distillation of

articulation into one variable is inevitably simplistic53 but is included to highlight the

perceptual interlinking of dynamic and timbral considerations with rhythmic elements in

the overall impression of time-feel.

With the three components of swing, latency and weighting in place, a succinct

description of time-feel can be made, particularly with the inclusion of the standard

deviations, or looseness, of these elements. Using the language of multi-dimensional

musical space (as laid out in M-Space and Expressive Contours), a particular time-feel may be

illustrated as a point in three-dimensional space (Figure 2.3.6 p 99). This subsection of

M-Space may be explored as an expressive medium and subject to the improvisational

mechanisms established in Section 1. CD1.17 performs three time-feels of swing, latency

and weighting - (1) (63,0,0) 2) (58,12,7) and 3) (50,22,20) – as sequenced clicks and

melodic phrases.

52 In learning both classical and jazz guitar, the author notes that slurs were approached differently in the two disciplines. On the beat for classical, off the beat for jazz, providing a significant musical difference, even without swing elements. 53 A useful survey of jazz articulation techniques is found in John McNeil’s The Art of Jazz Trumpet (McNeil 1999).

99

Figure 2.3.6 The SLW model of time-feel represented as a three-dimensional continuous subset

of M-Space. Three SLW time-feels: 1) (63,0,0) 2) (58,12,7) and 3) (50,22,20) are illustrated. These are

sequenced as clicks, and then performed as melodic phrases, on CD1.17.

With this overview of the SLW model in place, a formal mathematical model is

presented (2.4-2.6) followed by commentary on its employment and emergent concepts

(2.7-2.12). A selected collection of time-feel case studies and their integration with M-

Space and expressive contours are presented in 3 Case Studies (p 130-167).

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2.4 Where’s the Beat? Determining The Master Time-Line

Calculation of the master time-line begins by defining an ensemble ε with E

performers54 (Figure 2.4.1).

!

" = 1,2...E{ }

Figure 2.4.1 Ensemble ε with E performers.

Each performer has an individual series of values for the quaver set, with X

quavers{x0,x1,…xX}.55

For performer e, the timings of the quaver set are defined (Figure 2.4.2).

!

t0e ,t1e …tXe{ }

Figure 2.4.2 Quaver set for performer e.

Now from the ensemble, a series of master time points are derived for the quaver

set {x0,x1,…xX-1} as in Figure 2.4.3.

!

T0 ,T1…TX{ }

Figure 2.4.3 Master quaver set.

54 Rather than performers, these can include distinct musical strands e.g. each hand at the piano. 55 This approach is constructed on the scenario of only (near) quaver subdivisions, but can easily accommodate higher, and lower subdivisions as required. The model also starts with the very simplistic approach of all performers playing a continuous stream of quavers, but this is easily developed to accommodate the real world of music making (Section 2.12 p 125-9).

101

These can be thought of as a mutually negotiated time-value between the

performers, which may be calculated simply as the average of the individual E

performers (Figure 2.4.4).

!

TX =

txee=1

E

"E

Figure 2.4.4 Master quaver set determined by averaged time values across e performers.

More realistically, this calculation may be modified to accommodate a hierarchical

rhythmic component. Let Rxe will be a figure between 0 and 1, representing individual e’s

relative importance to the master placement of quaver x (Figure 2.4.5).

!

TX = txe( )* rxe[ ]e=1

E

" where

!

rxee=1

E

" =1

Figure 2.4.5 Hierarchically weighted time values. A click track or drummer may have all the authority in terms of the master time-line, or it may be distributed, or actively passed, between performers.

In a scenario with a guitar duo, the determination of a master time point may

dynamically move between the two players (during alternating solos) or fall between the

points during more balanced sections, such as a harmonized melody. Note that if an

accompanist gains all the command of time line definition, he alone can make the tempo

fluctuate, while the soloist is free to explore all manner of subtle and ‘preposterous’

lateness. Figure 2.4.6 graphically represents this model with a representation of the

master time reference during a harmonized solo (Rx1 = 1/2, Rx2 = 1/2), Guitar 1’s solo

(Rx1 = 0, Rx2 = 1), and Guitar 2’s solo (Rx1 = 1, Rx2 = 0).

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Figure 2.4.6 The same asynchronous events (tx1 and tx2) in three different moments of a

hypothetical guitar duo performance: a) Harmonized melody (Rx1 = 1/2, Rx2 = 1/2), b) Guitar 1’s solo

(Rx1 = 0, Rx2 = 1), and c) Guitar 2’s solo (Rx1 = 1, Rx2 = 0). These create three different calculations for

the master onbeat (Tx) and resulting descriptions of lateness or earliness for each guitarist.

103

Figure 2.4.6 demonstrates that the determination of lateness or earliness depends on

a hierarchy of importance of the performers. For asymmetry of latency to occur with two

performers, there must an asymmetry in hierarchy. Figure 2.4.7 (p 104) displays a

scenario with three performers (guitar, bass and drums). The resulting descriptions of

three onset times (

!

tx1 ,tx2 and

!

tx3 ) are shown in reference to three different hierarchical

weightings a) Equal weighting (Rx1 = 1/3, Rx2 = 1/3, Rx2 = 1/3) b) Oligopoly (Rx1 = 0,

Rx2 = 1/2, Rx2 = 1/2) and c) Monopoly (Rx1 = 0, Rx2 = 0, Rx2 = 1).

104

Figure 2.4.7 Varying determinations of lateness depending on hierarchical context. Master time

point Tx (dashed line) is determined by tx1, tx2 and tx3 in a) Equal weighting b) Oligopoly, performers 1

and 2 share responsibility, and c) Monopoly where performer 3 has all the metric responsibility.

105

The performer with the least input into time-keeping has the most opportunity and

range to explore latency mechanisms, as their actions do not pull the perception of the

master time-line towards them.56 One can think of this relationship as three objects of

differing mass and the resulting relative gravitational pull between them. In this case the

soloist has no mass and no influence on the ‘gravitational centre’. In contrast, the

drummer in scenario c) has no opportunity to explore latency, although he is free to

place offbeats as he chooses (determining his swing level). Given this scenario, the

drummer could theoretically command radical tempo shifts57, but there are of course

tight aesthetic and idiomatic limits particularly in the flow of a groove. It is the

expectation of generally metronomic tempo that most allows the freedom of time-feel

mechanisms. If a track were recorded to a click that would be the limiting factor, but

drummers, and contemporary musicians in general, are expected to have an internal

metronome (Crook 1997) - significant timing deviations should be intended, or at least

felt somatically, and every player is, for example, expected to feel a common time pulse

during stops and solo breaks. This unheard common pulse or master time-line,

perceptible to all the players and listeners during a performance, may be considered as

another - albeit inaudible - performer, just like the unbounced studio click.

56 Of course this, like most elements of time-feel, requires an element of repetition; one waywardly late attack is unlikely to feel like anything but an anomaly, but a string of notes behind the beat becomes a perceptible time-feel element. 57 Small but significant tempo shifts do in fact occur in metronomic styles like funk. (Millward 2001a)

106

2.5 Defining Swing: Offbeat Asymmetry.

Swing for each performer is defined as the timings of three adjacent quavers from

the performers quaver set {xo, x1, x2 … xx } starting and ending on a crotchet beat, for

example to, t1 and t2. Swing (S) is determined as the relative placement of t1 within the

time duration from t0 to t2 (Figure 2.5.1).

Figure 2.5.1 Calculation of swing (S) as the ratio of the time length from first onbeat to offbeat (t1

–t0) relative to the time length between onbeats (t2 –t0) .

So, as seen in Section 2.4, the traditional concept of the triplet jazz quaver yields a

swing value of 0.66̄ , a straight quaver gives a value of 0.5, and discernible values exist

along a continuum from around 50 – 75%.

It is necessary to track swing values over several occurrences to distinguish

significance from anomaly. Defining phrase P to contain a series of X continuous

107

quavers {x0,x1,…xX}58, occurring at time points {t0,t1,…tX}, the mean swing value of

quaver phrase P for performer e (

!

µsP ) can be defined (Figure 2.5.2).

!

µsP =

t1 " t0( )t2 " t0( )

+t3 " t0( )t2 " t0( )

+!+tX"1 " tX"2( )tX " tX"2( )

2X

Figure 2.5.2 The mean swing value of phrase P.

Another important component that can be derived from this model is the amount of

variance around mean time-feel values. This is experienced as the relative tightness or

looseness of a performance, the average variance from a mean value during a passage of

music. In the case of swing values the standard deviation of S within phrase P (δP) may

be calculated (Figure 2.5.3).

!

" P =12X

S0 #µP( )2 + S2 #µP( )2 +!+ SX#2 #µP( )2[ ]

Figure 2.5.3. The standard deviation of swing in phrase P consisting of X quavers.

58 This calculation presumes an even number of continuous quavers starting on an onbeat. Section 2.10 discusses swing calculations in the case of missing onbeats.

108

2.6 Ensemble Swing and Swing Friction

There are moments in performance when an ensemble locks in to a similar groove

(Berliner 1994, p 349-52). These elements can be explained and calculated from time-feel

components between performers. In terms of swing, it is possible to calculate the mean

swing of ensemble E during phrase P (

!

µsPE ) given mean swing values of each of e

performers (

!

µsP1 ,µsP2 …µsPe ) (Figure 2.6.1).

!

µsPE =1E

µsPee=1

E

"

Figure 2.6.1 Mean ensemble swing of Phrase P for ensemble E, where

!

µsPe is the mean swing for

performer e in phrase P.

How much the ensemble swing varies from the mean value is determined by the

standard deviation (σSp). Figure 2.6.2 shows the calculation as the average deviation per

quaver pair for each performer relative to µSp.

!

" SP=

12X

1ES01 + S02 +!+ S0E( )#

$ %

&

' ( )µSP

#

$ %

&

' (

2

+1ES21 + S22 +!+ S2E( )#

$ %

&

' ( )µSP

#

$ %

&

' (

2

+!+1ESX)21 + SX)22 +!+ SX)2E( )#

$ %

&

' ( )µSP

#

$ %

&

' (

2*

+ , ,

-

. / /

Figure 2.6.2 Ensemble swing standard deviation for E performers over X quavers in phrase P.

Varying swing values may occur simultaneously between ensemble members,

creating a time-feel dissonance. Swing friction (sfab) is defined as the discrepancy between

two performers’ (e.g. a and b) swing values. This may be calculated from mean values

over phrase P (Figure 2.6.3). The swing friction between a performer (e.g. c) and the

ensemble swing (SFc) may also be calculated for phrase P (Figure 2.6.4).59

59 Examples of swing friction are found in analyses of Johnny B. Goode (3.3 p 139-141) and Just Friends (3.6 p 149-152)

109

!

sfPab = µsPa "µsPb

Figure 2.6.3 Swing friction between performers a and b over phrase P.

!

sfPcE = µsPc "µsPE

Figure 2.6.4 Swing friction between performer c and ensemble over phrase P.

It is possible for performers to share swing values but not be aligned in terms of

offbeat (due to latency discrepancy), conversely swing friction may exist even when

offbeats are aligned. The interaction between swing, latency and offbeat is discussed in

section 2.10 p 116-120.

110

2.7 Latency

Whereas swing defines the displacement of the 2nd quaver, latency describes the

discrepancy between an individual performer’s crotchet point (for example ta) and the

master crotchet (Ta - as defined in section 2.4). This calculation is made relative to the

duration of the master crotchet (Ta+2 – Ta) . It can be seen as the placement of an

individual performer’s crotchet in reference to the click, leader or negotiated time

framework. It is to this parameter that such terms as “lazy”, “behind the beat”,

“rushing”, “on top of the beat” and so on, allude (Figure 2.7.1).

Figure 2.7.1 Calculation of latency for a performer at onbeat a’as the discrepancy between

individual and master onbeats relative to master crotchet.

A performer with positive latency is playing behind, and negative latency ahead of,

the beat. A latency value of 25% is equivalent to the duration of the master semiquaver60

60 The master semiquaver is determined as

!

Ta+2 "Ta( )4

.

111

Note that since latency has been distinguished from swing, it does not consider the

individual’s offbeat (ta+1) even though a latent phrase displaces the 2nd quaver.

As with swing values, several occurrences of latency (over X quavers in phrase P)

may be tracked and the mean value (µLp) calculated (Figure 2.7.2).

!

µLP=

t0 "T0( )T2 "T0( )

+t2 "T2( )T4 "T2( )

+!+tX"2 "TX( )TX "TX"2( )

#

$ %

&

' (

2X

Figure 2.7.2 Mean latency of phrase P over X quavers.

The standard deviation of mean latency, a component of ‘tight’ or ‘loose’ playing,

may also be calculated (Figure 2.7.3)

!

" LP=

t2x #T2 x( )T2 x+2 #T2x( )

$

% &

'

( )

2

x=0

X /2

*

2X

Figure 2.7.3 Standard deviation of latency in phrase P for X quavers.

112

2.8 Weighting

Another important aspect of time-feel is the relative weighting of the onbeat in

relation to the offbeat. Often a time-feel is established by accenting the offbeat quavers

(Coker 1964, Crook 1991, McNeil 1995). This can be thought of as a double-time

rendition of the familiar jazz crotchet walking bass-line.61 Weighting (W) may be defined

as the dB level of the offbeat relative to the onbeat in each crotchet phrase.62 Positive

weighting is defined as a more weighted offbeat than offbeat. Mean and standard

deviation values for W may also be calculated (Figures 2.8.1 and 2.8.2).

!

WP =12X

dBt2 x+1 ,t2 xx=0

X /2

" where

!

dBt1 ,t0 is the dB differential of t1 and t0

Figure 2.8.1 Mean weighting of phrase P over X quavers.

!

"WP=

12X

dBt2 x+1 ,t2 x#WP( )2

x=0

X /2

$

Figure 2.8.2 Standard deviation of weighting of phrase P over X quavers.

61 Berklee professor Ed Tomassi would give succinct and effective (albeit simplistic) instructions for good time-feel: Play legato, behind the beat, ‘straight 8ths’ and accent offbeats slightly. (Tomassi 1995) 62 As explained in Section 2.3, more sophisticated measures of weighting may be used.

113

2.9 Time-Feel Matrix

For mathematical analysis and integration with M-Space modeling the three

components of the SLW model may be consolidated into a 2x3 matrix for mean and

standard deviation values of swing, latency and weighting in phrase P (Figure 2.9.1).

!

P =

µSP" SP

µLP" LP

µWP"WP

#

$ %

& %

'

( %

) %

Figure 2.9.1 Time-feel matrix of Phrase P.

A complete solo (J) may be defined as consisting of a series of n discrete phrases J =

{P1,P2,…Pn} (Figure 2.9.2).

!

J =

µS1" S1

µL1" L1

µW1"W1

#

$ %

& %

'

( %

) % ,

µS2" S2

µL2" L2

µW2"W2

#

$ %

& %

'

( %

) % !

µSn" Sn

µLn" Ln

µWn"Wn

#

$ %

& %

'

( %

) %

Figure 2.9.2 Solo J comprising a series of n time-feel matrices.

Allowing the calculation of a host of interactive time-feel elements, including mean

swing of all n phrases in solo J (Figure 2.9.3).

!

µSJ=1n

µSpp=1

n

"

Figure 2.9.3 Mean swing of n phrases in solo J.

114

Or, as a further example, the standard deviation of latency between phrases in solo J

(Figure 2.9.4).

!

" LJ=

µLp#µL J( )

2

p=1

n

$

n

Figure 2.9.4 Standard deviation of latency of n phrases in solo J.

Employing the graphical language of M-Space, a particular time-feel may be

represented in three-dimensional continuous space, breaking the discontinuity of the

Wishart lattice63 while maintaining references to standard notational and conceptual

nodes such as semiquavers and triplets. Although there may be perceptual limits to the

discernment of adjacent points in this cube, it must be noted that Figure 2.9.5 (p 115)

represents a three-dimensional continuum and not a lattice, with expressive subtleties

available for exploration. Time-feel can thus be characterised as occupying a small space

in the time-feel M-Space (A), moving between various points during the course of a

phrase - or between phrases of a solo - (B-D); or by its looseness (three-dimensional

shape) within a particular field (E). CD1.18 plays a phrase with three different time-feels

as illustrated in Figure 2.9.5 (p 115). The first phrase stays in one time-feel position (A:

medium swing, behind the beat, light weighting) while the second moves through three

points (B-D) in time-feel space. The last phrase stays in one general position (light swing,

late and weighted) but has a slight looseness as illustrated by E’s relatively large shape.

63 See Wishart’s depiction of the standard notation lattice (Wishart 1996 p 33).

115

Figure 2.9.5 Time-feel represented as a three-dimensional continuum subset of M-Space. Time-

feel characteristics may be seen as tightly-defined areas (A), trajectories (B-D) or loose fields (E). CD1.18

plays a phrase with three different time-feels: 1) time-feel A (medium swing, behind the beat, very light

weighting), 2) time-feel B to C to D and 3) time-feel E, very behind the beat, slightly swung, weighted and

fairly loose.

116

2.10 Relationships between Swing, Latency and Weighting

Swing and latency are defined in this model as independent variables, it is possible

to perform, for example, even quavers with a positive latency (‘straight and late’) or

swung quavers on the beat. However there is a perspective from which they are

interlinked. Considering a time-feel of 65% and 50% swing (Figure 2.10.1a), if (T2 – T0)

= (t2 – t0) the offbeat (t1) will occur at 65% of the duration between master onbeats,

however a swing of 60% and a latency of 5% will create an offbeat at the same point in

time (Figure 2.10.1b, p 117). There is a continuum of swing and latency values that share

the same offbeat point, ranging from swung and on time to ‘straight and late’ (Figure

2.10.2, p 118). The two extremes of these time-feels have significantly different effects,

yet are difficult to explain without the differentiation of swing and latency provided with

the SLW model. Some of the jazz community’s difficulty in explaining clearly the

concept of swing may be due to this subtlety, examples a, b, c and d can all be said to

swing (in a general offbeat asymmetrical sense) but the means of placing the offbeat, and

the resulting effect, are significantly different and this differentiation is a key component

of jazz time-feel. Another implication of this model is that at higher tempos, when

performers are no longer able to maintain an asymmetric quaver pattern due to the short

second quaver, straight and late playing provides a technically easier alternative to

creating a similarly placed offbeat.

117

Figure 2.10.1 Four time-feels (a-d) sharing the same offbeat placement in relation to the master

timeline but with differing swing and latency values ranging from s heavy swing in time to ‘straight and

late’.

Given that there exists a series of time-feels that place an offbeat at 65% between

master time points, it is possible to build a library of swing and latency values for all

offbeat placements. Figure 2.10.2 (p 118) displays swing and latency values linked by a

common offbeat placement. Examples a-d, from Figure 2.10.1, appear along the 65%

diagonal line with on time swing playing in the top left and straight and late in the

bottom right. Parallel diagonal lines represent other levels of offbeat placement with

corresponding swing and latency values, and expressive potential.64 These are illustrated

at 5% intervals but exist on a continuum only limited by aural perception.65

64 3.6 Temporal Plasticity identifies the use of this time-feel mechanism in the playing of Pat Martino. 65 The issue of analysis and the limits of perception is discussed in Section 2.12 (p 125-9).

118

Figure 2.10.2 Offbeat placement values (the performer’s offbeat relative to the master timeline)

plotted against swing and latency. Examples a-d from Figure 2.10.1 (p 117) are plotted on the 65% offbeat

line. An oval area of common jazz quaver values is indicated.

There exists another important connecting mechanism between swing, latency and

weighting not yet discussed concerning displacement. A simplistic time-feel (swing 50%,

latency 0%, weighting 0%) may be displaced by a quaver and still retain its time-feel

pattern. However with the introduction of any weighting or non-straight swing values

exact quaver displacement (50%) alters the time-feel pattern. Figure 2.10.3 (p 119)

illustrates how only an unweighted straight time-feel can be displaced by a quaver and

still align with its original time-feel in terms of accent pattern or synchrony. In order to

imply a quaver displacement, while retaining the original time-feel, the accent pattern and

swing values must be adapted; delaying the phrase by 50% does not have the same effect,

as experience with digital audio editing will tell.

119

Figure 2.10.3 The comparison of 50% latency on four different time-feels. Only in example a) is a

50% latency exactly equivalent to a rhythmic displacement.

The same issue arises at the semiquaver level, unless the time-feel is unswung and

unweighted, a semiquaver displacement cannot be implied simply by delaying the phrase.

Furthermore, from a guitarist’s perspective a phrase starting on an offbeat semiquaver

(or a quaver depending on tempo) would normally start with an upstroke, so there is a

timbral and visceral distinction between an intended semiquaver displacement and a

latency of 25%.

120

Figure 2.10.4 The significant difference between the transformation of phrase a) through b) 50%

latency and c) quaver displacement.

Figure 2.10.4 illustrates the significant difference between a phrase transformed by a

50% latency and a quaver displacement. The implication here is that time-feel gives

quavers an identity that is not simply about their approximate alignment with the lattice,

there is a fundamental difference between latency and rhythmic displacement. This

would offer a reason of how hyperlatency is possible: A phrase could be played 25% (or

even up to 50%) behind the beat - particularly if the latency is introduced progressively -

and still feel like it is preposterously late rather than simply a rhythmic displacement,

challenging fundamental assumptions of a score-based perspective of musical experience.

121

2.11 SLW-Coach : A Computer Application for Time-feel Analysis

Music technology is an invaluable tool in the research of time-feel, allowing detailed

analysis of performance at a critically high resolution and exacting reapplication of

theoretical models. Various systems are employed extensively to inform the author’s

research into time-feel including 1) sequenced time-feel matrices (Figure 2.11.1) for

comparisons and selection of time-feels, 2) sonogram analyses allowing the simple

calculation of onset times (Figure 2.11.2, p 122) and 3) data algorithms for extended

calculations (Figure 2.11.3, p 122).

Figure 2.11.1 Sequencing of time-feel matrices in Logic Pro 9. Latency and swing transformations

displayed on the horizontal and vertical axes respectively. Weighting levels exist in hierarchical folders

making up the three dimensions of the SLW model.

122

Figure 2.11.2 Time-feel sonogram analysis of Pat Martino’s solo on Just Friends (See 3.6 Temporal

plasticity).

Figure 2.11.3 Extract of data analysis of time-feel in James Brown’s Lickin’ Stick (Mermikides

2005).

These systems are invaluable in the formation and development of the SLW model.

However they are all forms of post-hoc analysis and so somewhat divorced from the

music making process. To remedy this deficiency, a software patch was developed by the

author (using Cycling74’s MAX/MSP programming language) that gives real-time data

using the SLW model. This has proven to be a very useful analytical and practice tool.

The current version of SLW-Coach has the following features:

123

A master time-line is derived by one of the following methods:

- An internally generated metronome click to which the subject performs.

- An externally generated midi clock signal which may be triggered and controlled

live.

- A beat-detector/predictor patch. This employs an algorithm to derive a master

time-line from an incoming audio signal in real-time.

To this time-line the following calculations are made from audio or midi sources,

and displayed in real-time.

- Quaver swing, latency and weighting values.

- Mean swing, latency and weighting values for any of the performers within a

specified phrase in real-time.

- The standard deviation of swing, latency and weighting for any of the

performers within a specified phrase in real-time.

A phrase ending is determined by a predetermined beat duration where no event

occurs, or may be triggered manually by a midi-event (e.g. midi footswitch) This stores

the data for the previous phrase for later retrieval and resets all values for the subsequent

phrase. Current developments include an intuitive real-time graphical presentation of

these values that can also cross reference a database of styles and performers.

Figure 2.11.4 Screenshot of SLW-coach, a computer application for practising time-feel.

SLW-Coach has provided a pedagogical and practice tool to evaluate and develop

time-feel in the author’s playing, which acts an evolution of the improvisation studies

undertaken at Berklee College of Music (Boston, MA). The development of accurate and

124

consistent time-feel is a challenging but valuable exercise that trains technique and aural

skills. It is tools like these that complete the circle from practice to theory and back

again.

125

2.12 Real World Time-feel Analysis

The SLW model provides a variety of tools to analyse time-feel mechanics in the

recorded repertoire. However the complete model is only fully applicable in the analysis

of multitrack recording (an invaluable resource for contemporary music research) with

tracks recorded to click as the most amenable, or in carefully controlled studies. In the

absence of multitrack recording, or prepared live analysis, the model can be used like a

Swiss army knife, with the most relevant component applied to each given situation, and

with the occasional inevitable compromise. Regardless, analysis should be guided by the

listening experience, and serve as a way to explain and illuminate more clearly real

musical effects, rather than the uninvolved creation of data sets. Section 3 (p 131)

presents several case-studies showing the adaptive use of the model, in order to

illuminate the most salient and instructive time-feel aspects from each given context.

Care should always be taken to identify which time measurements are actually

perceptible from the high degree of detail obtainable through technology. The use of

sequenced time-feel patterns for aural discernment is a direct and useful way to identify

the listener’s limits of perception. Fernando Benadon suggests 50ms as a useful guide to

the limits of meaningful time discrepancy in the analytical process (Benadon 2009) 66. He

takes into account measurement error and the inevitable noise of human performance to

arrive at this figure. However, experience with digital recording suggests that latency

values from as low as 12ms are perceptible by some performers. The limit for most

listeners most probably falls between these extremes, and the extent to which meaning

may be derived from analysis depends on a host of factors including musical, context,

66 Benadon in fact suggests this 50ms benchmark in reference to increasing time values rather than onset times, as is the case here.

126

tempo and technique for deriving onset time.67 As a guide, Figure (2.12.1) displays the

nuance of detail, in terms of quaver swing and latency percentages, for a given tempo

and listener’s time discrepancy resolution. A listener with 30ms listening acuity, for

example, can at a moderate tempo of 100bpm theoretically discern 6 levels of quaver

swing from 50-75%. This sort of guide is helpful in maintaining a realistic approach to

time-feel analysis, and guards against the inclusion of negligible data in analysis. However

all data that is perceivable is not necessarily relevant. A spurious performance ‘slip’ or

technical difficulty should not always be classed as expressive latency. Repetition, groove

playing, tight standard deviations and honest reflection on the part of the analyst helps to

separate expressive intention and effect from anomaly.

Tempo

40bpm 60bpm 80bpm 100bpm 120bpm 140bpm 160bpm 180bpm 200bpm

10ms 0.6̄ % 1% 1.3̄ % 1.6̄ % 2% 2.3̄ % 2.6̄ % 3% 3.3̄ %

20ms 1.3̄ % 2% 2.6̄ % 3.3̄ % 4% 4.6̄ % 5.3̄ % 6% 6.6̄ %

30ms 2% 3% 3.3̄ % 5% 6% 7% 8% 9% 10%

40ms 2.6̄ % 4% 4.3̄ % 6.6̄ % 8% 9.3̄ % 10.6̄ % 12% 13.3̄ %

Tim

e D

iscr

epan

cy

Lim

it

50ms 3.3̄ % 5% 5.6̄ % 8.3̄ % 10% 11.3̄ % 13.3̄ % 15% 16.6̄ %

Figure 2.12.1 Quaver swing and latency perceptive limits for given listener perception (ms) and

tempo (bpm).

Figure 2.12.1 raises the issue of tempo. Can the internal ratios of time-feels be

maintained at all tempos with equal effect? Only up to a point. Cholakis (1995) notes

that swing ratios tend to decrease with higher tempos. As discussed previously, there is a

67 Incidentally, the case study of Django Reinhardt’s Swing 42 (3.1 p 131-33) demonstrates at least four clearly perceptible levels of swing between 50-75% at a tempo of 204bpm implying a clear perception of timing discrepancies of around 18ms.

127

technical limit to the shortness of a note performed, so straighter playing would be

expected as we reach progressively higher tempi (The offbeat placement relative to the

master time-line can be maintained by latency). However there is also a ceiling to the

listener’s perception of short durations (at 200bpm, there is only 50ms separating 50%

and triplet swing for example). So as tempos increase, both the ability to perform, and to

hear, swing decreases. It would be expected that at higher tempos, latency and weighting

would become the chief components of time-feel. This aligns well with Tomassi’s guide

for bebop time-feel (Tomassi 1995), perhaps the higher tempos of this style instilled,

through necessity, the idiomatic weighted straight and late playing. Further research with

the tools presented here may reveal some evolution of time-feel due to higher tempos, as

well as the South American straighter quaver influence68, if without Horace Silver’s help.

So tempo may impact swing values, but there are other stylistic considerations that also

do not align across tempi. The gypsy jazz quaver, in particular while comping, tends to

have an increasing swing ratio at slower tempi (Dunn 2005) which is not explained by

technique or perception; it is in fact a stylistic component implying the existence of

important and subtle relationships between tempo and time-feel values across idioms.

There exists a huge recorded repertoire ready to be researched that will inform greatly

the understanding of time-feel in terms of both style and individual artists.

There remains an analytical issue yet to be discussed, that is quite minimal but

included for completeness. How is swing to be analysed in the absence of adjacent

onbeats? Figure 2.12.2 illustrates four examples of offbeat quavers, only the first of

which (a) is addressed in the current model. Swing has so far been defined as the

placement of the offbeat relative the length of the performers crotchet (t2 – t0) but in the

absence of a performer onbeat (crotchet), either, or both, sides of the offbeat, this

68 South American music including Bossa and Samba do not in fact have absolutely straight quavers and semiquavers, there are light swing elements as well as other multi-dimensional microtiming elements (Naveda et al. 2009).

128

calculation cannot be made (b-d). The solution is simply to use the master crotchet as the

time reference (T2 – T0 ) which is assumed to be equal to the performer’s crotchet.69 With

a missing 2nd onbeat (t2), as in examples c) and d) swing may be easily derived from the

second quaver duration. Example d) presents an ambiguity. Is the displacement due to

swing or latency? In the absence of the musical context the situation is ambiguous.

Unless there is compelling evidence in the rest of the ensemble, a series of slightly late

offbeat semiquavers (as in an idiomatic guitar ska rhythm) may be thought as anywhere

along the relevant offbeat placement contour seen in Figure 2.10.2 (p 118).

Figure 2.12.2 Methods for calculating a performer’s swing with missing onbeats.

69 In certain situations, the use of the master crotchet as the time reference may be preferable even when both onbeats are present, as in example a) This may well be the case when the master crotchet is unequivocally stable as in a click track.

129

The SLW model was developed to highlight and explain the visceral experience of

good time-feel and provide a simple set of tools for its research and wide

implementation. Example analyses of the SLW model are presented in Section 3 Case

Studies. From the perspective of a practitioner and a listener, this approach aims to make

definable those musical mechanisms that are consistently reproducible by artists and

recognized by the appreciative listener. The measure of worth of music analysis is the

extent to which it identifies and illuminates an actual musical experience, and its ability to

improve pedagogical practice and reapplication, towards which goals this paper is

offered.

130

3. Case Studies

Introduction

This section presents selected time-feel and M-Space analyses in a range of stylistic

contexts. The salient features of each case study vary, so relevant parts of the model, and

different analytical approaches are used to most clearly underline the musical

mechanisms in question. The selection has been made to provide an overview of some

time-feel characteristics and analytical approaches possible, but the overwhelming wealth

of possibilities and potential examples in this field prevents a comprehensive summary

within the scope of the submission. Extended research into each of these examples, or

indeed into the huge resource of recorded repertoire available, will uncover many more

time-feel features that can explain effective musical mechanisms otherwise filtered out by

standard notational analysis. In 4.1 (p 168-9) a list of omitted, and ongoing analyses by

the author is presented.

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3.1 59% Swing on Swing ‘42

Characteristic swing in Django Reinhardt’s Swing ‘42

Figure 3.1.1. A series of quavers from Reinhardt’s solo on Swing ‘42 (1:04-1:06). Solo extract

CD1.19.

A phrase from Django Reinhardts’s solo on Swing '42 (Reinhardt 1949) provides a

very clear case study for analysis of swing values (CD1.19 plays a short extract from the

solo for context, followed by just the phrase in Figure 3.1.1). Although short, this

continuous sequence of quavers is performed along one string and with alternating

down-up picking, so technical considerations are unlikely to influence execution

significantly. The passage also has unmistakable gypsy-jazz feel, so it is of value to

discover the contributing time-feel components. Sonogram, and half-speed onset analysis

of quaver swing was performed using the standard SLW model, as well as mean and

standard deviation values (Figure 3.1.2).

Figure 3.1.2. Swing values for each quaver pair in Reinhardt’s phrase.

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The mean swing comes out at around 59.3% with a standard deviation of just 1.6%.

At this fast tempo (≈204bpm) each crotchet lasts about 294ms, so there is a mere 50ms

separating offbeat placement for 50% and 66.6̄ % swing. Reinhardt manages to sit tightly

between these extremes, occupying a time zone certainly no greater than 30ms, even

allowing for measurement ambiguity. Can the listener hear the difference between

straight and triplet quavers at this tempo, let alone a value in between? It is easy to check

the significance of these results. CD1.20 includes the recorded phrase followed by midi

sequences of the same passage at 50%, 59%, 66.6̄ % and 75% with all articulation,

timbral and weighting effects removed (The same sequence of swing values is then

repeated with pitch elements removed, where differences between the swing levels

become yet more pronounced). The difference between 59% and 66.6̄ % is fairly subtle

but each swing value is clearly differentiable with attentive listening. Reinhardt’s quavers

are certainly not played straight or with triplet swing, but close to the centre point in-

between these values. The musical effect of this swing value (coupled with the simple

polymetry in the phrase) is at least as important as the note choices, but is lost to

standard notation. A transcription may provide the notes, but the musician is left to

absorb this equally important aspect unconsciously.

The relevance of the swing curve, the changing swing values through the phrase, is

miniscule and of little perceptual significance other than perhaps the introduction of an

extremely subtle human looseness. CD1.21 plays the phrase with 59% swing, followed by

a faithful rendering of each swing value (rounded to the nearest 1%). In a blind test, the

author can just distinguish the difference between the two with some consistency, mainly

due to the more even quaver ‘kick’ at the end of the phrase (CD1.22 plays the last two

quavers at 59% then 54% swing) but this 5% distinction is difficult to hear in isolation

even with directed attention.

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As this style is traditionally (but uncritically) associated with the triplet quaver, could

this lightness of swing be due to technical limitation? This notion can be dismissed given

examples of Reinhardt’s picking virtuosity in his recorded repertoire. And since 50%

swing is technically easier than a swung rhythm and the standard deviation is low, it must

be concluded that this swing value was, at whatever level of consciousness, intentional.

This case-study demonstrates a useful strategy of listening, objective analysis,

theoretical modeling, directed attention and aural testing training of the ‘theory-filtered’

results. Analysis divorced from music perception is of little value, but music technology

now allows a powerful tool to marry theoretical analysis with subjective experience.

Pedagogical tools such as SLW-coach allow the conscious practice of this, and any time-

feel, with real-time feedback. These unearthed time-feel characteristics may also be

actively directed in composition, and with great accuracy by the use of electronics.

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3.2 A Little Drag

Swing, latency and hierarchy in Michael Jackson’s The Way You Make Me Fee l

The documentary This Is It (2009) includes footage of Michael Jackson rehearsing

his track The Way You Make Me Feel (Jackson 1987) in preparation for the final

performances of his career. The song is characterised by an offbeat keyboard stab, and

Jackson’s direction to the music director and keyboardist Michael Bearden concerning

the placement of this offbeat provides a remarkable insight into his attention to time-feel

and means of communicating it to his band. The language employed is a neat illustration

of the separation of swing and latency outlined in the SLW model.

Although there are many duple rhythms, the tune has a predominately shuffle

rhythm, and the introduction, the focus of this study, is at a slow tempo (≈82bpm). For

these reasons it would be tempting to consider this offbeat to be a 3rd triplet quaver,

however for the purposes of this study it will describe it as a 2nd quaver with 66.6̄ %

swing. The distinction has little bearing on the substance of the analysis, but this choice

has been made to keep terminology consistent within the thesis and explanations as clear

as possible.

The editing of this rehearsal is possibly jumbled, it seems that the chronological

sequence of rehearsal events is in fact first a comment about feel (appearing 32:39-32:52

in the film, that will be called Extract A (CD1.23) here) followed by a rehearsal of the

tune’s introduction (appearing earlier in the film at 32:05 – 32:29) here referred to as

Extract B (CD1.25).

Extract A starts with Jackson, apparently dissatisfied with Bearden’s feel on the

keyboard part, instructing him to introduce a ‘little drag’ and play ‘a little more behind

the beat’, ‘like you’re dragging yourself out of bed’ – a particularly evocative description

of the experience of latency. Bearden is more concerned with his keyboard sound and

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Jackson is soon distracted by an incorrect chord change, but in the short time available

he demonstrates the desired placement three times (CD1.23). The placement of these

offbeats is calculated in relation to Jackson’s foot stamps and finger clicks which are

taken, with as much accuracy as possible in the limited conditions, as the master time-line

(Figure 3.2.1).

Figure 3.2.1 Jackson’s directed offbeat placements in Extract A with tempo and swing values

(CD1.23 and 1.24 plays Extract A, followed by aural testing of these values).

At a tempo of 89bpm there is approximately 6.7ms for each percentage point of

crotchet duration. So comparing the swing values to a baseline of the triplet quaver

discrepancies of 1.3̄ % (≈9ms), 3.3̄ % (≈22ms) and 5.3̄ % (≈44ms) are found. The

perception of these deviations may be checked in CD1.25. At 89bpm, three repetitions

of the swing values of 68%, 71% and 73% are played sequentially (panned right) against

the baseline 66.6̄ % triplet quaver (panned left) while a click (panned centre) marks the

pulses. In the author’s experience the panning effect is barely noticeable at 69% but

clearly identifiable at 71% and above.

The deviation of offbeats in Extract A has so far been described in terms of

increased swing value. Taken in isolation, a 71% offbeat placement, with no adjacent

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onbeats (as in this ska type rhythm), may be considered to be heavily swung or straight

with high latency70 so context must dictate the best approach. In consideration of the

baseline shuffle framework in the tune’s accompaniment, and in reference to Jackson’s

‘dragging’ implication, a good case can be made that these deviations are latency

mechanisms acting on 66.6̄ %. The musical implications are identical of course, but the

consideration of this distinction is an instructive exercise in the full understanding of

swing and latency in other musical examples. For comparison, Extract A is rewritten in

terms of a 66.6̄ % swing with latency as the deviating force (Figure 3.2.2). The formulas

for deriving swing (S) and latency (L) for the first crotchet are included for completeness.

Figure 3.2.2. Latency values, given 66.6̄ % swing from Extract A. Jackson’s vocalized keyboard

stabs are labeled (t1, t3, t5) whereas footstamps and finger clicks represent the master time-line

Taking this perspective of offbeat placements as latent triple-swung quavers, Extract

B (CD1.25) may be approached. This section, presumably occurring after Extract A, is a

rehearsal of the same section of music with Jackson, Bearden on keys and Jonathan

70 As well as corresponding values in between, see 2.12 p 127.

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Moffett on drums. The edit includes seven bars and 26 quavers so a much more useful

data set than in Extract A. An analysis is taken with Jackson’s foot stamps marking beats

1 and 3, and the drums indicating beat 2-4. Up-beat placement of the keys is determined

by the offset between these markers. Tempo, which is slightly loose (within a ≈3 bpm

range) is calculated, in all but one case, between the first beats of each bar. Figure 3.2.2

shows the quavers, with tempo fluctuations, offbeat placements and latency relative to a

66.6̄ % swing reference. All values are rounded to the nearest percentage, which is a fair

approximation given the perceptual limits and measurement ambiguities.

Figure 3.2.2. Latency transcription of Extract B, with all values rounded to the nearest percentage

(CD1.25).

For the first two and a half bars, the offbeat placement stays consistently around

the 69% mark, with a subtle 2% behind the beat feel. Jackson vocalizes this rhythm from

the third chord closely, aside from a quickly corrected anomaly in bar 2 beat 1. However,

Bearden stabs the third chord of bar 3 playfully, and remarkably, late (13% latency,

around 90ms), which causes Jackson to share a laugh with him, thereon the offbeat

placement settles in either side of the 73% offbeat placement mark (6% latency, around

40ms later than the triplet quaver). The musical context makes these stabs feel like late

swung quavers, rather than 4th semiquaver placements, even though the latter are closer

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from a standard notation perspective. From bar 4 Jackson seems content with the

dragged feel and sings the string-line over the accompaniment. CD1.26 is a 2-bar

sequence of the keyboard part played at 67%, 69%, 71%, 73% and then 75% offbeat

placement. The 70-73% range would appear to cover Jackson’s desired feel, a no-man’s

land (or obtusely written) area of standard notation, but a perceptual and effective

musical experience nonetheless.

The playfully late chord (bar 3, beat 3) seems to cause Moffett to drop back a little

tempo (2bpm). The analytical context is not adequately controlled, the discrepancy small

and the technological limitations far from ideal, so little should be read into the event.

However, if the drummer did in fact feel compelled to accommodate the significant

latency with a reduction in tempo, this would suggest that the governance of tempo is

not entirely his responsibility. Using the terminology of the SLW model (see Section 2.4,

p 100-5) this would imply that master timeline determination is not a monopoly but an

oligopoly: The latency of Bearden’s (implied) onbeat actually stretched the master time-

line, so Moffett did not accept total responsibility for its placement. In this example the

situation is tenuous, but the calculation may as well be completed: A 2% drop in tempo

was caused by a 13% latency, so for that bar, the hierarchical weighting of master time-

line determination would be calculated as Moffett: ≈85%, Bearden ≈15%.71

This case study highlights the potential value in the analysis of rehearsal footage (and

multitrack recordings) of particular artists. Research of this kind is a powerful tool in the

identification of the practitioner’s intention - and perception - of time-feel, and a valuable

contribution to our understanding of the mechanics of rhythmic expression.

71 In may also be the case, that there is a non-linear response to latency fluctuations with, for example, accommodation being made only above a specific threshold.

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3.3 Constant Friction

Swing friction in Chuck Berry’s Johnny B. Goode (1958)

In Time-feel the concept of swing friction was described as the differential of swing

values between individual performers (or groups of performers) (see 2.6, p 108-9). If the

swing friction is significantly large and consistently maintained, it forms a characteristic

of ensemble feel.

Chuck Berry’s Johnny B. Goode (Berry 1958) provides an instructive example of swing

friction. Berry, often considered the father of rock n’ roll, was instrumental in

‘straightening out’ the blues 12/8 shuffle rhythm into the archetypal electric guitar riff.

Johnny B. Goode features this ‘straight 8th’ guitar rhythm, as well as equally straight lead

playing juxtaposed with a stubbornly bouncy drum, bass and piano feel. Heavily swung

quaver values occur in the ride cymbal pattern, often near the 67% mark, a significant

deviation of over 52ms from the straight quaver at 170bpm. The guitar rhythm part

however remains resolutely straight rarely venturing beyond 52% swing. This already

large 15% discrepancy of swing value is exaggerated with the guitar part often sitting on

top of the beat (ranging between 0% and -4% latency) leading to a mean separation of

about 17% (≈60ms). The lead guitar is equally straight, although not pushed, and

occasionally falling behind the beat. Piano interjections are loose but quavers are

generally quite swung, mainly in the 60-67% range and repeated quaver triplets prevail.

The bass plays mainly crotchets, with the occasional quaver (usually ≈67%). A

representative extract from the track can be heard on CD1.27. Figure 3.3.1 (p 140) shows

a composite two bar template for the lead, rhythm, bass and drum parts, with time-feel

components added. There is a huge gap between the swing values of the guitars and bass

and drums. The vocal track tends to fall in between these two extremes. In order to hear

the effect of swing friction, CD1.28 contains electronic sequences of this section with

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varying time-feel values: 1) as from Figure 3.3.1 2) all instruments at 67% 3) all at 52% 4)

all at a middle ground of 60% and 5) back to the ‘true’ values for comparison.

Figure 3.3.1. Composite swing and latency values for guitars, bass and drums in Johnny B. Goode

(CD1.28).

The sequences have been rendered with MIDI instruments on purpose; although

the section would sound better with human performers, but the elimination of the

inflection they would inevitably provide allows focus on the power - and limitations - of

the SLW model. Mean values for swing and latency have been provided, but the standard

deviations of these values introduce the component of looseness or tightness, again

different between players. Weighting elements also occur, (the cymbal has a slight

emphasis on offbeat quavers for example,) with both mean and standard deviations).

CD1.29 plays the sequence first as Figure 3.3.1 then with swing, latency, weighting

standard deviations from Figure 3.3.2 (p 141) introduced, which add a clearly-defined

randomness to each of three time-feel elements, and instruments, individually. There is a

subtle but appreciable difference between the sequences; attention to the cymbal pattern,

for instance, will reveal a slight offbeat emphasis and looseness.

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Figure 3.3.2 Mean and standard deviation values of swing, latency and

weighting (measured as dB level) (CD1.29).

An averaging out of time-feel components over the entire track runs the risk of

over-generalization and may incorrectly group specific mechanisms that occur only

occasionally. There are for example, brief moments when the bass seems to join with the

rhythm guitar’s straight quavers. There is also the assumption, with a single matrix per

instrument, that all beats of the bar are the same, which ignores the emphasis on

crotchets 2 and 4 in the drums. Matrices could be provided for beats 1 and 2, and beats 3

and 4 separately, or even weighting at the crotchet level, for greater sophistication when

needed.

Despite these acknowledged limitations, the discretionary use of this type of analysis

allows for an instructive and parsimonious description of ensemble time-feel elements.

Lead Guitar Rhythm Guitar Bass Drums

µs= 51 ∂s=1.5

µl= 2 ∂l=

µw= -3 ∂w= 2

µs= 52 ∂s=1

µl= -3 ∂l= 1

µw= -3 ∂w= 2

µs= 67 ∂s=2

µl= 0 ∂l= 1

µw= 4 ∂w= 2

µs= 67 ∂s=2

µl= 0 ∂l= 0

µw= 2 ∂w= 1

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3.4 Swing Blocks

Swing values as arrangement in Lit t l e Wing (1967)

Jimi Hendrix’s Little Wing (Hendrix 1967) is a seminal piece in the rock guitar

repertoire, with its blending of country double-stops, jazz chord-melody technique,

unorthodox guitar voicings and a sophisticated rhythmic feel. Although often included as

part of the electric guitarist’s pedagogy, it’s apparently moderate technical demands

disguise sophisticated time-feel elements that are notoriously difficult to recreate

convincingly. The introduction (CD1.30) is performed solo (with bell tones later added at

the onbeats of each bar) with quite a loose tempo (in the 65 to 72 bpm range) so it is

reasonable to take the performance as the master time-line, which focuses on swing

rather latency elements. Semiquaver swing values vary widely with a broad spread across

the 44-72% range with a wide standard deviation, so is it fair to call the swing ‘loose’ and

leave it at that? Not at all, a closer look at the values (Figure 3.4.1 p 143), and more

informed listening, suggests controlled groupings of similar swing values, here broadly

categorized as Straight (<53%), Light (53-56%), Medium (56-63%) and Heavy (>63%).

These values are not implicated with tight rigidity, some fields fall on the cusp between

two categories, and occasionally a member of a group may fall out of the range.

Furthermore, there are some ambiguities in measurement when embellishments are used,

or in the absence of adjacent onbeats. However the general shifts between swing value

groups are very clear, attention to which reveals an effective structural mechanism at

work. CD1.31 demonstrates a one bar rhythmic pattern played in the four swing

categories: Straight (50%), Light (55%), Medium (62%) and Heavy (69%). These are all

performed first with sequences electronic clicks and then live guitar for comparison.

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Figure 3.4.1. Semiquaver and quaver swing analysis of Little Wing introduction (CD1.30). Broadly

defined swing categories are grouped together in discernible blocks.

Swing analysis has so far been made in reference to the semiquaver, but a quaver

swing analysis, the length discrepancy between adjacent quavers within a crotchet, has

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also been conducted (lower part of stave in Figure 3.4.1). These values are generally

straight which leaves little to say on the matter. Furthermore most swing values at the

quaver level may actually represent rubato elements (an accelerando would create a

higher swing calculation, for example). Nonetheless, bar 7 beats 3 and 4, provide an

opportunity to discuss the topic of swing values existing on multiple levels, or swing

telescopy. For clarity, a simplistic approximation of this passage is taken, with Pattern A

possessing swing values of 60% (quaver) and 50% (semiquavers) (Figure 3.4.2a). Pattern

B has 50% quaver and 60% semiquaver swing values (Figure 3.4.2b).

Figure 3.4.2. Pattern A contains two equal length quavers each containing a pair of 60% swung

semiquavers. Pattern B has a swing of 60% at the quaver level, with each quaver containing straight

semiquavers. Timings at 60bpm are shown, only the 3rd semiquaver is different between Pattern A and B,

but the musical effect is significantly different (CD1.32).

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Semiquaver placements of Pattern A and Pattern B would be identical, apart from

the 3rd semiquaver (timings for 60bpm are shown in the central portion of Figure 3.4.2).

The musical effect of this distinction is huge, CD1.32 plays Pattern A followed by

Pattern B. This is heard as an electronically positioned click followed by a guitar

performance). A multi-level swing analysis allows clear description of otherwise

unfathomable rhythmic patterns, and in the use of double-time and half-time rhythmic

devices. Further analyses by the author have revealed for example in the playing of Wes

Montgomery the use of swung quavers followed by the use of straight quavers, to

accommodate swung semiquavers.

The typical viewpoint of swing is as a stylistic characteristic, or representative of a

particular artist. Little Wing however provides a clear example of widely varied swing

values used as a structural mechanism in performance (a far more sophisticated and

intuitive version of the ‘swing-latin-swing’ format found in some jazz arrangements) and

explains part of the virtuosity in its execution and the challenge in its convincing

reproduction.

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3.5 Push-Pull

Expressive Latency Contours in Comfor tab ly Numb (1979)

The simplicity of arrangement in Confortably Numb (Pink Floyd 1979) affords ample

opportunity for Nick Mason and Dave Gilmour’s effective use of latency in order to

build and release tension. In conversation with the author, Mason has said his time-feel

(in particular his ‘behind the beat’ playing) is often brought up in seminars and although

aware of it through this kind of feedback, he claims it is something he doesn’t think

about actively, and this element of his style is an unconscious knack rather than a pre-

conceived goal. Can a time-feel analysis reveal anything of this ‘knack’? Analysed here

are the hit points of four drum fills in Comfortably Numb demonstrating the use of a

general latency curve. Drum hit-points tend to start ahead of the beat, fall progressively

behind towards the end of the barline, and then make up for any lost time with a

shortened last note, in short, a push-pull effect (Hrab 2009). In Time-feel the model of a

mutually negotiated time-line was introduced (2.4 p 100-5), where pulse is determined by,

usually hierarchical, musical agreement. Once this pulse is established however, it is

somewhat rigid and does not need marking out for every beat, the responsibility for

time-keeping is, ideally, deferred to each musician’s inner clocks; if the previous 32 bars

have lasted about 1800 ms, ceteris paribus, so will the next. This is demonstrated in a

typical jazz solo break, when the rhythm section stops dead for one or two bars allowing

the soloist free reign in that prescribed time duration. Often quavers, or other simple

subdivision are continued by the soloist, but all manner of liberties may be taken in this

time, with the assurance that the rest of the ensemble will re-enter at the same onbeat,

due to the prior establishment of tempo. In the situation of a drum solo, the precision of

the musician’s inner clock can really be tested, sometimes to breaking point, depending

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on the drummer’s penchant for obtuse rhythms, or indeed, cruelty to other band

members.

Comfortably Numb maintains a tempo of around 128bpm, it was after all, as Mason

explained to the author, Pink Floyd’s attempt to write a ‘disco tune’. This analysis focuses

on the last bar of four drum fills, occurring at the end of eight bar sections in the outro

guitar solo. The length of these bars as marked by Mason’s drums ranges between 1869

and 1905ms (to Mason’s recollection the track was not recorded to click), and in each

case they only vary by a few milliseconds from their respective preceding bars. Distinct

marker points of these four drum fills are analysed here (occurring around song position

5:02, 5:17, 5:32 and 5:47 in the original track, 0:32, 0:47, 0:52 and 1:07 on CD1.33.

CD1.34-37 plays each fill individually), and compared to the metronomically ‘correct’

positions derived from equal subdivisions of the available time length. This can be

considered as changing latency values, or indeed changing time lengths between note

onsets (‘note separation’). Swing values are not calculated; the changing latency limits

their usefulness and the listening experience of these moments is undoubtedly one of

stretching time before the looming downbeat, rather than a changing swing feel.

Latencies are calculated as percentages of the metronomic crotchet (calculated as four

equal divisions of the absolute bar length).

Figure 3.5.1 Four fills from Comfortably Numb compared. The horizontal time position for hit

points is shown for each fill relative to an equal division of the bar. The vertical position of each hit point

represents the degree of positive and negative latency. All fills share a subtle but effective push-pull effect

(CD1.34-37).

148

Figure 3.5.1 (p 147) displays for each fill the onsets of each marker relative to the

metric subdivision. The four crotchet fills are very similar but not precisely the same

length, and have been normalized so they can be compared on the same graph. The

horizontal position of each hit point shows its latency relative to an equal-division of the

bar. This latency (relative to the metronomically derived crotchet) is also represented

vertically, so that an overall shape may be observed. A progressive falling behind the beat

would be seen as a rising latency curve, with correspondingly increasing onset separation

(‘note length’), with the last being accommodatingly short. These four fills essentially

follow a similar pattern of note separation increasing towards the end of the bar and then

rapidly diminishing for the last marker (A flat contour would indicate similar, and an

upward slope increasing, note separation). The contours all show a slight push ahead,

followed by progressive fall behind, an implicit metronomic beat, before catching up to

the next barline with a curtailed last note separation: an expressive contour of latency.

The hit points of these four fills are sequenced in CD1.38, each preceded by its

metronomic counterpart for reference.

This analysis goes some way to explaining the mechanics behind this aspect of

Mason’s playing and the emotive effect it has on its listeners. It also raises the question

of the plasticity of the crotchet (and other subdivisions). Does a gentle latency contour

allow a greater range of values for aesthetically acceptable latency values? In other words

if latency is increased (or decreased) gradually, can extreme values be tolerated (and

enjoyed) more than random stabs of onsets either side of the beat? One can visualize

this idea as a fabric that can be stretched slowly, but will snap if pulled too quickly. A

further example of this concept is found in the next case study, 3.6 Temporal Plasticity in

the context of Pat Martino’s melodic interpretation.

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3.6 Temporal Plasticity

Pat Martino’s time-feel and M-Space mechanisms.

Pat Martino commands high status in the world of jazz, for his prodigious talents as

a teenage jazz phenomenon, numerous awards, recording output and his remarkable

recovery from extreme amnesia following a life-saving brain operation in 1980.

Martino has been particularly praised, from a young age, for his ability to execute

long seamless improvised lines with a rhythmic feel which somehow manages to be both

precise and relaxed (Fewell 1996). This particular time-feel is evident on Martino’s

performance on the jazz standard Just Friends from his debut album El Hombre (Martino

1962, extract CD1.39). The tune is performed at around 230bpm, ≈260ms per crotchet,

so a keen listener able to distinguish 13ms time differentials may perceive 5% slivers of

the beat. This would imply the ability to distinguish at best five levels of swing from

straight to 70%, and a similar number of values from -10% to +15% latency.

A swing and latency analysis of the melody and first improvised chorus reveals

swing values mainly in the 50-63% range and latency (where possible to derive) is almost

exclusively positive (behind the beat), largely occurring from 0 to +15% range. The

calculation of latency, not always possible, was made in reference to the drums, who

commanded a time-line monopoly for the purposes of this analysis.

A swing friction exists between the drums (with swing values of 62-74% and

Martino’s lighter 50-63% range). However, Martino’s significant latency, particularly on

his straighter quaver groups, brings his offbeat more in line with the absolute placement

of the drums’ second quaver. Latency is only written in when directly calculable, but

analysis (through extrapolation of note separation) suggests a general latency 0-15%

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range. An analysis of the solo break (CD1.40) illustrates this mechanism (Figure 3.5.1).

Figure 3.6.1 Transcription of the solo break from Just Friends (CD1.40) with swing and latency

values annotated.

A glance into the analytical process for this passage is provided in Figures 3.6.2 and

3.6.3 (p 151). The sonogram has been annotated with these swing values, as well as the

drums’ ride pattern when distinct. Discrepancies between the drummer’s, and Martino’s,

onbeats are analysed where possible, and latency calculated.

Figure 3.6.2 A sonogram analysis of bars 1-3 of Figure 3.6.1. Swing and latency values, where

clear are annotated.

151

Figure 3.6.3 Sonogram analysis of bars 4-6 with swing values for guitar solo and ride pattern

annotated. The swing friction between these values is softened by Martino’s significant latency.

In this passage Martino’s swing value stays mainly between 50-63%, hardly crossing

the drums approximate range of 62-70%.72 However, Martino’s significant latency

softens this friction. Since we are dealing with a 5% benchmark, these values can be

approximated for the purposes of simple illustration. Consider a constant drum swing

value of 65%, and Martino’s characteristic swing values of 50%, 55% and 60%. Figure

3.6.4 shows values of swing and latency that match the drummers offbeat placement of

65%. Although these time-feels have the same offbeat placement, they have significantly

different effects, even at this brisk tempo. CD1.41 renders electronically a phrase in time-

feels i-iv, to a 65% swing backing.

72 An enquiry into the whole solo, in fact, shows Martino’s tendency to swing more on melody notes and idiomatic bebop phrase endings than on long sustained lines.

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Figure 3.6.4 Four swing and latency combinations (i-iv) that share an offbeat placement of 65%

(CD1.41).

Time-feel ii (60% swing and 5% latency) perhaps comes closest to a generalization

of Martino’s feel, but it’s still not quite right. A closer listen to CD1.36 suggests that the

first, and the last quaver pairs are generally more swung than the central material, and

there are passages that are clearly straight. Limiting a reconstruction to the time-feel

values along the red line (the 65% offbeat ‘iso-contour’) the feel of the solo break may be

reconstructed more convincingly, as outlined in Figure 3.6.5 (p 153). The reconstruction

generalises some of the details of the passage (in particular the swung and late quaver pair

in bar 5, beat one) but much of the feel is captured, demonstrating the effectiveness of

this sophisticated time-feel mechanism (CD1.42).

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Figure 3.6.5 A generalized reconstruction of the solo break (top line) from Just Friends using time-

feel values (i-iv) from Figure 3.6.4, all sharing 65% absolute offbeat placement (CD1.42).

How much of this sort of sophistication is apparent to Martino? The author was

given, as composer for the soundtrack to a movie documentary of Martino’s life73, an

opportunity to shed some light on this question.

Martino’s writings on music are lucid and intriguing, particularly after his recovery

when his representations and illustrations of harmony and the fretboard took on both a

conceptual and aesthetic beauty (Martino 2004, Martino 2005) so illumination on the

topic seemed likely. But, as is often the case with skilled practitioners, Martino does not

have the same clarity when it comes to explaining his rhythmic approach, however

refined it seems to be from an analyst’s perspective.

This hand [indicates right hand] is aggressive, and it’s

thoughtless, this side of me, this hand, is the drop out.

This side [indicates left hand] is the graduate. […] This side

[indicating left hand] is Spock, this hand [indicates right

73 Martino: Unstrung (2007) funded by the Wellcome Trust and released on Ken Loach’s Sixteen Films.

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hand] if I have to be honest with you, is not even

Kirk…this side is the Klingon.

(Martino:Unstrung 2007)

So while Martino can write entire books on fretboard visualization, his rhythmic

approach is described as “thoughtless”, even though this feature of his playing is highly

sophisticated. Fortunately, Martino was very helpful to the author, participating in a

specifically designed recorded session in order to dig deeper into his time-feel and

rhythmic mechanisms.74

An arrangement of Martino’s ballad Welcome To a Prayer (Martino 2001) provided

a suitable candidate for analysis of his rhythmic flexibility at a ballad tempo, and as this

was a favoured track in gigs, his confidence with it was not in question. A metronomic

backing track of the 24-bar chorus was made with as little ‘leading’ rhythmic information

as possible so as not to impose any particular time-feel to his performance. The

recording was prepared with a visual and audio quaver-click track, in this way it was

possible to track with a high degree of accuracy the rhythmic placement of the

performance against the master time-line.

A Gibson ES-175 fitted with heavy-gauge strings and a Roland GI-20 midi guitar

system allowed a confident tablature transcription (as each string’s data was sent out of a

unique midi channel), another method for retrieving micro-timing data, and the real time

realization of visual representations of his improvisation using a purpose-built

MAX/MSP patch (Show of Hands). These visualizations were inspired by Martino’s

writings (Nature of the Guitar and Sacred Geometry) and allowed him to witness, in real-time,

his theoretical concepts.75

74 Footage from the recording session appears in the movie documentary Martino:Unstrung (2007 Sixteen Films) (DVD1 45:08-46:03). 75 The real-time translation of music improvisation to digital visuals is also explored in Rat Park Live and, in a reversed configuration, Microcosmos and Head Music.

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At the start of the session, in an effort to calibrate the system as much as possible,

Martino was requested to play onbeats to click for 32 bars to provide a helpful indication

of how much, or little, rhythmic characteristics may be attributed to random noise and

how much to purposeful expression. The results showed onbeats falling within 11ms

either side of the click, providing a useful guideline to extract relevant data.

Four takes of two choruses each were recorded, included here is a detailed analysis

of chorus one from the first take CD1.43 (DVD1 45:08-46:03).

The four page transcription of Martino’s first take includes four staves (Figure

3.6.6). The top stave displays the published lead sheet, and the second a transcription of

Martino’s interpretation. The third stave describes latency in reference to the crotchet (at

47.5pm), with values below the central line representing notes that fall behind the

notated rhythm, and above the line, rushing. When appropriate this stave switches to

note separation values (see 3.5 Push-Pull ). In these moments (Bar 11.2-12.4) more

meaningful information is gained from this method rather than referencing the master

time-line placement. The lowest stave shows a guitar tablature transcription, Martino’s

fretboard concepts being an important focus in his literature. (Martino 2005, Martino

2007).

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Figure 3.6.6.a Transcription of Martino’s performance on Welcome To a Prayer. The top stave

displays the original lead sheet, below which is a standard transcription of Martino’s performance. A

latency contour and guitar tablature make up the lower two staves (CD1.43).

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Figure 3.6.6.b Page two of Martino’s performance on Welcome To a Prayer. In bar 11 the latency

contour is transformed into a note separation curve to better accommodate the fluctuating rhythmic

material (CD1.43).

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Figure 3.6.6.c Page three of Martino’s performance on Welcome To a Prayer (CD1.43). Almost all

melody notes are delayed.

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Figure 3.6.6.d Page four of Martino’s performance on Welcome To a Prayer (CD1.43). A rare (and

minimally) anticipated melody note occurs in bar 21.

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Between the Lead Sheet and Take One staves, there are a series of arrows that signal,

by their angles, the displacement of the rendered to the written melody. These are

divided into primary and auxiliary melody notes - the distinction being based somewhat

subjectively on note-length and melodic emphasis. What is immediately apparent is that

virtually all the melody notes are delayed, with only two rhythmically anticipated melody

notes, (bar 5 and 11 and these are auxiliary melody notes and only slightly early). In fact

the key melody notes are so delayed they are played, with considerable dissonance, on

the next bar’s harmony (See bars 4, 17, 21 in Figures 3.6.6.a, c and d respectively).

Melodic interpretation is a key component of jazz technique (Berliner 1994, p 187

and Crook 1999, p 119) and can offer as much improvisational expression as a ‘free’

solo. An illuminating way to reveal the degree of melodic transformation is by

superimposing the written melody on top of the recorded solo. In this way the dialogue

the performer holds with the melodic reference is revealed (CD1.44).

What may also be heard is that the delay in the melody notes tends to be

compensated in several ways, as if their postponement obliges a corresponding emphasis.

These late primary notes are often repeated (bars 2, 3, 6, 11, 13, 14, 15, 22 and 23),

played with greater intensity (bars 1, 9 and 12) or played with rhythmic precision on

identifiable subdivisions (twice in bar 3 and also in 6, 17, 19 and 23).

A musical effect is created by the varied delay of melody notes, and an expressive

contour may be traced to this end. This allows the observation of a hidden but powerful

musical mechanism: melodic shadowing76. Distance from melody (in this case rhythmic) may

change over time and this creates the opportunity for the jazz performer to impart

improvisational expression in the context of melodic interpretation. Figure 3.6.7 (p 161)

shows an analysis of the first eight bars of the performance and traces a contour

76 This concept of dynamic melodic shadowing is explored technologically in Strike, Omnia and 11th Light from the submitted portfolio.

161

describing the extent to which each melody note is displaced. The vertical height of the

blue contour indicates the distance that the melody note at that original bar and beat

position has been displaced. When a melody note is re-attacked, this is shown by

different shades of blue (as indicated on the legend), at progressively higher positions.

Figure 3.6.7 Melodic displacement expressive contour for the first eight bars of Welcome To a

Prayer, indicating the extent to which melody notes are displaced in the interpretation (melodic shadowing).

Figure 3.6.7 demonstrates the extent to which the melody is rhythmically displaced,

and since this changes over time, an expressive contour emerges. However, displacement

is not the only transformative mechanism employed by Martino. Insertion of approach

notes, interjected phrases, melody note repetition, articulation and time-feel mechanisms

all pull away from the written melodies by differing amounts in various musical

dimensions. The concept of M-Space (1.5 p 25-55) describes improvisation as the serial

procession of related phrases through multi-dimensional musical space, with dynamic

control of the degree of proximity between any new phrase and a dwindling memory of

preceding material. The concept of melodic shadowing however introduces the idea of

melodic interpretation as the improvisational control of musical proximity relative to a

pre-existing, if unheard, set of phrases, a tacit parallel improvisation. Figure 3.6.8

illustrates the first five phrase units from Welcome To A Prayer as variously proximate

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phrases to the ‘platonic ideal’ fixed melody units, with a changing set of salient

transformative mechanisms indicated.

Figure 3.6.8 An M-Space illustration of melodic shadowing for the first eight bars of Welcome To a

Prayer. Melodic interpretation is seen as the improvised transformation, along multiple dimensions, of the

‘fixed’ musical objects (A-E). The resulting interpretations (A’-E’) lie in varied proximal relationship with

their referenced, but unheard, counterparts (CD1.44).

The expression inherent in melodic interpretation is evidenced by listening to the

improvisation against the referenced melody (CD1.44) but what can be said of time-feel

in this performance? The slow tempo, variation of subdivision implications and stylistic

feel of Martino’s playing does not allow much value to come from a swing analysis. An

enquiry into latency should also be approached with care, and although recorded to click,

the rhythmic feel is in general nebular and without the sense of friction against a rigid

time-line usually associated with this mechanism. Indeed, the transcription of the

intended rhythmic placements of some notes is inevitably subjective, which limits

commentary on their latency. In the analysis of such musical nuances as micro-timing,

one must be constantly vigilant against pareidolia, the tendency to see patterns and

meaning where none exist. Awareness of perceptual limits, and blind aural testing of the

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hypothesis-filtered results can help prevent these Type I false positive errors.

Furthermore an enamoured focus on just time-feel runs the risk of missing other salient

characteristics contributing to musical expression. Again, the use of technology to strip

and recombine component musical parameters in order to understand further their role

in the listening experience is a valuable exercise. There are however two passages from

this excerpt that are clearly instructive and should be discussed. The first is the initial

phrase (Bar 0.2-1.2 in Figure 3.6.9 and CD1.45) in which the melody is pushed and

pulled micro-rhythmically either side of the metric quaver length. The second, a passage

where a series of notes bear little relevance to the master time-line, other than some

anchor points, and are best notated in terms of changing duration, rather than their

metric placement (Bar 11.3-12.4 in Figure 3.6.10 (p 165) CD1.46).

Figure 3.6.9 Latency contour of the first phrase from Welcome To a Prayer (CD1.45). The melody is

micro-rhythmically stretched to produce a hyperlatent last note.

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Figure 3.6.9 analyses the first phrase in terms of latency to the master time-line. At

47.5bpm, each percentage of latency is more than 12ms and perceptible, anything above

3% are clearly significant and beyond any reasonable error margin. The final G is played

over 250ms late, and could have been notated as its nearest major subdivision, the 2nd

semiquaver of bar 1. If there were no preceding quavers, this would clearly be the most

sensible transcription, however the elasticity of quavers 1-5, and the rising contour

implicates the G as a very late, or hyperlatent, downbeat rather than a semiquaver

displacement. A listen to the recording with, and without the referenced lead sheet

superimposed, seems to support this position (CD1.45). The fact that the latency

contour is smooth and in one down-up motion (lower diagram, Figure 3.6.9, p 163)

implies that the melody is micro-rhythmically stretched, rather than metrically displaced

or just played with loose, or inaccurate, time.

The concept of differential elasticity, the contoured micro-rhythmic pushing and pulling

of a phrase, is exploited to a much further extent in Bars 11.2-12.4 (CD1.46). The series

of notes is stretched with little metric relevance rendering a standard notation

transcription rather clumsy and inaccurate. The phrase can be seen as having three main

anchor points relative to the written melody, the initial note (F# which is also used as a

pivot note), the Bb at the beginning of bar 12 (which creates the b9 interval with the A7

harmony) and the A at the end of bar 12 (which is resolved two octaves lower and re-

resolved in the next bar, this time with the preceding B-natural from the melody). These

three notes form the melodic arch of the phrase and occur reasonably close to their lead-

sheet counterparts. There are also subsidiary skeletal melodic reference points as

indicated in Figure 3.6.10 (p 165).

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Figure 3.6.10 The melody in bars 11-13 is used as a skeletal structure to frame a series of notes

with little metric relevance other than stretching time to hit the middle and endpoint anchors. The lower

diagram tracks the interaction of the melodic register and metric length contours (CD1.46).

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Plotting onset separation for the phrase (which is equivalent to note duration given

the assumption of legato playing), a series of notes is observed that is used to fill time to

hit the key anchor points circled. Although these notes are very loosely in the semiquaver

range, they do not have a metric sense, rather they are variably stretched in order to

target the melody anchor points. Since the relevance to orderly subdivisions is dissolved,

so too is the sense of latency as defined in Time-feel (Section 2). This passage cannot be

explained satisfactorily by polyrhythms either, as the note durations are not of

sufficiently regular duration. Although the relationship to the master time-line is

momentarily abandoned, this is not an example of traditional rubato; the accompaniment

is completely rigid and unyielding, and Martino’s sense of form is clearly retained,

marking key melodic notes and re-joining the melody clearly in bar 13. Whereas rubato

concerns ‘stolen’ time, this mechanism only allows lending and borrowing of time, and

all debts must be repaid in full. The best definition is of a variable tempo

superimposition, like a tape speed being variably and purposefully manipulated in order

to target hit points in absolute time. This idea of tempo superimposition, be it a fixed

tempo (in a simple or complex ratio with the master time-line) or variably distorted,

explains much of the latency curves found in Figures 3.6.6a-d (p 156-9).77 A slower

tempo superimposition on to a master time-line causes a sloped latency curve, while a

varying tempo causes a latency curve as identified in Figure 3.6.9 (p 164).

Figure 3.6.10 (p 165) describes an expressive contour of onset separation (note

duration). To illustrate the idea of simultaneous expressive contours (see 1.6, p 56-68), a

curve of melodic register has been superimposed on the lower diagram. These two

contours are independent (as defined in Figure 2.5.4, p 64) and can theoretically move

freely against each other, however the expressive effect of these two contours moving

77 This concept correlates with Benadon’s description of shift (fixed tempo superimposition) and flux (variable tempo superimposition) in reference to early jazz (Benadon 2009).

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variously together and apart, is clear (see also Figure 2.4.7 (p 104) for a similar example),

but only explicitly defined with this type of analysis.

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4. Coda

4.1 Ongoing Theoretical Research

Case Studies presented a selection of time-feel and M-Space analyses. Omitted and

ongoing research includes a survey of ensemble mechanics of swing, latency and

weighting in the James Brown rhythm section, the identification of expressive latency in

Herbie Hancock’s Watermelon Man (Hancock 1962), differential elasticity in Bob Marley’s

Is This Love? (Marley 1978), swing quotation in Wes Montgomery’s No Blues

(Montgomery 1965), the use of latency in David Gilmour’s guitar style, a more complete

study into M-Space mechanisms in all the takes of Welcome To a Prayer (Martino 2001) and

a complete time-feel study of Stevie Wonder’s Superstition (Wonder 1972). Time-feel is an

effort to understand and explain sub-notational expression in terms of rhythm, but

research into microtones (the vertical dimension of Wishart’s lattice) has also been

undertaken by the author. This includes a categorisation and identification of blues

microtones in the blues guitar styles, as well as the construction of music software

(Mermikides 2005, 2007) to explore, identify and aurally test a catalogue of microtones

and tuning systems. Progress has also been made along the third dimension of Wishart’s

lattice, in the exploration of the expressive use of timbre in rock and jazz guitar

(Mermikides 2006). Ongoing research with time-feel suggests an important interaction

with articulation in the creation of good ‘feel’ so there exists symbiosis in the parallel

development of these fields. The addition of continuous note duration values for onbeat

and off-beat (so that 100% denotes legato, and lower values, staccato performance) to

the SLW model, would provide a simple conceptual foundation from which to make in-

roads into this field.

The ethos behind all the theoretical work in this submission is to provide a

supporting mechanism to practical and creative output in performance and composition,

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and not an end in itself. Ongoing and upcoming compositional and performance projects

employing the concepts presented in this collection of theoretical writings are presented

in the conclusion of Changes Over Time: Practice and a reflection on their outcomes will

undoubtedly enrich the theoretical foundation for future works and musical experience.

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4.2 Presentations

The theoretical research presented in this collection of writings has been

disseminated as lectures, seminars and papers at a number of conferences and research

events. Below is a selected list of relevant research output.

Temporal Plasticity (2010)

Time-feel studies in Pat Martino’s playing. Presentation 2 February 2010 Postgraduate Research Day, University of Surrey.

On Composing (2010)

Article in Computer Music Magazine Special: Making it February 2010. 5,000+ readership.

Eclipse Masterclass (2009)

Presentation on the practice of live interactive electronics. 2 November 2009 Trinity Church, Boston MA to Berklee College of Music students and faculty, and public.

New Works for Electric Cello (2008) Presentation of new works, Omnia and Event Horizon. 9 June 2008 Postgraduate Research Day, University of Surrey.

Sacred Geometry (2008)

An analysis of Pat Martino’s guitar improvisations on Welcome To A Prayer. 4 January 2008. Lecture. Royal Musical Association Conference, University of Surrey.

Possible Infinities (2007)

Lecture presentation exploring the electronic music and the contemporary realization of Omaggio and A Pierre for the Luigi Nono South Bank Festival. 23 November 20007 Public lecture. York Gate Gallery, Royal Academy of Music.

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The Science and Art of Tuning (2007)

Lecture presentation on the science and art of tuning, and intonation software Horatio.

7 February 2007 Public lecture at York Gate Gallery, Royal Academy of Music.

The Singing Bacteria (2007)

Paper outlining the composition of Microcosmos with collaborators Steve Downer (cameraman) and microbiologist Dr. Simon Park. 3 June 2007 Public lecture. York Gate Gallery, Royal Academy of Music. 1 September 2007 Public lecture. Digiville Event, Brighton. 26 November 2008 Public lecture in the Dana Centre’s Infective Art event, Science Museum.

Playing with Technology (2006)

Paper on the past, present and future of electroacoustic experimentalism.

9 November 2006 Public lecture given at the Royal Academy of Music.

Musical Being (2006) Lecture presentation on the translation of scientific phenomena to musical composition. 12 August 2006 Oulu Music Festival, Finland. The Architects of Noise (2006)

Paper on expression through timbral modulation in electric guitar music. 23 June 2006 Academic lecture. Postgraduate Research Day, University of Surrey.

Musical Landscape (2005)

Paper examining Villa Lobos’s millimetrization technique and the electronic development of the technique. 5 March 2005 Presented at York Gate Gallery, Royal Academy of Music as part of the Composer:Performer Exchange series.

That Swing (2004)

Paper presenting the SLW model of time-feel in jazz. 13 December 2005 Lecture presentation. Postgraduate Research day, University of Surrey.

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4.3 Glossary

There are several terms borrowed from the jazz vernacular that are used very

specifically within this submission. These, together with new terms coined by the author,

are defined below.

Cell. A short phrase or melodic structure amenable to transformation and recombination

into larger phrase units.

Chains of thought. An improvisational concept whereby every new phrase relates to a

preceding one through the maintenance of a variable set of musical parameters.

Consychronous. A description for parameters that both occur simultaneously and

continuously.

Dismodos, dismodal. An improvisational or compositional passage characterised by

changing scale or mode implications, while other parameters (e.g. tonal centre) remain

fixed.

Dispaesis, dispaesic. An improvisational or compositional passage characterised by changing

intensity or volume, while other parameters remain fixed.

Distimbre, distimbral. An improvisational or compositional passage characterised by

changing timbre, while other parameters remain fixed.

Downbeat. The first onbeat in each bar.

Ensemble Swing. A consolidated measure of an ensemble’s swing values.

Expressive Contour. A curve representing the gestural control of a musical parameter

through traditional performance, or electronic manipulation.

Field. A set of identifiably related phrases.

Field Series. An improvisation involved the repetition of reasonably related phrases,

followed by a leap to another area of M-Space to repeat a similar process.

Hyperlatency, hyperlatent. The particular case when a rhythmic placement retains the sense

of being an onbeat despite its absolute position being near another significant subdivision.

Most often found in the 15-25% latency range.

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Isokinetos, isokinetic. An improvisational or compositional passage characterised by the

maintenance of a specific expressive contour over multiple musical dimensions.

Isologos, isologic. An improvisational or compositional passage characterised by the

heterogenous use of a single broad concept, number system etc.

Isomelos, isomelic. An improvisational or compositional passage characterised by the fixing

of an order of melodic notes, while allowing other parameters to change.

Isomodos, isomodal. An improvisational or compositional passage characterised by the

fixing of a scale or mode implication, while allowing other parameters to change.

Isopaesis, isopaesic. An improvisational or compositional passage characterised by the fixing

of intensity or volume, while allowing other parameters to change.

Isotimbre, isotimbral. An improvisational or compositional passage characterised by the

repeated use of a particular timbre, while allowing other parameters to change.

Isoplacement. An improvisational or compositional passage characterised by the repeated

use of a particular metric placement, while allowing other parameters to change.

Isorhytmos, isorhytmic. An improvisational or compositional passage characterised by the

repeated use of a particular rhythmic pattern, while allowing other parameters to change.

Latency. An expressive mechanism by which an individual’s performance is micro-

rhythmically displaced against a mutually negotiated master time-line. More specifically the

percentile displacement of the performer’s onbeat relative to the placement and duration

of the master pulse.

Limit-and-variation. An improvisational strategy where several musical features or topics in a

phrase are fixed, allowing others to be altered expressively.

Master time-line. A reference pulse, achieved through the (often hierarchical) negotiation of

pulse.

Master pulse. The beat points of the master time-line.

Meta-contour. A curve representing the consolidation of multiple expressive contours.

M-Space. The concept of multi-dimensional musical space.

M-Sphere. A sphere of specified radius (i.e. musical proximity) in M-Space.

Merged. An improvisation where phrases drift seamlessly between fields.

Nuclear. An improvisation characterised by a series of closely related phrases.

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Offbeat. The second subdivision of a given pulse (i.e. ‘1 and’, ‘2 and’ etc. in the case of a

crotchet pulse, and ‘1 e and uh’ in reference to a quaver pulse.

Offbeat placement. The swing of an individual’s offbeat placement relative to the master

crotchet (in the case of quaver swing). Simply calculated as the individual’s latency added

to swing. For example a 10% latency, 55% swing has an offbeat placement of 65%.

Onbeat. On the beat, the beginning of each pulse. The first onbeat of the bar is the

downbeat, and between each onbeat lies an offbeat.

Phrase. An identifiable musical unit that has a, at least momentary, sense of autonomy.

Phrases may exist in hierarchical relationships, and may be edited, spiced, recombined

and otherwise transformed into new phrases.

Proximity. In the context of M-Space, the distance between musical objects along a

variable amount of transformative dimensions.

Seed. A musical phrase or idea used as a starting point for multiple ensuing phrases.

Slack theory. The aesthetic concept that the maintenance, or relaxation, of a set of

expressive contours, allows more flexibility to others.

Straight-and-late. A series of quavers with swing values near 50%, and a positive latency

value, resulting in an offbeat placement greater than 50%.

Swing. The relative offset of the offbeat in reference to the duration between.

Swung. A series of quavers (or other subdivision) with a swing value perceptively greater

than 50%.

Swing friction. The differential of swing values between performers and or groups of

performers.

Temporal plasticity. A general term regarding the extensive use of flexible micro-timing

mechanisms against a relatively stable master time-line.

Time-feel. A general term describing expressive micro-timing mechanisms including swing,

latency and weighting.

Topic. A musical feature or transformative mechanism that may be addressed during the

course of an improvisation.

Transitional phrase. A phrase that exists within two or more fields.

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Unbounded. An improvisation characterised by a series of unrelated, or distantly related

phrases.

Villa-Lobos lattice. A quantized pitch (horizontal axis) vs. metric rhythm (vertical axis)

expressive contour derived from a physical shape.

Wishart’s lattice. A conception of music wherein - for notational convenience - discrete

and discontinuous values are attributed to pitch, rhythm and timbre.

Weighting. The relative accent of the offbeat in relation to the onbeat.

Xenochrony, xenochronous. The, most often technological, juxtaposition of foreign tempi.

Zappa’s Glue. A term for the structural mechanisms that form a perceptual relationship

between phrases, or musical objects.

Zappa’s Noodles. A general term for a series of phrases, or musical objects, in an

unintelligible and unsatisfying musical relationship.

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4.4 References

Books and Articles

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Music. _________ (2000) Inside Improvisation Series: Vol. 5 Thesaurus of Intervallic Melodies. Rottenburg: Advance Music. _________ (2002) Inside Improvisation Series: Vol. 6 Developing a Jazz Language. Rottenburg: Advance Music. _________ (2004) Inside Improvisation Series: Vol. 7 Hexatonics. Rottenburg: Advance Music. Bilmes, J. (1993) Timing is of the Essence: Perceptual and Computational Techniques for Representing, Learning, and Reproducing Expressive Timing in Percussive Rhythm. Boston: MIT Press. Berio, L. (2000) Two Interviews. London: Marion Boyars Publishers Ltd. Bowman, W. (1988) Doctoral Research in Jazz Pedagogy: An Overview in Council for Research in Music Education Bulletin, no. 96, 47-76. Borges, J. L. (2000) The Library of Babel. New Hamphire: David R. Godine. Borgo, D. (2005) Sync or Swarm: Improvising Music in a Complex Age. London and New York: Continuum. Butterfield, M. H. (2006) The Power of Anacrusis: Engendered Feelings in Groove-Based Musics in Music Theory Online Volume 12.4, May 2006. Society for Music Theory. Byrt, J. (2007) Elements of Rhythmic Inequality in the Arias of Alessandro Scarlatti and Handel in Early Music 35.4, 609-26. Chadabe, J. (1997) Electric Sound: The Past and Promise of Electronic Music. Upper Saddle River, New Jersey: Prentice Hall.

Cholakis, E. (1992) DNA Grooves. Music Software. WC Music Research and Numerical Sound.

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Online Resources

Cholakis, E. (1995) Jazz Swing Drummers Groove Analysis. [Online] Numerical Sound. Available: http://www.numericalsound.com[Accessed 6 February 2010]. Frey, D. (2010) New York Skyline. [Online] Red Deer Public Library. Available: http://www.villalobos.ca/ny-skyline [Accessed 6 February 2010]. Gustavsen, T. (1999) The Dialectical Eroticism of Improvisation [Online]. English version, unpublished. Available: http://www.tordg.no/dialectics_of_improvisation.pdf [Accessed 2 February 2010]. Hrab, G. (2010) Geologic Podcast: Episode 172 [Online]. Available: http://www.geologicpodcast.com/rss [Accessed 2 August 2010]. Machover, T. (1992) Hyperinstruments - A Progress Report 1987 – 1991. [Online] MIT Media Laboratory, January 1992. Available: http://opera.media.mit.edu/hyper_rprt.pdf [Accessed 7 January 2010]. Machover, T. (2004) Shaping Minds Musically [Online] BT Technology Journal, 22.4, 171-9. Available: http://www.media.mit.edu/hyperins/articles/shapingminds.pdf [Accessed 10 October 2009].

Machover, T. (2006) Dreaming a New Music [Online] Available: http://opera.media.mit.edu/articles/dreaming09_2006.pdf [Accessed 2 January 2010].

Machover, T. (2010) On Future Performance [Online] The New York Times, 13 January 2010. Available: http://opinionator.blogs.nytimes.com/2010/01/13/on-future-performance/ [Accessed 6 February 2010].

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Unpublished Materials

Abel, R. (1996) An Investigation into the Operation of Swing in Jazz. Unpublished undergraduate project. University of Cambridge. Fewell, G. (1996) Pat Martino’s Linear Expression presented at Berklee College of Music, Boston, USA, 2 February, 1996. Mahdi, R. (1993) Improvisation Workshop. Berklee College of Music, 3 October 1993. Mermikides, M. (2005) That Swing. Lecture presentation, Postgraduate Research Day University of Surrey, 13 December 2005. ____________ (2006) The Architects of Noise. Lecture presentation, Postgraduate Research Day, University of Surrey, 23 June 2006. ____________ (2007) The Science and Art of Tuning. Lecture presentation, Royal Academy of Music, 7 February 2007. ____________ (2008) Sacred Geometry. Lecture presentation, Royal Musical Association, University of Surrey, 4 January 2008. ____________ (2010) Temporal Plasticity. Lecture presentation, Postgraduate Research Day, University of Surrey, 2 February 2010. Silver, H. (1994) Masterclass. Berklee College of Music, 10 May 1994.

Discography, Videography and Broadcasts

Aphex Twin (1992) Digeridoo. EP. UK: Outer Rhythm. Bailey, D. (1975) The Advocate. Album. UK: Tzadik. Berry, C. (1958) Chuck Berry is on Top. Album. USA: Chess. Brown, J. (1968) Say It Loud – I’m Black and I’m Proud. Album. USA: King. Coltrane, J. (1965) A Love Supreme. Album. USA: Impulse!. Hancock, H. (1962) Takin’ Off. Album. USA: Blue Note. Hendrix, J. (1967) Axis: Bold As Love. Album. UK: Olympic. Holdsworth, A. (1985) Metal Fatigue. Album. USA: Enigma.

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Jackson, M. (1987) Bad. USA: Epic. King, B.B. (2006) BB King Jamming. USA: Synergie. Keneally, M. (2007) Hat. USA: Exowax. Krantz, W. (1993) Long To Be Loose. USA: Enja. Marley, B. (1978) Kaya. USA: Tuff Gong Island. Martino, P. (1967) El Hombre. Album. USA: Prestige. Martino, P. (2001) Live at Yoshi’s. Album. USA: Blue Note.

Martino: Unstrung. (2007) Film. Directed by Ian Knox. UK: Sixteen Films. Mermikides, M. (2008) Standard Deviations. UK: Lucid Music. Metheny, P. (1976) Bright Sized Life. Album. USA: ECM. Montgomery, W. (1965) Smokin’ At The Half-Note. Album. USA: Universal. Pink Floyd. (1979) The Wall. Album. UK: Harvest/EMI. Reinhardt, D. (1949) Djangology. Album. UK: Recall. Scofield, J. (1998) A Go Go. Album. USA: Avatar. Smith, J. (1958) The Sermon! Album. USA: Blue Note. The Real Frank Zappa Show. (1989) Radio Broadcast. Frank Zappa and Michael Oliver. BBC Radio 3. Broadcast 1 September 1989. This is It. (2009) Film. Directed by Kenny Ortega. USA: Columbia.

Wonder, S. (1972) Talking Book. Album. USA: Tarnia.