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Microtiming deviations in groove ANU
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DECLARATION, The thesis and computational model comprising this submission are my. original work All sources of data and other information are. acknowledged in the list of references,Andrew McGuiness. April 2005,Physical creativity, I was originally drawn to study fine motor control in musical performance because of. a phenomenon I have experienced when performing at the piano I found that in. situations where a musical piece of Western notated art music in this case was. sufficiently well known and any technical difficulties sufficiently overcome the most. finely tuned and expressive execution of short passages was always unplanned and. in fact not the execution which I had practised I discovered that I could at times allow. my hands to take over the performance and that the result would be more subtle and. musically successful than I had consciously anticipated In light of the theory. described in this thesis it seems possible that those short passages were in fact. under the control of open loop motor programs The schemata for the motor. programs appear to have been dynamically generated and to have taken into. account both the musical structure of the piece as laid out in the notation and. ephemeral details of the current performance, According to the theory outlined in this thesis a series of open loop motor programs. triggered at intervals within the macroperiod control timing at finer temporal levels. than the tactus The short passages I played seemed outside of cognitive control and. yet took account of the musical context at different levels If they were in fact under. open loop motor program control it would seem that the mechanism for generating. the schemata for the motor programs is capable of dynamically integrating input and. making creative decisions a kind of physical creativity. I gratefully acknowledge the support of the MARCS Auditory Laboratories and of the. Centre for New Media Studies at the Australian National University. Microtiming deviations in groove 1,DECLARATION 2,List of figures 7.
List of equations 8,List of tables 9,List of Appendices 9. Extended Abstract 11,Overview 11,What is groove microtiming 11. A new theory of rhythmic timing and entrainment 12. Original contribution 13,The Covert Clock Theory 13. The VROOGE model 14, Chapter 1 Psychological and musicological approaches to groove. microtiming 15,1 1 Defining terms 15,1 1 1 Pulse beat tactus tatum 16.
1 1 2 Meter 16,1 1 3 Rhythm 17,1 1 4 Groove 17, Chapter 2 Review of theories of meter and entrainment 19. 2 1 The concept of an internal clock 19,2 1 1 The tempo range of rhythmic behaviour 20. 2 1 2 Spontaneous tempo and the referent time level 20. 2 2 A multiple clock model 23,2 3 Hierarchical clocks 25. 2 3 1 Evidence for an hierarchical clock system 25. 2 3 2 Nested clocks and better timing performance 30. 2 4 Timing control below the level of the fastest central clock 34. 2 4 1 Motor programs 34,2 4 2 Motor program schema 35. 2 4 3 Evidence for a different mechanism for timing below the tactus. 2 4 4 Functional anticipation 38, 2 4 5 Possible functions of microtiming deviations in a musical context.
Chapter 3 The macroperiod in groove music and the psychological. present 43, 3 1 Hierarchical planning of movement sequences 43. 3 1 1 Hierarchical meter and timing 44,3 2 The psychological present 44. 3 2 1 Rhythm the body and the psychological present 46. 3 3 Period segmentation in various groove like musics 46. 3 3 1 Cross meters 47, 3 3 2 Asymmetrical bisection of the macroperiod 48. 3 3 3 Bell patterns in Central and West African drumming and other. reference patterns 50,3 3 4 The clav pattern in Afro Cuban music 51. 3 3 5 The tal in North Indian music 51,3 3 6 Duration of the macroperiod interval 52.
3 4 Summary 53,Chapter 4 The Covert Clock Theory 55. 4 1 Review of studies of microtiming deviation in groove music 55. 4 1 1 Consistency of microtiming deviation patterns 55. 4 1 2 Recreating and applying microtiming deviation patterns 56. 4 2 The Covert Clock theory of microtiming deviations 56. 4 2 1 Contrasting properties of cross rhythms and hierachical meter 58. 4 2 2 Some predictions of the Covert Clock Theory 59. Chapter 5 An examination of the Covert Clock Theory using. microtiming data analysis 61, 5 1 Extraction of microtiming data and general approach to analysis 61. 5 2 The Funky Drummer 62,5 2 1 Data acquisition and treatment 63. 5 2 2 Analysis 66,5 2 3 Swing 68, 5 2 4 Application of the Covert Clock Theory to The Funky Drummer. deviations 69,5 3 Tumba Francesca 73,5 3 1 Data acquisition and treatment 73.
5 3 2 Application of the Covert Clock Theory to Tumba Francesca. deviations 74,5 4 O Grande Amor 84,5 5 Summary 85, Chapter 6 Design and implementation of the VROOGE model of. entrainment and microtiming deviation 87,6 1 Outline of the VROOGE model 87. 6 2 Existing models of microtiming deviations 88,6 2 1 Groove templates 88. 6 2 2 Bilmes s approach 89, 6 2 3 Simulating Expressive Timing By Modulated Movements. Waadeland s model 92,6 3 Development of the VROOGE model 98.
6 3 1 The basic model for repetitive timing and correction processes98. 6 3 2 The introduction of correction processes to the basic two. process model 99,6 3 3 Pressing s Referential Behaviour Theory 99. 6 3 4 Simultaneous phase and period correction 102. 6 3 5 Period correction triggered by different conditions from phase. correction 102, 6 3 6 Separating phase and period correction processes 103. 6 3 7 First and second order correction processes 106. 6 3 8 Entrainment latency 110, 6 3 9 Adding microtiming deviations to the model 110. 6 3 10 Two different approaches to generating microtiming deviations. Chapter 7 The VROOGE software 113,7 1 Entrainment 113. 7 2 Sequence 114,7 3 Microtiming deviations 114,7 4 User set parameters 114.
7 5 Evaluation of the VROOGE software 114,Chapter 8 Summary and conclusion 118. 8 1 Impetus for research on microtiming and groove 118. 8 2 Summary of achievements 118, 8 2 1 Clarification of the relationship between entrainment and. planning processes in rhythm 118, 8 2 2 Integration of entrainment processes with microtiming deviation. processes 119,8 3 Outstanding issues for the current topic 119. 8 4 Broader issues to be addressed 120,8 4 1 Issues for psychological research 120.
8 4 2 Issues for musicological research 121,8 4 3 Issues for music technology 121. References 123,Appendices 137,List of figures, Figure 3 1 An 8 beat cross rhythm to 4 main tactus beats is a different subdivision of. the tactus 48, Figure 3 2 A 6 beat cross meter to 4 main tactus beats is a different grouping of. subdivisions 48, Figure 3 3 Period layers in a song from the Aka people from a figure provided in. Arom 1994 49, Figure 3 4 Drawn from figures given in Anku 2000 51.
Figure 3 5 Cuban clav pattern 51, Figure 3 6 North Indian jhaptal metric pattern from a figure in Clayton 1997. clap o wave 51,Figure 4 1 3 4 hemiola against a 6 8 meter 57. Figure 5 1 Microtiming deviations for the drum break in The Funky Drummer by bar. Figure 5 2 Funky Drummer odd even deviation differences by bar 69. Figure 5 3 Deviations generated by a covert 3 4 clock against a 4 4 tactus with 16th. tatums see text An absolute swing value of 12msec has been added to. every even numbered tatum onset time 71, Figure 5 4 Deviations for t3he cat bul I and bul II of the toque macota of the. Yub dance Individual drum strokes on successive eight notes the. smallest rhythmic value are joined by lines 76, Figure 5 5 Cat and bul deviations for the Frent dance The cat appears to. follow a deviation strategy which is independent to that of the bul 78. Figure 5 6 Bul I deviations using a covert clock of 5 against 12 scaled by 0 17 79. Figure 5 7 Bul II deviations using a covert clock of 5 against 12 scaled by 0 29 80. Figure 5 8 Tambora deviations for the Mas n using a covert clock of 5 against 12. scaled by 0 22 81, Figure 5 9 Bul deviations for the Mas n using a covert clock of 5 against 12.
scaled by 1 0 82, Figure 5 10 Hi hat deviations for Getz Gilberto s O Grande Amor 83. Figure 7 1 VROOGE model output for the Bul 2 part for the Macota toque of the. Yub dance 115, Figure 7 2 Covert Clock model results for the Bul 2 part for the Macota toque of the. Yub dance The model results are scaled by 0 29 115. List of equations,Equation 6 1 93,Equation 6 2 93,Equation 6 3 93. Equation 6 4 94,Equation 6 5 94,Equation 6 6 98,Equation 6 7 100. Equation 6 8 101,Equation 6 9 104,Equation 6 10 105.
Equation 6 11 105,Equation 6 12 105,Equation 6 13 106. Equation 6 14 111,List of tables, Table 2 1 Summary of experimental findings for period of referent time level and. spontaneous tempo 22, Table 5 1 Covariance of 1 1 deviations with preceding 4 4 deviations 67. Table 6 1 Feature comparision of microtiming deviation models 96. Table 6 2 Experimentally determined gain parameter estimations for entrainment. models 109,List of Appendices, Appendix A Models of expressive timing in music 139. A 1 The relation of musical structure to deviations 139. A 1 1 Significance of musical structure for expressive deviations 139. A 2 Application of structural information to models of expressive deviation in. A 3 Models of analysis and generation of expressive deviation 141. A 4 Relevance to this thesis 146,Appendix B Raw data 149.
B 1 The Funky Drummer 149, B 1 1 The Funky Drummer break onset time data provided courtesy. of Peter Freeman Freeman Lacey 2001 149, B 1 2 The Funky Drummer break calculated deviations 151. B 1 3 The Funky Drummer covariance of the rate of change of bar. first deviations relative to bar end deviations from the previous. B 1 4 The Funky Drummer difference between odd and even. deviations 155, B 1 5 The Funky Drummer application of the Covert Clock model 155. B 2 Tumba francesca values 156,B 2 1 Yub 156,B 2 2 Mason 158. B 3 O Grande Amor 160, Appendix C Paper read at the 7th International Conference on Cognitive.
Science Sydney July 2003 169,Extended Abstract, Much work has and is being done on the topic of timing variation in Western notated. art music see Appendix A to this thesis and representatively Bresin 1998 2000. Bresin De Poli Vidolin 1992 Canazza De Poli Di Federico Drioli 1999. Canazza De Poli Drioli Roda Zamperini 2000 Canazza De Poli Roda. Vidolin 1997 Canazza Roda Orio 1999 Cannazza De Poli Di Sanzo Vidolin. 1998 Clynes 1983 Clynes 1986a b Clynes 1987 Clynes 1992 Clynes 1995. Clynes Walker 1982 Desain Honing 1991 1992 1993 1996 Epstein 1988. Friberg 1995 Friberg Bresin 1997 Friberg Bresin Fryden Sundberg 1998. Gabrielsson 1982 Honing 1992 Honing 2001 Mazzola Zahorka 1994a b. Palmer 1989 1996 Palmer 1997 Palmer Pfordresher 2003 Palmer van de. Sande 1995 Repp 1990 1992 1998 Shaffer 1980 1981 Shaffer 1985 Shaffer. Clarke Todd 1985 Sundberg Friberg Fryden 1991 Timmers Ashley Desain. Heijink 2000 Todd 1985 1989 Widmer 1994 1996 2000 2001 However less. investigation has been undertaken into microtiming deviations in repetitive musics. with globally stable tempo Such musics are here referred to inclusively as groove. musics some examples are traditional African drumming funk and Latin music. This thesis presents a theory the Covert Clock Theory and proposes a model of the. production of musical groove The computer model presented rests on arguments. regarding what constitutes groove both in a musical sense and beyond the scope. of musicology in terms of how and why humans produce and respond to groove. Through the examination of human perception and production of rhythm I propose to. develop a model based on the Covert Clock Theory of the generation of. microtiming deviations characteristic of groove Ideally the model should be. intuitively controllable by a musician setting a small number of parameters and. should generate deviation patterns which are musically useful and have similar. characteristics to those generated by human musicians. What is groove microtiming, Groove musics can be characterised as synchronic and repetitive A macroperiod is. defined within the music and material is repeated with variations in successive. macroperiods Systematic consistent and musically significant variations from the. temporal grid of strictly proportional timing have been found to exist in these musics. with deviations typically in the range 5ms to 50ms Some limited musicological. studies see eg Bilmes 1993b Cholakis 1999b Freeman Lacey 2001 Freeman. Lacey 2002 of microtiming deviations in groove have been undertaken but these. do not attempt to account for microtiming in terms of underlying timing processes. This thesis represents an attempt to integrate the musicology of microtiming with. psychological and human movement theories of rhythmic timing control in order to. develop a theory of the process by which performers generate microtiming. deviations The theory and results have implications for the psychology of rhythm for. music technology for musicology and music performance and for motor planning. theory in general,A new theory of rhythmic timing and entrainment. Theories and models of human rhythmic entrainment musical timing and motor. control are critically reviewed in light of the experimental and musicological literature. Evidence is presented for different psychological or perceptual processes for a. timing control within the range of rhythmic synchronisation and b time intervals. below that range, A new theory of production is presented in which a system of interlocking interval. timers or clocks provides trigger signals to motor programs at the start of each. isochronous interval Interval timers with resting periods close to the period of the. driving stimulus which may simply be an isochronous pulse train alter their period to. entrain to the driving stimulus Entrainment may be in any harmonic relation to the. stimulus clock triggers and stimulus pulses may be in a one to one relation or a. 1 2 1 3 1 4 2 1 3 1 or 4 1 relation The ratios of clock period to stimulus period are. effectively limited by the range of synchronisation which is approximately between. 200ms and 1500ms Within this range nested harmonic clocks may occur with the. longest period perhaps four times the shortest period Harmonic relations between. clock periods are more stable because they lead to most reinforcement between. clocks but non harmonic ratios although less stable are also possible. Interval timers with onsets which are temporally close interact to reset phase so that. their onsets tend to occur together without the involvement of any period correction. process In this way clocks with harmonically related periods help to stabilise each. other to produce more precise timing No phase information is available from interval. timers between triggers, Timing control at intervals smaller than the current synchronisation period ie.
between the triggers of the fastest active interval timer is achieved by open loop. motor programs triggered by the interval timer Timing at this lowest level might. hypothetically be achieved by means of a very fast perhaps 1000Hz oscillation. and a counter mechanism which are not available to cognitive control Revisions to. timing in the motor program schema are made following execution of the motor. program on the basis of sensory feedback, The delay for revisions to take effect following execution is equal to the time needed. for planning sensory feedback and any other delays attributable to the. neuromuscular system At least some of these delays contribute to the necessity for. functional anticipation by the timer trigger of the sensorimotor goal Functional. anticipation is defined as the time between the timer trigger and the completion of the. action For instance a sensorimotor goal of eg producing a drum attack to be heard. at a defined time within the rhythmic stream requires a functional anticipation at least. equal to the time needed to convey the command to the muscles and for the physical. completion of the action, Phase correction is modelled in the implementation of the Covert Clock Theory as a. separate process from period correction although referencing the same. asynchronies between sensory feedback and expected sensory feedback following. the interval timer trigger Phase correction is thus a motor implementation process In. the theory phase correction involves an adjustment to the amount of functional. anticipation The phase correction process functions in the same temporal range as. microtiming deviations ie below 50ms and may be invoked in response either to. subliminal timing perturbations of the driving stimulus or to asynchronies resulting. from interval timer errors or motor implementation errors. Original contribution,The Covert Clock Theory, A new theory and computational model of microtiming deviations in groove music are. presented The Covert Clock Theory of microtiming deviations posits the existence of. an internal clock or interval timer at a cross rhythm to the tactus clock that is with a. period at a non harmonic ratio to the tactus period Such cross rhythms are made. explicit in eg African traditional drumming where a cross rhythm of three beats. against four beats of the tactus is often established. The Covert Clock Theory suggests that the covert clock and the tactus interact so. that a given clock onset may occur earlier or later but without the actual period of the. clock being adjusted Early or delayed triggering of the beginning of the interval timer. cycle will of course result in some inter trigger periods being shorter or longer than. the clock period but a key point of the theory is that the clock retains its previously. established period, The coincidence of the main and covert clocks at every four beats of the tactus and. every three beats of the covert clock in the example given defines the start of the. macroperiod The macroperiod has duration within the capacity of echoic memory. the psychological present, The Covert Clock Theory can be seen as a means of extending the duration of motor.
programs Other devices found in traditional African drumming are also discussed as. fulfilling the same function,The VROOGE model, The VROOGE model of microtiming deviations in groove is a software. implementation of the microtiming process described by the Covert Clock Theory. The name VROOGE is simply an anagram of groove The VROOGE model. entrains to an external isochronous pulse train through period correction of a main. tactus interval timer Weighted referencing by the motor timing process to both the. tactus and the covert clock results in changes to the local tempo of motor program. implementation without altering the period of the underlying clock This facet of the. model corresponds to expansion or contraction of motor program duration as. described in the Covert Clock Theory Local tempo changes in motor program. implementation from one tactus trigger to another result in progressively increasing. or decreasing deviations through the duration of the tactus The deviation amount is. in fact the integral of the tempo change relative to the base tempo given by the. unchanged tactus clock, The VROOGE model is evaluated through analysis of microtiming data of examples. of groove music and comparison with model generated data Predictions of the. theory are tested against the data and some agreement is found. The VROOGE model is successful in providing a means of generating new musically. meaningful microtiming deviation patterns by making a low number of parameter. settings to which the model responds in a musically intuitive way. Chapter 1 Psychological and musicological,approaches to groove microtiming. The first section of the thesis comprises a review of the literature dealing with the. psychology of musical rhythm and meter to provide the basis for developing a. theory of microtiming deviations As with the rest of the thesis the focus will be on. groove music in this section in its relation to the perception and production of. rhythm and meter Chapter 3 provides relevant musicological background while. Chapter 4 relates the musicological material of Chapter 3 to psychological theory. The musicological characteristics of groove are dealt with more fully below For. the present it is enough to note that groove music has a focus on rhythm. expressed via repetitive patterns usually of the same length within the framework. of a tempo which is apparently invariant The musicological section will mainly. discuss various relevant aspects of traditional African drumming practice from. several different cultures although the main thrust of the theory is applicable to. the wider range of musics which could be called groove including some of the. musics of the African diaspora such as Cuban music and funk. The Covert Clock Theory of microtiming deviations is presented in Chapter 5. while Chapter 6 tests results of the Covert Clock theoretical model against. microtiming data from a range of musics Chapter 7 reviews existing. computational models of entrainment and such models of microtiming which are. relevant for groove music Chapter 8 presents the VROOGE model of microtiming. deviations based in the Covert Clock theory described in Chapter 5. Appendix A reviews models of microtiming which are not relevant to groove music. These are mainly related to stylistic structural aspects of Western notated art. We turn now to a definition of terms used in the thesis. 1 1 Defining terms, Before attempting to define groove music and what separates it from say 18th. century classical music it is necessary to clarify the meaning of commonly used. terms relating to rhythm Words such as beat meter measure accent and even. rhythm are used at different times with a variety of overlapping meanings.

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