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Micro-rhythm and macro-movementsMicro-rhythm and macro-movementsin performance of swing groovesin performance of swing grooves

Carl Haakon WaadelandCarl Haakon Waadeland

Department of MusicDepartment of Music

Norwegian University of Science and Technology (NTNU)Norwegian University of Science and Technology (NTNU)

TrondheimTrondheim

E-mail: E-mail: carl.haakon.waadeland@hf.ntnu.nocarl.haakon.waadeland@hf.ntnu.no

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IntroductionIntroduction

A swing groove in jazzA swing groove in jazz::

The The performanceperformance of this groove might: of this groove might:

(a)(a) Identify the Identify the individualindividual drummer,- in terms of: drummer,- in terms of:

AccentuationAccentuation SubdivisionSubdivision Push/laid backPush/laid back

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(b)(b) Show Show discrepanciesdiscrepancies from the note values in from the note values in the written representation abovethe written representation above

(c)(c) At different times be At different times be ”swinging””swinging”

Make the listener want toMake the listener want tomove move along with the along with the

rhythmrhythm

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Rehearsing to play swing grooves requires:Rehearsing to play swing grooves requires:

(a)(a) Excercises in coordinated movements of hands Excercises in coordinated movements of hands and feetand feet

(b)(b) Coordination of drumstick, hand, wrist and Coordination of drumstick, hand, wrist and elbowelbow

OutputOutput

various various movement strategiesmovement strategies for relaxed for relaxed performances of swing grooves performances of swing grooves

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A main focus of this investigation:A main focus of this investigation:

To achieve analytical insight into swing To achieve analytical insight into swing performances by studying the drummers’ performances by studying the drummers’ movements in the performance movements in the performance

Basic question asked:Basic question asked:

How are movement patterns related to rhythmic How are movement patterns related to rhythmic phrasing in performance of swing grooves?phrasing in performance of swing grooves?

.... To study this we have constructed .... To study this we have constructed a series of a series of experiments:experiments:

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Empirical investigation

Subjects:Subjects:Jazz drummers, students and teachers at Dept. of Jazz drummers, students and teachers at Dept. of Music, NTNU – section of jazz education.Music, NTNU – section of jazz education.

Aim:Aim:Study possible relations between the drummers’ Study possible relations between the drummers’ movementsmovements and the following performance and the following performance parameters:parameters: TempoTempo DynamicsDynamics Rhythmic subdivisionRhythmic subdivision

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Method/Equipment for Measuremets

(Measurements assisted by Geir Oterhals(Measurements assisted by Geir Oterhals

Section of Movement Science, NTNU)Section of Movement Science, NTNU)

Cameras (6) transmitting infra red light

Markers (5) reflecting the light

”Force plate” measuring force from drumstick

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The following equipment is used:The following equipment is used:

6 cameras (Proreflex camera system) are6 cameras (Proreflex camera system) are used to used to measure measure movementsmovements of the arm and the drumstick of the arm and the drumstick (kinematics). Sampling rate: 240 Hz(kinematics). Sampling rate: 240 Hz A force plate (Kistler) is used to give accurate A force plate (Kistler) is used to give accurate measurements of measurements of attack points attack points and and musical musical dynamicsdynamics. Sampling rate: 960 Hz. Sampling rate: 960 Hz A minidisk is used for audio recording of the A minidisk is used for audio recording of the experimentexperiment

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Results from a case study

Experiment (0): Experiment (0):

Subject: S09Subject: S09

Task: Play swing groove on the force plate (120bpm)Task: Play swing groove on the force plate (120bpm)

b1 b1 b2 b3 b1´ b2´ b3´b2 b3 b1´ b2´ b3´

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Vertical displacement of drumstick/hand/wrist:Vertical displacement of drumstick/hand/wrist:

b1 b2b1 b2

ii)) Periodic-like movement patterns Periodic-like movement patterns iiii)) On b2 and b2´ the drumstick strokes precede the minima On b2 and b2´ the drumstick strokes precede the minima of hand and wrist movementsof hand and wrist movements iiiiii)) b1 and b1´ are performed with the hand and wrist b1 and b1´ are performed with the hand and wrist moving moving upwardsupwards, preparing strokes on b2 and b2´, preparing strokes on b2 and b2´

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Looking at 4 measures of drumstick movement:Looking at 4 measures of drumstick movement:

b1 b2 b3 b1 b2 b3b1 b2 b3 b1 b2 b3

iv)iv) Largest Largest preparatory heightpreparatory height (hp) for b2. (hp) for b2.In fact: hp(b1) < hp(b3) < hp(b2) (*)In fact: hp(b1) < hp(b3) < hp(b2) (*)

Natural explanation:Natural explanation: (*) is reflecting the (*) is reflecting the inter-onset intervalsinter-onset intervals (IOI) (IOI) (*) is reflecting the distribution of (*) is reflecting the distribution of accentsaccents (which is also (which is also related to related to striking velocities, acceleration striking velocities, acceleration and and force dataforce data) ) (c.f. also S. Dahl)(c.f. also S. Dahl)

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vv)) For For timing analysistiming analysis we measure the IOIs we measure the IOIs (over an(over an interval of 4 measures):interval of 4 measures):

Let Let d1d1 = IOI(b1,b2); i.e.: the = IOI(b1,b2); i.e.: the durationduration of the first beat, and of the first beat, and let let d2d2 and and d3d3 be similarily defined. be similarily defined.We find: We find: (d2 + d3) > d1(d2 + d3) > d1Average, 4 measures:Average, 4 measures: (d2 + d3)/d1 = l.03(d2 + d3)/d1 = l.03(in this tempo (124bpm): d2 + d3 = d1 + 15ms)(in this tempo (124bpm): d2 + d3 = d1 + 15ms)

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vi)vi) Swing ratioSwing ratio (SR) is defined as: (SR) is defined as: SR = (d2/d3)SR = (d2/d3)(cf. Friberg & Sundström)(cf. Friberg & Sundström)

Observe:Observe:SR = 1:SR = 1: Eighth note subdivisionEighth note subdivisionSR = 2:SR = 2: Eighth note triplet subdivisionEighth note triplet subdivisionSR = 3:SR = 3: Sixteenth note subdivisionSixteenth note subdivision

Calculating SR for every pair of (d2,d3) intervals, and Calculating SR for every pair of (d2,d3) intervals, and averaging over the 8 pairs, we get:averaging over the 8 pairs, we get:

SR(average exp(0)) = 2.1SR(average exp(0)) = 2.1

i.e. a i.e. a triplet-close triplet-close subdivision in the performance, slightly to subdivision in the performance, slightly to the the sixteenth note sidesixteenth note side

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Next series of experiments:Next series of experiments:Impose Impose additionaladditional playing conditions: playing conditions:

With count-in tempo 120bpm, play swing grooveWith count-in tempo 120bpm, play swing groove

on the force plate with accent onon the force plate with accent on

1) every first1) every first

2) every second2) every second

3) every third3) every third

beat (resp.) in the swing cyclebeat (resp.) in the swing cycle

Question:Question:

How do these additional conditions affect the How do these additional conditions affect the performance performance compared to the (neutral) situation incompared to the (neutral) situation in Experiment (0)Experiment (0) ? ?

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We exemplify by:We exemplify by:

Experiment (3): Experiment (3):

> > > >

b1 b2 b3b1 b2 b3

Look at vertical displacement of drumstick, hand and wrist:Look at vertical displacement of drumstick, hand and wrist:

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Exp (3):Exp (3):

b1 b2 b3b1 b2 b3

Exp (0):Exp (0):

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Compared to Exp(0) we find:Compared to Exp(0) we find:

i)i) Totally different periodic-like movement patterns Totally different periodic-like movement patterns

ii)ii) On b2 the hand and wrist have started an On b2 the hand and wrist have started an upwardupward

movement, preparing the accented stroke on b3movement, preparing the accented stroke on b3

iii)iii) Minor vertical movement of hand and wrist on b1 Minor vertical movement of hand and wrist on b1

iv)iv) Looking at drumstick movement: Largest preparatory Looking at drumstick movement: Largest preparatory

height for b3 whereas hp(b1) and hp(b2) are about the sameheight for b3 whereas hp(b1) and hp(b2) are about the same

This reflects the distribution of This reflects the distribution of accentsaccents, but does, but does

notnot reflect the reflect the IOIsIOIs (as was the case in Exp(0)) (as was the case in Exp(0))

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Measuring IOIs and comparing to Exp(0) we find:Measuring IOIs and comparing to Exp(0) we find:

v)v) In the performance of Exp(3) the interval starting with the In the performance of Exp(3) the interval starting with the

accent is lengthend (cf. also S.Dahl)accent is lengthend (cf. also S.Dahl)

vi)vi) The lengthening takes duration from both intervals 1 and 2 The lengthening takes duration from both intervals 1 and 2

vii)vii) The inequality (d2 + d3) > d1 is The inequality (d2 + d3) > d1 is enlargedenlarged

(In Exp(3): Average (d2 + d3)/d1 = 1.08 (as compared to 1.03))(In Exp(3): Average (d2 + d3)/d1 = 1.08 (as compared to 1.03))

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viii)viii) Calculating swing ratios and averaging over 8 measures, Calculating swing ratios and averaging over 8 measures,

we get:we get:

SR(average exp(3)) = 1.8 SR(average exp(3)) = 1.8 (compared to 2.1)(compared to 2.1)

i.e. still a triplet-close subdivision in the performance, buti.e. still a triplet-close subdivision in the performance, but

now slightly to the now slightly to the eighth note sideeighth note side

(This is also indicated in the previous figure)(This is also indicated in the previous figure)

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Conclusions for this case studyConclusions for this case study

The additional playing conditions imposed in Exp(3) have:The additional playing conditions imposed in Exp(3) have: Major effect on movement strategies in the performanceMajor effect on movement strategies in the performance Noticable effect on timing, especially on:Noticable effect on timing, especially on:

- The duration of the accented note- The duration of the accented note

- The swing ratio- The swing ratio

- Strengthening an occurence of shorter-longer - Strengthening an occurence of shorter-longer

durations of the 1-2-3-4 in the swing 4/4-durations of the 1-2-3-4 in the swing 4/4-measuremeasure

Next step:Next step: A comparison between several subjectsA comparison between several subjects Develop new tools for classification of movementsDevelop new tools for classification of movements

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Further analysis of movements

A method of analysis which gives additional information of A method of analysis which gives additional information of

movement patterns and appears useful as a tool formovement patterns and appears useful as a tool for

distinguishing between movement categories, isdistinguishing between movement categories, is

spectral analysisspectral analysis

By this method the By this method the sinusoidal componentssinusoidal components of the movement of the movement

patterns are detectedpatterns are detected

The analysis is done by using Matlab calculating FFTThe analysis is done by using Matlab calculating FFT

(Fast Fourier Transform)(Fast Fourier Transform)

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Example: Example: FFT of Exp(0)FFT of Exp(0)

f1 f2 f3 f4f1 f2 f3 f4

Observe:Observe:

i) i) FFT gives sinusoidal components with frequencies f1, f2, f3,….FFT gives sinusoidal components with frequencies f1, f2, f3,….

ii)ii) HarmonicHarmonic spectrum, reflecting spectrum, reflecting periodicperiodic movement curve movement curve

iii)iii) The frequencies represent The frequencies represent note valuesnote values::

f2=2.067Hz, i.e. 124bpm, which corresponds to f2=2.067Hz, i.e. 124bpm, which corresponds to quarter notequarter note

f1: f1: half notehalf note, f4: , f4: eighth noteeighth note, etc., etc.

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FFT of Exp(3):FFT of Exp(3):

Compared to FFT of Exp(0):Compared to FFT of Exp(0):

iv)iv) Same spectral components, but noticable differences in relative Same spectral components, but noticable differences in relative amplitudes (reflect the distribution of preparatory heights)amplitudes (reflect the distribution of preparatory heights)

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Conclusion for FFT analysis of swing (so far)Conclusion for FFT analysis of swing (so far)

FFT represent differences in movement patterns by FFT represent differences in movement patterns by differences in relative strength of sinusoidal differences in relative strength of sinusoidal components corresponding to note values in the components corresponding to note values in the performanceperformance

The detection of sinusoidal components might be used The detection of sinusoidal components might be used to make to make modelsmodels that that simulatesimulate the movements of the the movements of the performanceperformance

FFT detects mean tempo, but does FFT detects mean tempo, but does notnot convey (local) convey (local) timingtiming information (in order to do that it is more information (in order to do that it is more appropriate to apply short time FFT or wavelet analysis) appropriate to apply short time FFT or wavelet analysis)