synchronization in duet performance: testing the two-person...
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![Page 1: Synchronization in duet performance: Testing the two-person …cspeech.ucd.ie/rppw/rppw10/vorberg/presentation.pdf · 2008-03-14 · Duple 612 18 24-30-20-10 0 10 Triple IRI & Synch](https://reader033.vdocument.in/reader033/viewer/2022050119/5f4fba539c70fe036a79baac/html5/thumbnails/1.jpg)
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Dirk Vorberg
Institut für PsychologieTechnische Universität Braunschweig
Braunschweig, Germany
RPPW2005, Alden Biesen
Synchronization in duet performance:Testing the two-person
phase error correction model
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Overview
1. How do ensemble players manage to remainsynchronized?
2. Sensorimotor synchronization, tapping alongperfect metronome.
Synchronization is achieved by linear phaseerror correction.
3. Extend model to duet performance.Major advantage: Use computer to simulateone of the duet partners.
4. Experimental study.Preliminary data.
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task: tap in close synchrony with the metronome
metronome
overtresponses
In In+1
An An+1
Definition of interresponse intervals and synchronizationerrors
interresponse intervals
synchronization errors („asynchronies“)
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In In+1
An An+1
overtresponses
metronomeCn Cn+1
The phase-correction model
(Vorberg & Wing, 1994, 1996; Vorberg & Schulze, 2002; Schulze & Vorberg, 2003)
Mn Mn+1 Mn+2
Tn Tn+1timercommands
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Mn Mn+1 Mn+2
An An+1
In In+1
Tn Tn+1timercommands
overt responses
metronomeCn Cn+1
The two-level timing model augmented by phase errorcorrection
1. basic assumption: Tn* = Tn + (1– α)An
1. testable consequence:An+1 = (1– α)An + (Tn+Mn+1-Mn) - Cn
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Model predictions I:response to experimental perturbations
-30
-20
-10
0
10
20 IRI synch err
Sync
h Er
r; IR
I - T
empo
(ms)
10 20
-30
-20
-10
0
10
20
Sync
h Er
r; IR
I - T
empo
(ms)
Response and interval no.10 20
Response and interval no.
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Results (Antje Fuchs, 2003)
-2 -1 p1 p2 p3 p4 p5 p6 1 2 3 4
-40
-30
-20
-10
0
10
20
30
TimekeeperTriple
session 1-3 session 4-6
IRI a
nd S
ynch
Err
[ms]
-2 -1 p1 p2 p3 p4 p5 p6 1 2 3 4
-40
-30
-20
-10
0
10
20
30
TimekeeperDuple
session 1-3 session 4-6
-2 -1 p1 p2 p3 p4 p5 p6 1 2 3 4
-40
-30
-20
-10
0
10
20
30 Motor DelayTriple
session 1-3 session 4-6
IRI a
nd S
ynch
Err
[ms]
Position within Period-2 -1 p1 p2 p3 p4 p5 p6 1 2 3 4
-40
-30
-20
-10
0
10
20
30
Motor DelayDuple
session 1-3 session 4-6
Position within Period
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Results (Antje Fuchs, 2003)
6 12 18 24
-30
-20
-10
0
10
Triple
session 1-3 session 4-6
IRI &
Syn
c Er
r (m
s)
6 12 18 24
-30
-20
-10
0
10Duple
6 12 18 24
-30
-20
-10
0
10
Triple
IRI &
Syn
ch E
rr (m
s)
Position within Period6 12 18 24
-30
-20
-10
0
10
Duple
Position within Period
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Model predictions II:serial or auto-covariance function (acvf)
AnAn-1...…Ai+1AiAi-1…A3A2A1
serial variance = acvf at lag 0 = acvf(0)
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Auto-covariance function (acvf)
AnAn-1....Ai+1AiAi-1…A3A2A1
AnAn-1....Ai+1AiAi-1…A3A2A1
lag 1 auto-covariance = acvf(1)
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Auto-covariance function (acvf)
An-1An-2..Ai+1AiAi-1…A3A2A1
AnAn-1....Ai+1AiAi-1…A3A2A1
lag 2 auto-covariance = acvf(2)
auto-correlation function acf(lag) = acvf(lag) / acvf(0)
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Predicted asynchrony acf (as a function of lag)
0 < α < 1 1 < α < 2
Note:
Synchronization performance is unstable if α outsidethis range.
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Basic assumption: Each player serves as metronome for theother one.
Parameters:Player A (subject)
timekeeper variance σT²motor variance σM²error correction α
Player B (metronome)timekeeper variance σU²motor variance σN²error correction β
Extension of the model to duet performance
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Predicted 2-person asynchrony acvf
var(A) = [(σT²+σU²)+2(α+β)(σM²+σN²)]
/ [1-(1-(α+β))²]cov(An,An+k) =
[1-(α+β)]k-1[var(A)(1-(α+β)) – (σM²+σN²)]
Predicted 1-person asynchrony acvf
var(A) = [( σT² ) + 2( α )( σM² )]
/ [1-(1-( α ))²]cov(An,An+k) =
[1-( α )]k-1[var(A)(1-( α )) – ( σM² )]
Two-person phase synchronization model: Main result
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Predicted asynchrony acf for two-person model:
1. Synchronization performance is unstable if α+β outside thisrange.
2. Predictions:Stable but oscillatory acf for β positive .Unstable synchronization for β negative.
0 < α+β < 1 1 < α+β < 2
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Experiment: Conditions
1. tempoIOI=450 ms / 300 ms
2. meterduple / triple / quadruple
3. metronome gain factorβ=0β=.4 / .8β=-.25 / -.50
4. seven subjects6 one hour sessions18 sequences/condition
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Results
1. Exemplary time series after six hours of practiceasynchroniesinterresponse intervals, IRI (subject)interonset intervals, IOI (metronome)
2. Auto-correlation functions, acf
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subject an: asynchronies(x-axis: tap no. 1 – 48; y-axis: tap-metronome asynchrony in ms)
β=0 β=.4 β=.8 β=-.25 β=-.50
slow
fast
50 ms
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subject an: IRIs (top) and IOIs (bottom)(x-axis: tap no. 1 – 48; y-axis: deviation from nominal IOI, in ms)
β=0 β=.4 β=.8 β=-.25 β=-.50
100 ms
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subject an: acf.s for slow (top) and fast tempi (bottom) (x-axis: lag 0 to 6; y-axis: correlation size)
β=0 β=.4 β=.8 β=-.25 β=-.50
duple triple quadruple
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subject bv: asynchronies slow (top) and fast (bottom)
β=0 β=.4 β=.8 β=-.25 β=-.50
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subject bv: IRIs (top) and IOIs (bottom)
β=0 β=.4 β=.8 β=-.25 β=-.50
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subject bv: acf.s for slow (top) and fast (bottom) tempi
β=0 β=.4 β=.8 β=-.25 β=-.50
duple triple quadruple
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subject eh: asynchronies, slow (top) and fast (bottom)
β=0 β=.4 β=.8 β=-.25 β=-.50
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subject eh: IRIs (top) and IOIs (bottom)
β=0 β=.4 β=.8 β=-.25 β=-.50
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subject eh: acf.s for slow (top) and fast (bottom) tempi
β=0 β=.4 β=.8 β=-.25 β=-.50
duple triple quadruple
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Empirical asynchrony acf.s (all subjects)
β=0 β=.4 β=.8 β=-.25 β=-.50
dupletriplequadruple
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Empirical asynchrony acvf.s (average across subjects)(x-axis: lag 0 to 6; y-axis: autocovariance at lag k)
β=0 β=.4 β=.8 β=-.25 β=-.50
dupletriplequadruple
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Summary and conclusions
1. Two-person model is in qualitative agreement withobservations.
As predicted, acf becomes oscillatory as metronomegain β increases.For negative gain β, performance is unstable for mostsubjects.
2. Subjects can to adapt their phase-correction strategy to that of the duet partner.
3. Next step: Quantitative model fit.4. Model-based experimental paradigm is a promising tool for
studying duet synchronization. The model is easilyextended to musically more challenging conditions.