Effects of Metrical Subdivision
on Perceived Beat Rate
Bruno H. Repp
Haskins Laboratories,
New Haven, Connecticut
The anticipation tendency in
sensorimotor synchronization
• When people tap in synchrony with an isochronous
sequence of tones, they typically tap ahead of the
tones by several tens of milliseconds.
• Wohlschläger and Koch (2000) proposed that this
occurs because of a perceptual underestimation
of the tone inter-onset interval (IOI).
Wohlschläger, A., & Koch, R. (2000). Synchronization error: an error in time
perception. In P. Desain & L. Windsor (Eds.), Rhythm perception and production
(pp. 115–128). Lisse, The Netherlands: Swets & Zeitlinger.
Subdivision reduces or eliminates the
anticipation tendency
• Wohlschläger and Koch (2000) found that making additional
finger movements between taps or inserting additional,
randomly timed soft tones (“raindrops”) between the tones
reduces or eliminates the anticipation tendency.
• Thus, interval subdivision seems to reduce or eliminate the
perceptual underestimation of the interval duration.
• This is in agreement with psychoacoustic studies on the filled
duration illusion: Filled or subdivided auditory intervals are
judged to last longer than unfilled intervals between sounds
(e.g., Buffardi, 1971; Goldfarb & Goldstone, 1963; Thomas &
Brown, 1974; Wearden et al., 2006).
Continuation tapping
• If participants underestimate the IOI duration, their continuation
tapping should be faster than their synchronized tapping.
• This was indeed found by Flach (2005) in a study where the
continuation taps produced tones (also, Repp & Knoblich, 2007).
The degree of acceleration depended on the magnitude of the
anticipation tendency during synchronization.
• However, Wohlschläger (reported in Caspi, 2002) found no such
acceleration in a study where the continuation taps were not
accompanied by tones, which suggests accurate perception of IOIs,
contrary to the underestimation hypothesis.
• However, adding “raindrops” during synchronization resulted in a
pronounced slowing of continuation tapping. This suggests that
the duration of subdivided IOIs was overestimated.
A perceptual study
• In a perceptual matching task, Caspi (2002)
demonstrated that a sequence containing “raindrops”
sounds slower (by about 3%) than a sequence
containing empty intervals. In this study,a standard
sequence (8 tones) was followed by a comparison
sequence (5 tones) without a break.
Caspi, A. (2002). The synchronization error: Attentional and timing aspects.
Unpublished doctoral dissertation, Tel Aviv University.
Flach, R. (2005). The transition from synchronization to continuation tapping.
Human Movement Science, 24, 465–483.
The present research
• Can the “raindrop” findings be replicated by
subdividing the IOIs into equal sub-intervals
(i.e., metrical subdivision)?
• Will the effects of subdivision be shown by
musically trained participants?
• Hypothesis: Metrical subdivision will result in
a subjective lengthening of the IOI duration
that will be reflected in a slower tempo during
continuation tapping.
Experiment 1
•
•
•
•
•
•
•
•
•
Eight musically trained participants
Isochronous sequences of 12 tones (“beats”)
IBI = inter-beat interval
Five IBI durations (600, 700, 800, 900, 1000 ms)
Baseline (sub-0 = no subdivision) and three forms of subdivision
(sub-1, sub-2, sub-3 = 1, 2, or 3 subdivision tones)
Subdivision tones were 3 semitones lower and 3 dB softer than
beat tones.
All sequence types were randomized together.
Participants tapped in synchrony with the beat tones and
continued to tap at the same tempo for about 10 taps after the
sequence ended.
The continuation taps did not produce tones.
Three conditions (schematic)
(sub-2 not shown)
Deviation of continuation ITI from IBI (ms)
Deviation of mean continuation
inter-tap interval (ITI) from IBI
60
40
20
0
F
H
F
F
H
H
J
J
J
H
F
J
B
B
J
B
B
-20
-40
H
F
B
B
sub-0
H
sub-2
J
sub-1
F
sub-3
-60
600
900
800
700
Inter-beat interval (ms)
1000
Experiment 2
• Inspired by Wohlschläger’s “raindrop” study (Caspi, 2002), in
which he added raindrops not only during synchronization but
also during continuation, or during both.
• (1) Will the subdivision effect disappear when participants tap
the subdivisions during continuation tapping? (It did, pretty
much.)
• (2) Will a subdivision effect be obtained when participants
themselves tap the subdivisions during synchronization? (Yes.)
• (3) Will there be an effect of hearing tones contingent on the
continuation taps? (Yes, people tended to tap faster.)
Experiment 3
(with help from Finnoh Bangura)
• Can an effect of metrical subdivision on
subjective IBI duration be demonstrated in a
perceptual matching study, as Caspi (2002)
did with the effect of raindrops?
Stimuli
Standard
|
|
Comparison
sub-0
|
|
|
|
|
sub-1
| | | | | | |
|
|
|
sub-2
||||||||||
|
|
|
sub-5
(not shown)
Design and methods
• 10 participants (various degrees of musical training)
• Standard IBI = 600 ms
• Comparison IBI differs from standard by -12, -8, -4, 0, 4, 8 or 12%
• Four subdivision conditions (sub-0, sub-1, sub-2, sub-5)
• 10 repetitions of 28 stimuli
• Participants responded “faster”, “same”, or “slower” to the
comparison sequence
Response percentages
sub-0
Response percentage
100
80
sub-1
100
E
E
B
80
H
B
E
E
60
"faster"
B
H
"same"
B
60
"slow er"
40
B
H
E
0
-16 -12
H
E
H
H
-8
E
B
20
-4
H
B
0
B
4
B
B
E
8
12
16
H
E
0
-16 -12
E
H
-8
sub-2
H
E
B
H
H
B
B
B
-4
0
4
8
12
E
H
16
sub-5
100
Response percentage
H
H
E
40
20
80
E
E
100
B
E
B
80
B
E
60
B
E
E
B
40
E
E
H
60
B
H
40
H
E
H
20
H
E
E
H
H
H
B
B
E
B
20
E
B
0
-16 -12 -8 -4 0
4
8 12
Change in inter-beat interval (%)
H
16
E
H
E
H
B
H
H
B
B
B
0
-16 -12 -8 -4 0
4
8 12
Change in inter-beat interval (%)
16
Subjective points of equality
N=10
4
(without BR and FB)
3
5
2
1
0
sub-0
sub-1
sub-2
Subdivision condition
sub-5
Subjective point of equality (%) ± SE
Subjective point of equality (%) ± SE
5
N=8
4
3
2
1
0
sub-0
sub-1
sub-2
Subdivision condition
sub-5
Experiment 4
(with help from Finnoh Bangura)
• Matched perception and reproduction tasks
(order counterbalanced)
• Short pause between first sequence
(standard, model) and second sequence
(comparison, reproduction)
• Taps produced tones
• Two subdivision conditions: sub-0, sub-3
• Comparison of musicians and non-musicians
Stimuli
Comparison
(reproduction)
Standard
(model)
sub-0
|
|
|
|
|
|
|
|
|
|
sub-3
|||||||||||||||||
|
|
|
|
|
Methods
• 8 musicians, 7 non-musicians
• Perception: standard IBI = 600 ms;
comparison IBI deviates by 0, ±4, ±8,
±12% (528 to 672 ms)
• Reproduction: model IBI varies from
528 to 672 ms
• Subdivision tones 1 semitone lower and
3 dB softer than beat tones
Results: Perception
Non-musicians (N = 7)
Musicians (N = 8)
Percent "same" responses
100
80
sub-0
E
sub-3
100
J
J
E
E
J
80
J
J
J
60
E
60
E
E
40
40
E
E
J
20
0
500
SPE deviation (%) ± SE
J
E
E
J
J
E
E
J
J
0
500
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
J
20
J
550
600
650
700
Comparison interval duration (ms)
E
E
J
E
550
600
650
700
Comparison interval duration (ms)
-2
sub-0
sub-3
sub-0
sub-3
Results: Reproduction
Nonmusicians
Reproduced interval duration (ms) ±SE
Musicians
700
700
E
E
N=8
E
E
J
650
E
E
E
650
E
J
J
J
E
E
600
N=5
J
E
600
J
J
E
550
E
J
500
500
J
E
J
J
sub-0
J
550
J
E sub-3
550
600
650
700
Presented interval duration (ms)
J
J
500
500
550
600
650
700
Presented interval duration (ms)
Conclusions
• Musicians show robust metrical subdivision
effects in perception and (re)production.
• Nonmusicians show smaller effects in
perception but larger effects in reproduction.
• Negative correlation of perception and action
effects!
• Suggested explanation: The perceptual effect
is obscured by inaccurate judgment, whereas
the action effect is enhanced by inaccurate
memory for the beat rate.
Implications for Music Perception
and Performance
• If performers want to keep the tempo, they
should tend to play faster when there are
more notes. Yet, listeners (including the
performers themselves) should not perceive
any change in tempo.
Some Data from Beethoven’s Piano
Sonata in C minor, op. 111
Variation 1 (mean beat duration in seconds)
2.5
2
E
1.5
1
E
E
E
EE E
E
E E
E EEE E E E
E
E
E
EEE
EEE
E
E E
0.5
0.5
1
1.5
2
2.5
Theme (mean beat duration in seconds)
Thank you for listening!
Any questions?