Effects of Metrical Subdivision on

Perceived Beat Rate

Bruno H. ReppHaskins 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 mean continuation inter-tap interval (ITI) from IBI

B B

B B

B

J J JJ

J

HH

H H

H

FF F

F

F

600 700 800 900 1000-60

-40

-20

0

20

40

60

Inter-beat interval (ms)

B sub-0

J sub-1

H sub-2

F sub-3

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

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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

B

B

B

B B

B B

E

E

E

E

E

E

EH H

H H

H

H

H

0

20

40

60

80

100

-16 -12 -8 -4 0 4 8 12 16

BB

B

BB B

BEE

E

E

E

E

EH

H H H

H

H

H

0

20

40

60

80

100

-16 -12 -8 -4 0 4 8 12 16

sub-0 sub-1

B

B

B

BB B

B

E

E

E

EE

E

EH

HH H

H

H

H

0

20

40

60

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100

-16 -12 -8 -4 0 4 8 12 16Change in inter-beat interval (%)

B B

B

B

B BB

EE

E

E

E

E

E

HH

HH

H

H

H

0

20

40

60

80

100

-16 -12 -8 -4 0 4 8 12 16Change in inter-beat interval (%)

sub-2 sub-5

"faster" "same" "slower"

Response percentages

Subjective points of equality

sub-0 sub-1 sub-2 sub-50

1

2

3

4

5

Subdivision condition

N=10

sub-0 sub-1 sub-2 sub-50

1

2

3

4

5

Subdivision condition

N=8

(without BR and FB)

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

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Standard (model)

Comparison(reproduction)

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

JJ

J

J

J

JJ

EE

E

EE

E

E

0

20

40

60

80

100

500 550 600 650 700Comparison interval duration (ms)

J sub-0

E sub-3

J

J

J

JJ

J

JE E

E

E

E

E

E

0

20

40

60

80

100

500 550 600 650 700Comparison interval duration (ms)

-2

-1

0

1

2

3

4

-2

-1

0

1

2

3

4

sub-0 sub-3-2

-1

0

1

2

3

4

-2

-1

0

1

2

3

4

sub-0 sub-3

Musicians (N = 8) Non-musicians (N = 7)

Results: Reproduction

J

J

J

J

JJ

J

E

E

E

E

E

E

E

500

550

600

650

700

500 550 600 650 700Presented interval duration (ms)

J sub-0

E sub-3

Musicians

JJ

JJ

JJ

J

E

EE

E

EE

E

500

550

600

650

700

500 550 600 650 700Presented interval duration (ms)

Nonmusicians

N = 5

N = 8

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

E

E

EE

E

E

E

E

E

E

EE

EE

E

E

E

E

E

E

E

E

E

EE

EE

E

EE

E

0.5

1

1.5

2

2.5

0.5 1 1.5 2 2.5Theme (mean beat duration in seconds)

Thank you for listening!

Any questions?