Journal of Sound and Vibration
Manuscript Draft
Manuscript Number: JSV-D-10-00826
Title: Does filled duration illusion occur for very short time intervals?
Article Type: Rapid Communication
Keywords: time perception; illusion; empty interval; filled intervals; cluster analysis
Abstract: Subjective durations of filled time intervals (marked by the onset and offset of a sound) and
empty time intervals (marked by onsets of two successive brief sounds) of 20-180 ms were measured,
utilizing the method of adjustment. Whereas many previous studies employing longer intervals had
reported that filled time intervals had been perceived as longer than empty time intervals of the same
physical duration (filled-duration illusion), the present results showed that this illusion occurred only
for less than a half of the participants, and that, for the other participants, filled time intervals were
perceived as shorter than empty time intervals.
Manuscript
Click here to download Manuscript: HasuoNakajimaUeda_r2.doc
Click here to view linked References
Does filled duration illusion occur for very short time
intervals?
Emi Hasuo
Graduate School of Design, Kyushu University
4-9-1 Shiobaru, Minami-ku, Fukuoka, 815-8540, Japan
[email protected]
Yoshitaka Nakajima and Kazuo Ueda
Department of Human Science, Kyushu University
4-9-1 Shiobaru, Minami-ku, Fukuoka, 815-8540, Japan
[email protected], [email protected]
Corresponding author:
Emi Hasuo
Graduate School of Design, Kyushu University
4-9-1 Shiobaru, Minami-ku, Fukuoka, 815-8540, Japan
phone: +81 92 553 4564
e-mail: [email protected]
1
Abstract
Subjective durations of filled time intervals (marked by the onset and offset of a sound) and
empty time intervals (marked by onsets of two successive brief sounds) of 20-180 ms were
measured, utilizing the method of adjustment. Whereas many previous studies employing
longer intervals had reported that filled time intervals had been perceived as longer than
empty time intervals of the same physical duration (filled-duration illusion), the present
results showed that this illusion occurred only for less than a half of the participants, and
that, for the other participants, filled time intervals were perceived as shorter than empty
time intervals.
Keywords: time perception, illusion, empty interval, filled interval, cluster analysis
Nomenclature: 130 M Human responses to sound and vibration: laboratory studies, field
trials, exposure metrics, dose-response relationships; human–structure interaction; hearing
protection; vibration protection
2
1. Introduction
The present article examines the “filled duration illusion” with very short time
intervals. The filled duration illusion refers to the phenomenon that a filled interval is
perceived to be longer than an empty interval of the same physical duration, and it has been
demonstrated repeatedly in many psychophysical studies (e.g., Craig [1]; Zwicker, [2];
Wearden et al. [3]).
We refer to a filled interval as the duration between the onset and the offset of a
continuous sound, and an empty interval as the duration between two very brief sounds
(e.g., Grondin [4]). Wearden et al. [3], who utilized such stimuli, found that the amount of
the filled duration illusion increased as the stimulus duration lengthened, for intervals
ranging from 77 to 1183 ms. The authors explained the results by suggesting that the
pacemaker in the clock-switch-accumulator model runs faster during a filled interval.
Wearden et al.’s [3] study is highly important for its implication on the mechanism
underlying the perception of filled and empty time intervals. Examining their results closely,
we noticed three interesting points: First, for stimulus durations shorter than approximately
300 ms, the amount of the filled duration illusion seemed very small and even almost
vanished in the shortest interval of 77 ms. Second, if the relationship between the stimulus
3
duration and the subjective duration held, the subjective duration for a 0-ms stimulus
should be a positive value, not zero, according to their data. This is qualitatively consistent
with the “processing time hypothesis” proposed by Nakajima [5], which assumes that the
subjective duration of a short time interval is proportional to its physical duration plus a
positive constant of about 80 ms. Third, the standard deviation of the responses for filled
intervals in their data were constantly larger than those for empty intervals when the
stimulus duration was shorter than 500 ms. It seemed possible that short time intervals
below 500 ms are perceived in a different way from the way longer intervals are perceived,
and additional theories to the pacemaker-speed hypothesis may be useful for very short
time intervals. This is in line with some theories (e.g. Rammsayer [6]) suggesting different
timing mechanisms for shorter (<~ 0.5 s) and longer (> 1 s) time intervals. There had not
been many studies on filled duration illusion with such short intervals. Zwicker [2] utilized
intervals as short as 5 ms, and the results did not seem to show clear filled duration illusion
for intervals below 100 ms. As a first step, we focused on time intervals shorter than 200
ms, and examined the occurrence of the filled duration illusion. Perception of short time
intervals within this range can be closely related to speech and music perception (e.g., Patel
[7]; Fraisse [8]).
4
2. Method
2.1. Participants. Twenty-four undergraduate students of Department of Acoustic Design,
Kyushu University, participated for course credits. All of them had received training in
technical listening for acoustic engineers (Iwamiya et al. [9]). This training focused mainly
on developing the ability to discriminate timbres and levels of sounds, and did not include
training related to time perception.
2.2. Stimuli and apparatus. Each presentation consisted of a standard and a comparison in
this order. The standard began 2-2.5 s after the participant clicked the “play” button on the
computer screen, and the comparison began 2.5-3 s after the standard ended. The duration
of these silences was randomized in a range of 500 ms for each presentation in order to
prevent the participants from anticipating the beginnings of each stimulus too accurately.
The standard duration was marked by either the onsets of two 20-ms sounds
(empty-interval condition), a continuous sound (filled-interval condition), or the onsets of
two 2-ms sounds (control condition). The comparison duration was always marked by two
2-ms sounds (an empty time interval as in the control condition). Sound duration included a
rise and a fall time, which were 1 ms for the 2-ms sounds, and 10 ms for the other sounds of
20 to 180 ms. The envelope of the rise and fall portions was cosine-shaped in the intensity
5
dimension (Figure 1). All stimulus sounds were 1000-Hz pure tone bursts, and the total
energy of each sound was kept constant. The presentation level of the 20-ms sound was 71
dBA, measured as the level of a continuous tone of the same amplitude. The levels of the
sounds were measured with a sound level meter (Node, 2072 or 2075) and an artificial ear
(Brüel & Kjær, 4153).
The standard duration was 20, 60, 100, or 180 ms (Figure 1). Thus, there were 12
experimental conditions (3 [filled, empty, and control] × 4 [standard durations]). As empty
intervals, we utilized onset-onset intervals. This was different from Wearden et al. [3] who
defined their unfilled (click) intervals as offset-onset intervals. However, utilizing
onset-onset intervals was important for us, because human auditory system is more
sensitive to sound onsets than to offsets (e.g., Fastl & Zwicker [10]), and high sensitivity
was necessary to investigate the perception of very short intervals as in our case. Another
point was that, we were interested in relating the results to rhythm perception as in speech
and music, which had been known to be based on onset-onset intervals (e.g., Handel [11]).
The stimulus patterns were generated digitally (16 bits; a sampling frequency of
44,100 Hz) on a computer (Asus, EeePC 4G), and presented diotically via a
digital-to-analog converter (Onkyo, Wavio SE-U55GX), an active low-pass filter (NF,
6
DV8FL, 8300 Hz), an amplifier (Sansui, AU-α607XR), and headphones (Sennheiser,
HDA200) to the participant. The stimulus patterns were presented to the participant in a
soundproof room.
2.3. Procedure. Participants adjusted the comparison interval to make it subjectively equal
to the standard interval. Printed instruction with words and illustrations was shown and read
to each participant, and it was clarified that the empty interval was from the onset of a
sound to the onset of a subsequent sound, and that the filled interval was from the onset to
the offset of one continuous sound. The final duration of the comparison interval in each
trial was recorded as the point of subjective equality, PSE. The lower limit for the
comparison interval was set to be 5 ms, for shorter intervals may cause the two sounds
marking the comparison interval to be perceived as one sound rather than two distinct
sounds (Plack [12]). When the participant tried to adjust the comparison interval to be
shorter than 5 ms, this intention was recorded, but the comparison interval in the next
presentation was 5 ms. For each standard interval, there were an ascending series and a
descending series, and the PSEs from these series were averaged for each participant. Thus,
the total number of trials was 24 (12 [experimental conditions] × 2 [ascending and
descending]).
7
3. Results and discussion
Figure 2a shows the mean PSEs plotted as a function of the standard duration and
the interval types (empty, filled, and control). The PSEs of the empty, the filled, and the
control condition were very close to each other. The filled duration illusion did not appear
in this graph; the mean PSEs of the filled interval condition were not larger than those in
the empty or the control condition. This was unexpected, given that the overestimation of a
filled interval had been reported repeatedly.
Although we did not find much difference between interval types in the mean
PSEs, the standard deviations between participants seemed to be larger in the filled interval
condition than in the other conditions; within 7.3-28.5 ms for the empty interval condition,
3.5-16.5 ms for the control condition, and 18.9-74.8 ms for the filled interval condition
(always the lowest values are for the 20-ms standards, and the highest are for the 180-ms
standards). This led us to wonder whether the large variability in the filled interval
condition was due only to task difficulty or to different listening strategies employed by
each participant.
Thus, we calculated the amount of overestimation of the filled interval [(filled
PSE) – (control PSE)], and of the empty interval [(empty PSE) – (control PSE)], for each
8
participant, and submitted their normalized values to a hierarchical cluster analysis.
Clusters were determined by the Ward method, which analyzed the squared Euclidean
distance between points. For the filled interval condition (Figure 3a), participants were
divided clearly into two groups, with 16 participants in one cluster (Cluster 1) and 8
participants in the other (Cluster 2). No such clear clusters appeared for the empty interval
condition (Figure 3b).
We calculated the mean PSEs for Clusters 1 and 2 separately, and plotted them
against standard duration (Figure 2b, c). The graphs showed clearly that participants in
Cluster 1 underestimated the filled intervals, whereas participants in Cluster 2
overestimated. This tendency was consistent throughout all standard durations, and
indicated that the large variability for the filled time intervals was due to different listening
strategies rather than to task difficulty only.
The main effect of the cluster difference was significant in the results of a two-way
(cluster × standard duration) ANOVA, performed utilizing the PSEs of the filled interval
condition, [F (1, 22) = 35.420, p < .001] (It was natural and trivial that PSEs changed as the
standard duration changed). We also performed a two-way (interval type × standard
duration) ANOVA for each cluster. For Cluster 1, the main effect of the interval type was
9
significant, [F (2, 30) = 18.567, p < .001]. Dunnett’s post hoc test was performed to
compare the control condition with the empty and the filled interval condition, and revealed
significant difference between the filled and the control condition (p < .001). The difference
between the empty and the control was not significant (p > .05). For Cluster 2, the main
effect of the interval type was also significant, [F (2, 14) = 9.510, p < .05], and Dunnett’s
post hoc test revealed significant difference between the filled and the control condition (p
< .001), but not between the empty and the control condition (p > .05). The interaction
between the interval type and the standard duration in the two-way ANOVA was not
significant (p > .05) in both clusters.
Summarizing, the filled interval condition was significantly different from the
control, but the empty interval condition was not, in both clusters. The differences, however,
were in different directions. For very short time intervals of 20-180 ms, some participants
overestimated filled intervals, as had been reported in previous studies (e.g., Wearden et al,
[3]; Zwicker, [2]), whereas the other participants underestimated them. This was the first
time such systematic underestimation of filled intervals was observed, and the occurrence
of two different types of perception (overestimation vs. underestimation of filled intervals)
could not be predicted from any of the previous studies. Although our results were
10
unexpected, they were still consistent with Wearden et al. [3] in one way; for time intervals
below 500 ms, the standard deviations for the filled intervals were larger than those for
empty intervals in Wearden et al.’s [3] results. Some participants may have overestimated,
and others may have underestimated the short filled intervals, also in their case. One
noticeable point about our results was that even in the Cluster-1 participants, the amount of
underestimation of the filled interval decreased, i.e., the mean PSE of the filled interval
condition approached those of the empty and the control condition, at the longest standard
duration of 180 ms. This could mean that the underestimation appears clearly only for very
short time intervals as in the present experiment, and it should be interesting to test whether
the underestimation for these participants would disappear for longer time intervals.
4. Conclusions
We found that the well-established filled duration illusion (i.e., the phenomenon
that a time interval filled with, for instance, a tone tends to appear longer than an empty
interval of the same duration bordered by click sounds), does not occur for very short
intervals (< 200 ms). Twenty-four participants were clearly divided into two groups; usual
overestimation of the filled intervals occurred in one group, but in the other group with the
majority of participants, a paradoxical underestimation occurred stably. The present results
11
should be important showing a possibility that human listeners perceive very short time
intervals differently from longer ones.
Acknowledgments
The authors thank Simon Grondin and Hiroshige Takeichi for their valuable comments.
This research was supported by grants to YN and KU from the Japan Society for the
Promotion of Science (19103003, 20330152, and 20653054).
References
[1] J. C. Craig, A constant error in the perception of brief temporal intervals. Perception &
Psychophysics 13 (1973) 99-104.
[2] E. Zwicker, Subjektive und objective Dauer von Schallimpulsen und Schallpausen
[Subjective and objective duration of sound impulses and sound pauses]. Acustica
22 (1969/70) 214-218.
[3] J. H. Wearden, R. Norton, S. Martin, O. Montford-Bebb, Internal clock processes and
the filled-duration illusion. Journal of Experimental psychology: Human Perception
and Performance 33 (2007) 716-729.
12
[4] S. Grondin, Methods for studying psychophysical time, in: S. Grondin (Ed.),
Psychology of Time, Emerald, Bingley, 2008, pp. 51-74.
[5] Y. Nakajima, A model of empty duration perception. Perception 16 (1987) 485-520.
[6] T. H. Rammsayer, Neuropharmacological evidence for different timing mechanisms in
humans. Quarterly Journal of Experimental Psychology 52B (1999) 273-286.
[7] A. D. Patel, Music, Language, and the Brain, Oxford University Press, New York, 2008.
[8] P. Fraisse, Rhythm and Tempo, in: D. Deutsch (Ed.), The Psychology of Music,
Academic Press, New York, 1982, pp. 149-180.
[9] S. Iwamiya, Y. Nakajima, K. Ueda, K. Kawahara, M. Takada, Technical listening
training: Improvement of sound sensitivity for acoustic engineers and sound
designers. Acoustics, Science and Technology 24 (2003) 27-31.
[10] H. Fastl, E. Zwicker, Psychoacoustics: Facts and models, Springer-Verlag, Berlin,
2007.
[11] S. Handel, The effect of tempo and tone duration on rhythm discrimination. Perception
& Psychophysics 54 (1993) 370-382.
[12] C. J. Plack, The Sense of Hearing, Erlbaum, New Jersey, 2005.
13
Figure Captions
Figure 1. The illustration of stimuli in the empty (a), filled (b), and control
condition (c). The stimuli of the comparison were the same as those in the control condition.
The temporal midpoints (or the beginnings depending on how we describe the patterns) of
the rise/fall time were considered as the beginning and the end of a time interval. Time
intervals of the standard were 20, 60, 100, and 180 ms.
Figure 2. Mean points of subjective equality (PSEs) plotted as functions of the
standard duration and the interval types. Open squares show the PSEs of the empty interval
condition, closed circles those of the filled interval condition, and gray downward triangles
those of the control condition. Error bars represent the standard deviations between
participants. (a) all participants (n = 24), (b) Cluster 1 (n = 16), and (c) Cluster 2 (n = 8).
Participants in Cluster 1 underestimated the filled intervals, whereas participants in Cluster
2 overestimated.
Figure 3. Dendrograms of 24 participants established by hierarchical cluster
analysis. (a) filled interval condition and (b) empty interval condition.
14
Intensity
20 ms
Time interval
10 ms 10 ms
a
Time
10 ms
Time interval
10 ms
b
Time
Time interval
1 ms
2 ms
1 ms
c
Intensity
Figure 1
Time
Figure(s)
Intensity
PSE (ms)
60
100
180
Standard duration (ms)
Empty
Filled
Control
20
20
100
140
180
220
260
300
60
20
a
PSE (ms)
60
100
140
180
220
260
300
Figure 2
20
60
100
180
Standard duration (ms)
b
20
60
100
140
180
220
260
300
20
60
100
180
Standard duration (ms)
c
Figure(s)
PSE (ms)
Participant
number
a
16
21
6
7
23
24
8
15
17
18
13
4
19
11
20
1
12
14
10
3
5
2
9
22
Figure 3
Rescaled Distance Cluster Combine
0
5
10
15
20
25
Participant
number
b
5
7
4
17
10
1
15
21
22
23
20
3
24
11
13
14
16
19
2
9
12
18
6
8
Rescaled Distance Cluster Combine
0
5
10
15
20
25
Figure(s)