dimension l800r

volume 38, pages 411-428
Perception,2009,
doi:1
0.1
068/p6032
Effectsof spectraand sound pressurelevels
on the occurrenceof the gap transferillusion
YoshitakaNakajimatl,ShimpeiTsunashima$,
TatsuroYasutakeS
TsuyoshiKuroda'lJ,
4-9-1 Shiobaru,
Departmentof Acoustic Design,GraduateSchool of Design,KyushuUniversity,
Minami-ku,Fukuoka 815-8540,Japan; e-mail:[email protected],
[email protected];
SKORG Inc.,Tokyo,Japan; #Trend Micro lnc.,Tokyo,Japan
Received29 January 2008, in revisedform 11 November2008; publishedonline 10 March 2009
experimentsto determinethe requirements
Abstract.We conducteda seriesof phenomenological
for the occurrenceof the gap transferillusion in stimuluspatternsconsistingof harmonic glides.
The gap transfer illusion is an auditory phenomenonin which a temporal gap in a long glide is
perceivedas if it were in a crossing short glide that is physically continuous.We employed
glide crossingat their temstimuluspatternsof a long and a short three-harmonic-component
poral middles,and varied the spectralslopeof eachglide independently.
The gap transferillusion
took place only when the crossingglides had the same spectralslope.To examinewhether we
could generaliseour finding we employedstimulus patterns of the same type and made more
typesof spectra.The gap transferillusiontook placeonly whenthe crossingglideshad the same
spectrumand the same sound pressurelevel (SPL) at the crossingpoint. We also used stimulus
patternsconsistingof single-componentglides,and found that the gap transfer illusion occurred
when the long and the short glide had the sameintensity,and also when the short glide was
somewhatlessintensethan the long glide.The equalityor similarity of spectraand SPLsbetween
crossingglideswas crucial for the occurrenceof the gap transferillusion.
I Introduction
The gap transfer illusion is an auditory illusion discovered by Nakajima and Sasaki
(1993).Two glide tones cross at their central positions in a typical situation. One is a
glide tone of around 1500ms or longer ascending or descending in frequency, and
the other is a glide tone of around 500 ms or shorter with the frequency moving in the
opposite direction. A temporal gap of around 100 ms is introduced into the temporal
middle of the longer glide tone, but observers often report that the gap, despite its
physical position, occurs in the shorter tone (see figure la). Nakajima et al (2000)
presented a model, the event construction model, to explain the occurrence of this
illusion. In this model, there are auditory sub-eventssuch as onsets (<) and terminations (>) (see also Kanafuka et al 2007). In stimulus patterns that can cause the gap
transfer illusion, onsets and terminations are detected at the temporal edges of the
glides (figure la). The principle of proximity, one of the Gestalt principles, is applicable
to these auditory sub-events; an onset and a termination that are close to each other
in time and frequency are likely to be connected perceptually to form an auditory
event, Because the onset and the termination preceding the gap are close to each other
in a pattern as in figure la, they are perceptually connected with each other. The onset
and the termination succeeding the gap are also connected. Because the perceptual
system tends to avoid double allocation of the same cue (Bregman 1990), once onset
cues and termination cues are allocated perceptually, they are not allocated again without a specific reason. Consequently,the residual onset and termination form a long
continuous tone (see also Remijn et al 2007).
The event construction model was supported by the fact that it was able to predict
a new auditory phenomenon, the split-off effect (Nakajima et al 2000; Remijn and
Nakajima 2005); when two glides typically longer than 500 ms have a short temporal
to eitherof the first two authors.
shouldbe addressed
fl Correspondence
T Kuroda,
Y Nakajima,
S Tsunashima,
T Yasutake
Stimulus pattern
Percept
o
o
(b)
Time
Figure 1. Examples of the gap transfer illusion (a) and the split-off effect (b). The horizontal axis
representstime, and the vertical axis frequency (on a logarithmic scale) or pitch.'<'represents
'>' representsa termination. An onset and a termination that are close to each
an onset, and
other are circled.
overlap, an illusory short tone is often perceived around the temporal middle of the
stimulus pattern, and these two glides are often perceived as if they were connected
temporally with each other, resulting in a single continuous tone covering the whole
duration of the pattern (figure 1b). The event construction model is basically a hypothesis related to the formation of auditory events and auditory streams (Nakajima 2006;
Nakajima and Sasaki 1996). Bregman (1990) presented a representative view about the
relationship between auditory events and auditory streams:
"Consider a long sound, such as a steady pure tone .... Is our experience of it built up
of smaller perceptual units [ie auditory events]? If so, where do the units start and
stop?... [Gestalt psychologists argue:] A homogeneous perceptual input contains no
units. Only when it is broken up by some sort of discontinuity does it organize itself
into units. According to this way of thinking, the perceptual unit is itself formed by a
process of perceptual organization. After being formed, units can be grouped by similarity
and other factors to form higher-order organizations [ie auditory streams]i' (page 70)
An important point is that auditory events themselves should be formed by some principles, such as the proximity of onsets and terminations. Much is known about principles
of auditory-stream formation (see Alain 2007; Bregman 1990; Carlyon 2004; Handel
1989; Micheyl et al 2007; van Noorden 1975; Snyder and Alain 2007; Warren 1999),
but little is known about the principles of auditory-event formation (see Crum and
Bregman 2006 for an example)
In the current experiments we examined whether we could extend the event construction model to multiple-component crossing patterns.We investigatedthe gap transfer
illusion employing stimulus patterns of crossing harmonic glides, while until now the
gap transfer illusion had been studied mainly with single-componentcrossing patterns
(Kanafuka et al2007; Nakajima et al 2000).
Gap transferillusion
413
We varied the spectra of glides in experiments lA and 1B. It is known that
differences of spectra or timbre facilitate auditory-stream segregation (eg Cusack and
Roberts 2000; Iverson 1995;van Noorden 1975;Singh 1987;Tougas and Bregman 1985;
Wessel 1979).For example, van Noorden (1975)reported that two sequencesof tones
that had the same pitch but different harmonics were segregated into different streams.
Wessel (1979) demonstrated that different spectral energy distributions, causing a difference in brightness, could lead to the formation of different auditory streams. Cusack
and Roberts (2000) reported that it was easier to segregatea melody sequencefrom a
distractor sequence when they consisted of sounds of different types (pure tone versus
noise). In order to understand the relationship between the gap transfer illusion and
auditory-stream formation, we examined whether spectral difference between crossing
glides affected the occurrence of the gap transfer illusion.
2 Experiment 1A
We employed stimulus patterns in which two three-harmonic-componentglides crossed
each other, and varied the spectral slope (the relative amplitude levels of spectral components; see figure 3) of each glide independently.
2.1 Method
2.1.1 Observers.Twelve observers,six males and six females aged19-24 years, participated. They were students at the Kyushu Institute of Design. All observers had received
basic training in music. Two observers had received training in technical listening for
acoustic engineers (Iwamiya et al 2003). The stimulus patterns were presented to the
left ear in six observers and to the right ear in six observers.All observershad puretone thresholds of 20 dB HL or below, at all frequenciesin the range of 250-4000 Hz,
in the ear to which the stimulus patterns were presented.
2.1.2 Stimulus patterns and apparatus.54 multiple-component crossing patterns (2 glide
directions x 3 gap conditions x 3 long-glide spectral slopesx 3 short-glide spectral slopes)
and 6 single-component crossing patterns (2 glide directions x 3 gap conditions) were
generated (60 patterns in total; see figure 2). The multiple-component crossing patterns
had a long and a short glide consisting of three harmonic components each. The long
glide was 4000 ms and ascended or descendedat a constant rate of l/3 octave s-r,
in logarithmic frequency, maintaining a harmonic relationship between components.
The short glide was 400 ms, and moved in the opposite direction at the same rate. The
long and the short glide crossedeach other at their temporal middles in the same phase.
The crossing frequencies of the harmonic components were 500, 1000, and 1500Hz.
Multiple-component, Multiple-component, Single-component,
gap-in-short-glide,
gap-in-long-glide,
no-gap,
descending:
ascending:
ascending
long-gtide +6101-6, long-gtide0/0/0,
-6101+6
short-glide
short-glide
+6101-6
N
+r
I 500
1000
500
L\-y
:
\
Tirne/ms
Figure 2. Stimuluspatternsin experimentlA. The horizontal axis representstime, and the vertical
axisfrequency(on a logarithmicscale).The thicknessof linescorresponds
to the levelof components.
414
T Kuroda,Y Nakajima,S Tsunashima,
T Yasutake
We call the stimulus patterns in which the long glide ascended, the ascending patterns,
and the stimulus patterns in which the long glide descended,the descendingpatterns.The
amplitude of each glide rose and decayedtaking l0 ms at the beginning and at the end.
The l0-ms rise and decay times were included in the duration of each glide, and a cosineshaped envelopewas applied to these amplitude transitions.
There were three 'gap'conditions: in the no-gap condition, neither of the two glides
had a gap; in the gap-in-short-glidecondition, a gap was inserted at the temporal middle
of the short glide; in the gap-in-long-glide condition, a gap was inserted at the temporal
middle of the long glide. The duration of the gaps (excluding rise and decay times) was in
all cases100 ms.
The long and the short glide had the following types of spectral slopes (figure 3):
in the 0/0/0 type, all three components of the glide were at 0 dB; in the +6101-6
type, the fundamental component was at +6 dB, the second component at 0 dB,
and the third component at -6 dB; in the -6101+6 type, the fundamental component
was at -6 dB, the second component at 0 dB, and the third component at +6 dB.
The level of 0 dB was calibrated to 65 dB SPL.
+6
6
U
Figure 3. Spectral slopes employed in experim e n t l A . T h e n u m b e r s , 1 , 2 , a n d , 3 ,o n t h e
horizontal axis represent the fundamental,
the second, and the third component, respectively.
F]
Harmonic numbers
We also generated single-component crossing patterns in order to check the stability of the gap transfer illusion as in the previous research (Nakajima et al 2000),
The long and the short single-component glide crossed at 1000 Hz at the same level
of 0 dB. The gliding speed, duration, and rise/decay time were the same as in the
multiple-component patterns.
All the stimulus patterns were generated digitally (16-bit quantisation and a sampling frequency of 44100 }Jz) and controlled by a computer (Dell Dimension L800R)
with an audio card (Sek'd Prodif 32). The stimulus patterns were presented via a DAT
recorder (Thscam DA-30 MK II), which acted as a digital-to-analog (D/A) converter;
an active low-pass filter of a cutoff frequency of 8300 Hz (NF DV-8FL) for anti-aliasing;
a parametric equaliser (Kenwood GE-100D to keep the frequency response of the system flat between 100 and 4000 Hz; an ampliher (Stax SRM-Xh); and headphones (Stax
Lambda Nova). The levels were measured with a sound-level meter (Nagano Keiki 2075)
and an artificial ear (Briiel & Kjeer 4153).
The stimulus patterns were presented to the observer in a sound-attenuating chamber,
where background noise was below 30 dBA. The observer started each presentation by
clicking on a button on the display connected to the computer, which was located
outside the chamber. There was alwavs a silent interval of I s between the click and the
onset of the pattern.
2.1.3 Procedure.We employed phenomenologicalmethods. The observer and the experimenter stayed in the sound-attenuatingchamber.The observer was allowed to listen to
each pattern as many times as he/she wanted. The observer reported his/her perceptual
impression by writing words and drawing a figure (figures) with a pencil on a blank
Gap transferillusion
415
sheet of paper, using the horizontal axis for time and the vertical axis for pitch. The
observer handed this sheet to the experimenter when he/she finished the observation
of the pattern. When there was more than one type of percept, the observer reported
all types and indicated the order of dominance if possible.When some part of the
phenomenological report was ambiguous or contradictory the experimenter asked for
more clarification, but did not mention anything about the contents of the report.
Before the experiment, the observer listened to all stimulus patterns twice in
random order by clicking on a button on the display. The experimental observations
of 60 stimulus patterns were divided into four blocks, and thus a block contained
15 experimental observations.The stimulus patterns were presented in random order.
At the beginning of each block, a warm-up of 2 observations was carried out in the
same way as in the experimental observations,and the warm-up patterns were selected
randomly from all the stimulus patterns. Breaks of a few minutes were inserted betwesn
blocks, Each block took 60 min on average and the observer completed the experiment
in3or4days.
2.2 Resultsand discussiort
Most of the observers' reports indicated the perception of a long tone and a short
tone. Typical examples of drawing descriptions are shown in figure 4. 18 reports out of
720 suggestedthe observers'analytic listening (Houtsma and Fleuren 1991)where the
observers seem to have perceived the individual harmonic components as separate
tones (see figure 4, type A). These reports were omitted from further analyses.One
report did not contain any indication of a short tone in drawing and in writing
description, and indicated that the observer perceived the stimulus pattern as two long
tones (seefigure 4, type B). This report was also omitted.
Classifiable reports
/
.
/
Unclassifiable reoorts
Figure 4. Typical examples of drawings by a few
observers. We could classi$ the continuitydiscontinuity of the long and the short tone in
reports at the top (classifiable reports), but could
not classify the continuity-discontinuity in
reports at the bottom (unclassifiable reports).
Type A of the unclassifiable reports indicated
that the observer segregated harmonic components perceptually (analytic listening). Type B
indicated that the observer heard the stimulus
pattern as two successive long tones. These
unclassifiable reports were omitted from the
present analyses.
Time
The observers' reports included sufficient information to classi0r the continuitydiscontinuity of each tone in the following categories: D-completely
discontinuous;
P-partially discontinuous (eg a decreaseof loudness around the temporal middle);
and C-completely continuous. The frequencies of reports in these categories are
indicated in table l. When more than one percept appeared in a single observation,
only the most dominant percept was classified. 5 reports were omitted from further
analyses because they contained more than one percept without clear dominance.
We checked whether the long or the short tone was more continuouS, and conducted
a sign test (two-tailed) for each stimulus pattern. The results are shown in table L The sign
test was basedon 12 comparisons for the twelve observersif no report had been omitted.
T Kuroda,Y Nakajima,S Tsunashima,
T Yasutake
Table 1. Frequency distribution of categorisedcontinuities in experiment lA.
Gap condition
Ascending
long tone
short tone
D
P C
D
0 t 2
0 1 2
0 1 2
2 0 l 0
t 2 0 0
r 2 0 0
Single-comporxentpattenx
No-gap
0
Gap-in-short-glide
0
Gap-in-long-glide
0
Spectral slope of
glide/dB
long
short
Descending
P C
sign
test
Ascending
short tone
D
D
0t2
012
012
0 12
0 11
0 12
0 12
012
0 12
D
0
0 t 2
C
P C
P C
D
12
12
ll
0
0
0
0 t2
0 r 2
0 t 2
1 0 1l
0 0 1 2
0 0 1 2
00
00
00
lz
0
0
0
0 t 2
0 1 2
0 t 2
0 0 1 2
0 0 1 2
0 0 t 2
0
0
0
0 1 2
0 r 2
0 lr
0 0 1 2
0 0 1 2
2 Q 9
0
3
2
0 1 2
l 7
0 7
t 2 0 0
6 1 4
5 0 4
lz
l2
t2 0
11 0
l2 0
P C
slgn
test
0
0
0
2
0
7
o 8
0 12
|
2
70
t2 0
10
3
0
9
1
0
5
0 9
0 t 2
0 6
7 t 2
t 2 0 0
5 1 5
0/0/0
4
- 6 1 0 1 + 6+ 6 1 0 1 - 6 8
-6/0/+6
0
0 7
0 3
0 1l
61
4
1010
l1 0 0
4
7
0
0 7
|
3
0 1 2
5 1 5
1 0 1 0
1 20 0
+6/01-6
slgn
test
l 0 l l
D
t2 0 0
t2 0 0
t2 0 0
Multiple-component
pattern,gap-in-longglide condition
0/0/0
0 0 12
ll 0 I
01010 +6/01-6 l
l
7
s2
2
-6/0/+6
3 0 7
s 0 s
0/0/0
+6101-6
-6/0/+6
P
short tone
0/0/0
0 0 t1
0 0 ll
- 6 1 0 1 + 6+ 6 1 0 1 - 6 0 0 1 2
00
t2
-6/01+6 0 012
00
t2
pattern, gap-in-short-glide
Multiple-component
condition
0/0/0
0 0 12
t2 0 0
0/010
12 0 0
+6101-6 0 0 t2
-6/0/+A
o 0 t2
t2 o 0
0/0/0
0
+6/01-6 +6101-6 0
-6101+6 0
0/0/0
0
- 6 1 0 1 + 6+ 6 1 0 1 - 6 0
-6/0/+6
0
D
long tone
slgn
test
P C
pattern, no-gapcondition
Multiple-component
0/0/0
0 012
00
0/010
00
+610/-6 0 012
-6/01+6 0 0t2
l0
0/0/0
0
+6/0/-6 +610/-6 0
-6/0/+6 0
short tone
Descending
long tone
P C
long tone
Note. The continuity of each tone was classifiedinto one of the following categories:D-discontinuous,
P-partially discontinuous, and C-continuous. The frequency of each category is indicated for
each tone. The statistical tests are also indicated to compare crossing glide tones in terms of
continuity. > : the long tone is significantly more continuous than the short tone at the 5% level
(): at the l% level). <: the short tone is significantly more continuous than the long tone at the
Sohlevel. Since some reports were omitted from the analysis, the sum of classifications in a pattern
could be below 12.
Gap transferillusion
417
When both tones belonged to the same category,the comparison was regarded as a tie
and was not included in the calculation.
ln the single-component gap-in-short-g1idepatterns, the percept of the long tone
was significantly more continuous than the percept of the short tone, indicating veridical perception. In the gap-inJong-glide patterns, the gap belonged to the long glide
physically, but the percept of the long tone was signif,rcantly more continuous than the
percept of the short tone. The occurrenceof the gap transfer illusion was thus confirmed
in the single-component patterns.
In the multiple-component gap-in-short-glide patterns, the percept of the long
tone was significantly more continuous than the percept of the short tone, indicating
veridical perception.
More complicated results appeared in the multiple-component gap-in-long-glide
patterns. when the two crossing glides had equal spectral slopes, the percept of the
long tone was always significantly more continuous than the percept of the short
tone, ie the gap transfer illusion took place. Conversely,the percept of the short tone
was significantly more continuous than the percept of the long tone in the following
conditions: (i) the ascending pattern with a long +610/-6 glide and a short -6/0/+6
glide, (ii) the ascendingpattern with a long -6/01+6 glide and a short +6lal-6
glide,
and (iii) the descending pattern with a long -610/+6 glide and a short +6/0/-6
glide. The effects of spectral difference on the perception are indicated in figure 5.
The gap transfer illusion gradually disappeared with increasing difference in spectra
between the crossing glides. These results indicate that spectral equality or similarity between crossing harmonic glides at the crossing point is crucial for the occurrence
of the gap transfer illusion.
The above finding implies a possibility that the percept of the whole pattern is
decided after the perceptual integration of the harmonic components into single complex
tones, rather than being decided by local organisations that act upon each individual
pair of crossing components. This can be a finding that constrains the neural locus
of the gap transfer illusion. It also suggests a hierarchy in the relevant 'simultaneous'
and 'sequential'integration (Bregman 1990).
o 100
u
d
a
9
7 5
o
9s o
4
.E .r\
.d
I
M
Gap transfer
Veridical
n
m
Both continuous
Both discontinuous
o
g 100
d
o
9
o
-
, J
i 5 0
6
s
o
o
O
0
Long +6/0/-6 +6/o/-6 a/0/o -6/0/+6 -6/01+6
Short -6/0/+6 0/0/0 0/0/o 0/0/0 +6/01-6
Spectralslope of glide/dB
Figure 5. The proportions of four types of percepts
in the twelve observers' reports in the gap-inJongglide patterns of experiment lA. The five spectral
conditions to be compared are indicated at the
bottom. Gap transfer: tl.re long tone was more
continuous than the short tone (the gap transfer
illusion). Veridical: the short tone was more continuous than the long tone (veridical perception).
Both continuous: both tones were continuous. Both
discontinuous: both tones were discontinuous.
Since some reports were omitted from the analysis,
the sum of the proportions in a pattern could be
below 100%.
418
T Kuroda,Y Nakajima,S Tsunashima,
T Yasutake
3 Experiment 18
We varied only spectral slopes of harmonic glides in experiment lA, so the next step
was to make more types of spectra of crossing harmonic glides in order to examine
whether we could generalise our findings. We employed stimulus patterns of crossing three-harmonic-component glides again, and varied the levels of the components
systematicallyto make more types of spectra.
3.1 Method
3.1.1Observers.Eleven observers,six males and five females aged 22-29 years, including one of the authors, participated. Ten were students and one was a post-doctoral
researcher in the Department of Acoustic Design, Kyushu University. All observers
had received basic training in music. Nine observers had received training in technical
listening for acoustic engineers (Iwamiya et al 2003). The stimulus patterns were
presented to the left ear in six observers and to the right ear in five observers.All
observers had pure-tone thresholds of 15 dB HL or below, at all frequencies in the range
of 250*4000 H4 in the ear to which the stimulus patterns were presented.
3.1.2 Stimulus patterns and apparatus. 108 patterns (2 glide directions x2 gap conditions
x 3 fundamental-component-levelcombinationsx 3 second-componentJevel
combinationsx 3
third-component : level combinations) of a long and a short three-harmonic-component
glide were generated. The duration of each glide, the gliding rate, and the crossing
frequenciesof the harmonic componentswere the same as in experiment lA. The amplitude rise and decay times were 20 ms with cosine-shapedramps.
There were two 'gap' conditions: in the gap-in-short-glide condition, a gap was
inserted at the temporal middle of the short glide; in the gap-in-long-glide condition,
a gap was inserted at the temporal middle of the long glide. The duration of the gaps
was always 100 ms.
We varied the level difference between the long and the short harmonic component
crossing at each frequency (500, 1000, and 1500Hz) in order to control the spectral
difference between the crossing glides. This manipulation was conducted in each pair
of crossing cornponents as follows: when the level combination was +61-6, the long
component of the crossing pair was at +6 dB and the short component at -6 dB;
when the level combination was 0/0, both components were at 0 dB; when the level
combination was -6/*6, the long component was at -6 dB and the short component at +6 dB. Because there were three pairs of crossing components, there were
27 (3x3x3) spectral conditions. We thus named the spectral conditions by indicating the level combinations at 500, 1000, and 1500Hz in this order. Suppose that the
fundamental components of a long ascending and a short descending glide were both
at 0 dB (0/0 dB), the corresponding second components were at *6/-6 dB, and the
corresponding third components were at -61+6 dB. Then, the stimulus pattern was
named "the ascending0f0, +6/-6, -61+6 pattern". The level of 0 dB was calibrated
to 60 dB SPL.
All the stimulus patterns wcre generated digitally (16-bit quantisation and a sampling frequency of 44100 Hz) and controlled by a computer (Frontier FXNQ-C24CO/S)
with an audio card (Sek'd Prodif PLUS). The stimulus patterns were presented via a
D/A converter (Fostex VC-8); an active low-pass filter of a cut-off frequency of 15000 Hz
(NF DVSFL) for anti-aliasing; a digital graphic equaliser (Roland RDQ-2031) to keep
the frequency response of the system flat between 100 and 4000 Hz; an amplifier (Stax
SRM-313); and headphones (Stax SR-303).The levels were measured with a sound-level
meter (Nagano Keiki 2072) and an artificial ear (Brtel & Kjaer 4153).The placement of
the equipment was the same as in experiment lA. There was always a silent interval
of 2 s between the click and the onset of the pattern.
Gap transferillusion
419
3.t.3 Procedure. The experimental procedure was the same as in experiment lA, but
the horizontal and vertical axes were drawn in advance on each paper sheet. Before the
experiment, the observer listened to all stimulus patterns once, in random order,
by clicking a button on the display. The experimental observations of 108 stimulus
patterns were divided into nine blocks, and thus a block contained 12 experimental
observations. The stimulus patterns were presented in random order. At the beginning
of each block, a warm-up of 2 observations was carried out in the same way as in
the experimental observations,and the warm-up patterns were the same as the stimulus patterns that were to be presented in the last 2 experimental observations of the
block. Breaks of a few minutes were inserted between blocks. Each block took 33 min
on averageand the observer completed the experiment in 3 to 5 days.
3.2 Resultsand discussion
There were 108reports out of I188 suggestinganalytic listening.This large number of such
reports may be due to the fact that the spectral slopes of the glides were not gradual
in some stimulus patterns (eg the +61-6, -61+6, and *6/+6 patterns). There were 17
reports out of 1188suggestingthat the observerhad perceivedthe stimulus pattern as one
long tone or two long tones. These types of reports were omitted from further analyses.
The observers' reports included sufficient information to classify the continuitydiscontinuity of each tone into the following categories:D-completely discontinuous,
P-partially discontinuous (eg a decreaseof loudness around the temporal middle),
and C-completely continuous. The frequencies of these categories are indicated in
table 2. We checked whether the long or the short tone was more continuous in each
report, and conducted a sign test (two-tailed) for each stimulus pattern. The sign test
was based on 11 comparisons for the eleven observersif no report had been omitted.
when both tones belonged to the same category, the comparison was regarded as a
tie and was not included in the calculation. The results are shown in table 2. In all
gap-in-short-glide patterns, the percept of the long tone was significantly more continuous than the percept of the short tone, thus indicating veridical perception. In the
gap-in-long-glide patterns, the gap transfer illusion appeared, but only when the long/
short components were at 0/0 dB at all crossing points. In this condition, the percept
of the long tone was significantly more continuous than that of the short tone.
We introduced a level difference always at two crossing points in experiment lA,
and this resulted in the disappearanceof the gap transfer illusion. In the present
experiment, the gap transfer illusion disappearedeven when the levels of the crossing
components differed only at a single crossing point.
There was evidence of spectral weighting; the fundamental crossing components
whose levels were equal seem to have promoted the occurrence of the gap transfer
illusion. In order to evaluate this e{fect as a whole, we analysed the data for the
gap-in-long-glide patterns as follows: the stimulus patterns were classified, according
to the level conditions (+61-6,0f0, and -61+6) of the fundamental components, into
three groups. we counted, in each group, the number of reports indicating that the
percept of the long tone was more continuous than the percept of the short tone
(the gap transfer illusion). The results are shown in table 3. We also evaluated the
effect of the second and the third components on the occurrence of the gap transfer
illusion in the same way. We found that the gap transfer illusion most frequently took
place when the levels of the fundamental componentswere equal.
When all componentsof one glide were *6 dB and all componentsof the other glide were
-6 dB (the +6/-6, +6/-6, +6/-6 patternsand the -61+6, -61+6, -6/+6 panerns),rhese
crossingglides had equal spectral slopes,but the gap transfer illusion did not take place (see
figure 6). The present data indicate that the crossing glides may have to have the same
spectrum and the same sound pressurelevel (SPL) for the occurrence of the gap transfer illusion.
420
T Kuroda,Y Nakajima,S Tsunashima,
T Yasutake
Table 2. Frequency distribution of categorised continuities in experiment lB.
Level of long/short
cornponent/dB
fundamental
second
Ascending
third
Descending
long tone
short tone
D
P
D
0
0
0
0
0
0
0
0
0
0 ll
9 0
0 1l
l1 0
0 ll
ll 0
0 11 11 0
0
9
9 0
0 1 0 1 0 0
10 0
0 l0
0 1 0 1 0 0
0 l 0 1 0 0
C
P
C
slgn
test
sign
test
long tone
short tone
D
P C
D
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 0
11
1 0
1 0
1 0
1 0
9
1 0
9
9 0 1
11 0 0
1 0 0 0
1 0 0 0
1 0 0 0
1 0 0 0
9 0 0
r 0 0 0
9 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
ll
11
1 0
ll
1l
1 0
1 0
11
ll
ll 0
11 0
1 0 0
il 0
ll 0
1 0 0
1 0 0
11 0
il 0
0
0
0
0
0
0
0
0
0
>
>
>
>
>
>
>
>
>
0
0
0
0
0
I
0
0
0
0
0
0
0
0
0
0
0
0
ll
ll
11
r 0
1l
9
ll
r0
il
11 0
ll 0
ll 0
1 0 0
l l 01 0 0
lt 0
10 0
11 0
0
0
0
0
>
>
>
>
0
0
0
0
0
>
>
>
>
P C
Gap-in- short-g lide condition
+61-6
+61-6 0/0
-61+6
+6/-6
0/0
+6/-6 0/0
-61+6
-6/+6
+6/*6
0/0
-6/+6
+6/-6
+6/-6 0/0
-61+6
0/0
0/o
+6/-6
010
-61+6
+61-6
-6/+6 0/0
-6/+6
+6/-6
+6/-6 0/o
-6/+6
-6/+6 0/0
+61-6
0/0
. -61+6
+6/-6
-61+6 010
-61+6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
ll
9
l 0
l 0
1 0
1 0
1 0
1 0
tl
tl 0
8 1
1 0 0
r 0 0
1 0 0
1 0 0
1 0 0
1 0 0
ll 0
0 0 11 11
0 0 ll
ll
0 0 ll
ll
0 0 l 0 1 0
0 0 ll
l1
0 0 ll
ll
0 0
9
9
0 0 11 tl
0 0 r 0 r 0
0
0
0
0
0
0
0
0
0
>
Note. The continuity of each tone was classifiedinto one of the following categories:D-discontinuous,
P-partially discontinuous, and C-continuous. The frequency of each category is indicated
for each tone. The results of statistical tests are also indicated to compare crossing glide tones
Table 3. Effects of the levels of components on the occurrence of the gap transfer illusion.
kvel
condition/dB
+61-6
010
-6/+6
Component
fundamental (l)
second (2)
third (3)
45
80
30
53
68
57
J+
27
t ,
Note. The frequency of reports indicating that, in the gap-in-long-glide condition, the long glide
was perceived as more continuous than the short glide (the gap transfer illusion) is indicated.
(1) The stimulus patterns were classified into three groups according to the level conditions of
their fundamental components. (2) The stimulus patterns were classified into three groups according
to the level conditions of their second components. (3) The stimulus patterns were classified into
three groups according to the level conditions of their third components. Thus, the maximum value
in each cell is 198 (2 glide directions x 9 level conditions x 11 observers).
Gap transferillusion
Table 2 continued.
Level of long/short
component/dB
Ascending
Descending
long tone
short tone
D
P
C
D
5
6
7
5
3
6
3
4
6
0
0
0
0
0
0
0
I
0
4
4
3
5
5
4
4
3
3
4
1
2
3
0
I
2
3
3
+ 6 / - 65
4
+ 6 / - 6 0 / 0
- 6 / + 65
+ 6 / - 66
-6/+60/0 0/0
4
- 6 1 + 64
+ 6 / - 6 3
- 6 / + 6 0 / 0 4
- 6 1 + 6 2
fundamental
second
third
slgn
test
long tone
short tone
P C
D
P C
D
0
0
0
0
0
1
0
0
0
4
6
8
4
3
8
5
7
8
7
4
6
5
4
4
4
4
6
0
1
0
0
1
|
0
0
0
4
3
3
5
5
3
4
4
3
6
2
2
7
6
2
|
2
1
0
0
0
0
0
1
0
0
0
0
I
0
I
0
0
0
0
0
5
6 0 3
7
7 0 2
2 r 6
7
6
6 1 3
l0 1 0 0 0
1 0 8
8
7
4 0 5
4 0 5
6
7
| 0 9
5
3
3
4
0
0
0
|
5
6
6
6
4
6
4
6
0 6
0 3
0 5
0 5
4
I
4
4
0
0
0
0
5
6
6
6
1 0 8
2 0 5
4 0 6
2 0 8
0
A
0
0
0
0
0
0
0
4
6
5
4
5
5
6
6
7
5 0
6 0
' 7
0
5 0
4 0
4 0
s 0
6 0
3 0
4
4
3
4
s
5
s
4
7
2 0 7
3 0 7
1 0 9
2 0 7
3 06
1 0 8
2 0 8
1 0 9
r 0 9
sign
test
P C
Gap-in- long-glide condition
+6/-6
+6/-6 0/0
-6/+6
+6/-6 010
+6/-6
010
-6/+6
+61-6
-61+6 010
-6/+6
+61-6
+6/-6 0/0
-61+6
0/0
+6/-6
0/0
-6/+6
+61- 6
-6/+6 0/0
-6/+6
0/0
5
4
2
6
5
|
2
1
1
2 0 7
3 0 7
1 0 9
1 0 9
207
0 0 9
2 0 7
1 0 9
1 t ' . 7
5
6
7
3
4
5
7
6
8
in terms of continuity. > : the long tone is significantlymore continuousthan the short tone
atthe 5o/olevel(): at the l% level).Sincesomereportswereomittedfrom the analysis,the sum
ofclassificationsin a pattern could be below ll.
The continuity illusion (Ciocca and Bregman 1987;Dannenbring 1976;Miller and
Licklider 1950; van Noorden 1975;Petkov eI al 2007; Riecke et al 2008; Sugita 1997;
Thurlow 1957;Warren 1999;Warren et al 1972,1994) seemsto have appeared in some
cases. In a typical case of the continuity illusion, a sound with a temporal gap is
perceived as continuous when the gap is filled with a sound more intense than the
discontinuous sound. In the present experiment, both the long and the short harmonic
glides were perceived as continuous in many cases in the gap-in-long-glide patterns
when the short glide was 12 dB more intense than the long glide (ie the -61+6,
-6/+6, -6/+6 patterns-figure 6). This level difference should have been enough to
produce the continuiry illusion in the long glide (Riecke et al 2008). To investigate
this issue, we conducted another experiment to examine how SPL difference between
crossing single-component glides affects the perceptual continuity of the glides.
T Kuroda,Y Nakajima,S Tsunashima,
T Yasutake
+zz
o 100
{
T
N
9 7 5
Both continuous
d
Both discontinuous
d
.E rs
! - -
Figure 6. The proportions of four types of percepts in the eleven observers' reports in the
gap-in-long-glide patterns of experiment 1B.
The three spectral conditions to be compared
are indicated at the bottom. Gap transfer: the
long tone was more continuous than the short
tone (the gap transfer illusion). Veridical: the
short tone was more continuous than the long
tone (veridical perception). Both continuous:
both tones were continuous. Both discontinuous: both tones were discontinuous. Since
some reports were omitted from the analysis,
the sum of the proportions in a pattern could
be below 100%.
a
o lon
d
-
Veridical
n
m
9 5 0
9
Gap transfer
-
o
8 5 0
a
o
A
0
Third +6/-6
Second +6/-6
Fundamental +61-6
0/0
0/0
0/0
-61+6
-6/+6
-61+6
Level of long/short component/dB
4 Experiment 2
In order to examine the effect of SPL difference on the perceptual continuity of crossing
glides, we employed stimulus patterns consisting of crossing single-componentglides.
4.1 Method
4.1.1 Observers. TWelve observers, five males and seven females, aged 22*28 years,
participated. Ten observers were students and one was a post-doctoral researcherin
the Department of Acoustic Design, Kyushu University. One observer was an office
worker. Seven of these observers participated also in experiment 18 (four participated in this experiment after experiment lB, and three before experiment 1B). Eleven
observers had received basic training in music. Nine observers had received training
in technical listening for acoustic engineers (Iwamiya et al 2003). The stimulus patterns
were presented to the left ear in six observers and to the right ear in six observers.
A11 observers had pure-tone thresholds of 15 dB HL or below, at all frequencies in the
range of 250-4000 Hz,in the ear to which the stimulus patterns were presented.
4.1.2 Stimulus patterns and apparatus.60 stimulus patterns (2 glide directions x 3 crossing frequenciesx 2 gap conditions x 5 glide level combinations) of a long and a short
single-componentglides were generated.The long glide lasted 4000 ms and ascendedor
descendedat a constant rate of 1/3 octave s-' in logarithmic frequency.The short glide
lasted 400 ms and moved in the opposite direction at the same rate. The amplitude rise
and decay times were 20 ms with cosine-shapedramps.
The long and the short glides crossed each other at their temporal middles in the
same phase. The crossing frequency of the long and the short glide was at 500, 1000,
or 1500Hz. Thus, there were three 'crossing-frequency'conditions.
There were two 'gap'conditions: in the gap-in-short-glide condition, a gap was inserted
at the temporal middle of the short glide; in the gap-in-long-glide condition, a gap was
inserted at the temporal middle of the long glide. The duration of the gaps was always
100 ms.
Gap transferillusion
423
The levels of the long/short glides were varied simultaneously from *6/-6 dB to
-61+6 dB in steps of -31+3dB, resulting in five'level'conditions. The level of 0 dB
was calibrated to 60 dB SPL.
The apparatus was the same as in experiment lB.
4.1.3 Procedure. The experimental procedure was the same as in experiment 18. The
experimental observations of 60 stimulus patterns were divided into four blocks, and
thus a block contained 15 experimental observations. The stimulus patterns were presented in random order. At the beginning of each block, a warm-up of 2 observations
was carried out in the same way as in the experimental observations,and the warm-up
Table 4. Frequencydistribution of categorisedcontinuitiesin experiment2.
Crossing
frequency
lHz
Level of
long/short
glide/dB
Ascending
Descending
Long tone
Short tone
D
P
C
D
+6/-6
+3/-3
0la
-31+3
-61+6
0
0
0
0
0
0
0
0
l
0
1 2
1 2
t2
ll
t2
8 0
1 0 0
t2 0
t2 0
t2 0
1000
+61-6
+31-3
010
-31+3
-61+6
0
0
0
0
0
0
0
0
0
0
1 2
1 2
t2
t2
12
7 0
1 0 0
t2 0
12 0
12 0
r500
+61-6
+31-3
0/0
-3/+3
-6/+6
0
0
0
0
I
0
0
0
0
0
1 2
t2
12
t2
1l
8 0
11 0
t2 0
t2 0
t2 0
Sign
P C
Long tone
Short tone
D
P C
D
0
0
0
0
I
0
0
0
0
0
t 2
t2
t 2
t 2
ll
9 0
11 I
t 2 0
1 20
t2 0
0
0
0
l
l
0
0
0
0
0
r 2
t2
t 2
l1
lt
8 0
lt 0
1 20
t2 0
12 0
0
0
0
l
2
0
0
0
0
0
t 2
t 2
t 2
lr
t0
9
t 2
t 2
12
12
6 r
0
0
0
3 0
4 |
Z
0
0
2 0
2 0
5
il
12
t 0
9
8 0 4
t2 0 0
120 0
4 3
5
I 0 ll
7
r 0
t 2
r 0
10
lt 0 |
i l 0
r
t 2 0 0
3 l
8
I 0 11
P
Sign
C
Gap-in- short-g lide condition
+
z
0
0
0
5
z
0
0
0
.I
I
0
0
0
0
0
0
0
0
3
0
0
0
0
4
l
0
0
0
3
0
0
0
0
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
Gap-in- long-glide condi tion
1000
+61-6
+3/-3
0/0
-3/+3
-6/+6
6
1
5
8 1
I
0 l1
ll 0
l
0 0 1 2 1 00 2
0 0 t 2 s1 6
I
0 1l
2 0 1 0
+61-6
+31-3
0/0
-31+3
*61+6
5
1
6
90
3
4
1
1
9 U
J
0 0 t 2 t 2 0 0
2 0 1 0 3 1
8
2 0 1 0
I 0 11
+6/-6
3
2
0
2
2
r?/-?
l 500
010
-61+6
I
8
0 10
0 ll
0 l 0
0 1 0
ll
ll
ll
5
1
0
l
0
l
0 0
0
0 1l
3
7
2
5
r 9
ll 0 I
0t2
t2 0 0
0 t 2
1 20 0
0 1 0 4 t
7
0 7
I 0 ll
Note. The continuity of each tone was classifiedinto one of the following categories:D-discontinuous,
P-partially discontinuous, and C-continuous. The frequency of each categofy is indicated for
each tone. The results of statistical tests are also indicated to compare crossingglide tones in terms
of continuity. >: the long tone is significantly more continuous than the short tone at the 5oZleve!
(): at the 1% level). Since a few reports were omitted from the analysis, the sum of classifications
in a pattern could be below 12.
424
T Kuroda,Y Nakaiima,S Tsunashima,
T Yasutake
patterns were the same as the stimulus patterns that were to be presented in the last
2 observations of the block. Breaks of a few minutes were inserted between blocks.
Each block took 34 min on average and the observer completed the experiment in one
or two days.
4.2 Resultsand discussion
A single report out of 720 tndicated that two short tones were perceived simultaneously. This report was omitted from further analyses.
The observers' reports included sufficient information to classify the continuitydiscontinuity of each tone into the following categories:D-completely discontinuous,
P-partially
discontinuous (eg a decrease of loudness around the temporal middle),
and C-completely continuous. The frequencies of these categories are indicated in
table 4. We checked whether the long or the short tone was more continuous in each
report, and conducted a sign test (two-tailed) for each stimulus pattern. The results
are shown in table 4. The sign test was based on 12 comparisons for the twelve observers if no report had been omitted. When both tones belonged to the same category,
the comparison was regarded as a tie and was not included in the calculation.
In all the percepts of the gap-in-short-glide patterns, the long tone was significantly
more continuous than the short tone, indicating veridical perception. In the gap-inlong-glide patterns, however, the results were more complicated. when the long and
the short glides were at the same level (0/0), the gap transfer illusion appeared always
clearly. The illusion also tended to take place when the short glide was less intense,
especially in +31-3 conditions. When the short glide was more intense, however,
the illusion did not take place, exaept in one condition (the ascendine -3/+3 500-Hzcrossingcondition). Reported perceptsof the gap-in-long-glidel000-Hz-crossingpatterns
are shown in figure 7. It is to be noted that both the long glide and the short glide
tended to be perceived as continuous when the short glide was more intense.
o
bo
100
H
zs
o
i 5 u
I
Gaptransfer
ffi
Veridical
I
notncontinuous
ffi notfrdiscontinuous
bo
.= 1<
p - J
o
U
100
o
bo
(€
o
9
--
o
9 5 n
6 - "
bo
€ r s
o
o
U
+6/-6 +3/-3
010 -31+3 -6/+6
Level of long/short glide/dB
Figure 7. The proportions of four types of percepts
in the twelve observers' reports in the gap-inlong-glide patterns of experiment 2. The glides
crossed at 1000 Hz. The five level conditions to
be compared are indicated at the bottom. Gap
transfer: the long tone was more continuous
than the short tone (the gap transfer iltusion).
Veridical: the short tone was more continuous
than the long tone (veridical perception). Both
continuous:both toneswere continuous.Both discontinuous: both tones were discontinuous.
Gap transferillusion
5 General discussion
We investigatedwhether the gap transfer illusion could take place with crossing glides
each consisting of three harmonic components. This was planned as a first step in
the study of this illusion in contexts closer to our everyday life, where almost all the
sounds have more than one component. We thus focus the present discussion upon
the perception of stimulus patterns in which short glides were physically continuous
and long glides were discontinuous (gap-in-long-glidepatterns).
Major findings in the present study are: (i) the gap transfer illusion can take place
in stimulus patterns of crossing harmonic glides, but it disappears when the crossing
glides differ in their spectra at the crossing point; (ii) the gap transfer illusion takes
place when the long glide and the short glide have the same intensity, and also when
the short glide is somewhat less intense than the long glide.
We found that the gap transfer illusion takes place in a stable manner when the
crossing glides have the same spectrum and SPL at the crossing point. The event
construction model (Nakajima et al 2000) is based on the assumption that an onset
and a termination that are close to each other in time and frequency are connected
to each other perceptually even when they belong to different sounds physically. This
model worked, but not in a simple manner, in the present experimental situation.
When the spectra of the crossing glides were diflerent at the crossing point, the
short glide tended to be perceived as continuous, ie veridically. Even when onsets and
terminations were close to each other in time and frequency, it seemed difficult for
them to be connected perceptualiy. The auditory system seems to avoid constructing
an auditory event that would require big and rapid spectral changes.
Both the long glide and the short glide were perceived as continuous when the short
glide was sufficiently more intense than the long glide, and the perceived continuity of
the long glide in this case can be considered a special case of the continuity illusion.
Howeveq the perceived continuity of the long glide in the gap transfer illusion should
occur in a different way. Warren et al (1994)assumedthat, when the continuity illusion
takes place, a portion of the sound energy of the inserted sound is reallocated to fill
the gap of the discontinuous sound. The basic framework of this idea has been widely
accepted. The gap transfer illusion took place, however, even when the short glide
was 6 dB (or 12 dB in some cases) less intense than the long glide (table 4). It is
difficult to assume that there was enough sound energy of the short glide to fill the
gap in the long glide in Such cases. If part of the sound energy of the short glide
were reallocated for bridging the gap in the long glide, there should appear an intensity
dip of 100 ms and 6 dB, or more, at the temporal middle of the long glide.{r) It is
therefore difficult to assume that the above-mentioned mechanism of the continuity
illusion worked also in the gap transfer illusion. We do not yet know much about
what types of percepts could appear in this kind of paradigm. As the next step we
propose to investigate how the perception of crossing-glide patterns changes when the
relative levels of the crossing components are varied more systematically.
The gap transfer illusion disappearedwhen the short glide was much less intense
than the long glide. The results in this case were not simple, but the continuity/
discontinuity of each glide was determined rather clearly in each individual report.
(r)In order to examineobservers'ability
to detectintensitydips,we conductedan informalexperiment employingglides that had the samephysicalparametersas in experiment2. We employed
glidesof 4000ms with an intensitydip of 100ms and 6 dB at their
ascendingand descending
temporalmiddle,wherethe instantaneous
frequencywas 500,1000,or 1500Hz. As a result,completeor partial discontinuity(a gap or a decreaseof loudness)appearedin 37 out of 42 reportsby
sevenobservers.
Thus, the dip of 6 dB shouldbe detectedand reportedeasily.In order to examine
the perceivedcontinuity of the long glide in the gap transferillusion more precisely,we need to
carryout an experimentemployingcrossing-glide
pairsand singleglidesin the samesessions.
z+zo
T Kuroda,Y Nakajima,S Tsunashima,
T Yasutake
Few reports indicated partial discontinuity. This indicates that the sound energy at
the temporal middle of the stimulus patterns was rarely split between the long tone
and the short tone in the present case when the continuity of these tones was determined perceptually.
The auditory system may have chosen whether tones were continuous or discontinuous without reallocating sound energy. In choosing these alternatives, the auditory
system may have even ignored part of the sound energy at the temporal middle of the
stimulus patterns in some cases;some reports indicated that both the long glide and
the short glide were perceived as completely discontinuous when the short glide was
12 dB less intense than the long glide (figures 6 and 7). It is possible that part of the
sound energy is not reallocated to any tones in some stimulus conditions as was demonstrated by recent studies employing temporal sequencesof tones and vowels (Lee and
Shinn-Cunningham 2008; Shinn-Cunningham et al 2007).
On the other hand, reallocation of sound energy may have taken place when both
glides were perceived as continuous in a condition where the short glide was more
intense than the long glide; a portion of the sound energy of the short glide may have
been reallocated to fill the gap of the long glide. There should be an alternative
explanation based on the event construction model, however, if we assume that the
termination and the onset that bound the gap are masked by the more intense short
glide. Since the termination and the onset bounding the gap disappear perceptually,
only the onset and the termination of the short glide are left around the temporal
middle of the pattern. Because they are close to each other, they form a short continuous tone. The residual onset and termination of the pattern form a long continuous
tone. Note that this explanation works also for typical cases of the continuity illusion.
It is necessary to further investigate the effects of SPL difference in order to improve
the event construction model to make this a more comprehensive theory.
A few studies revealedthe neurophysiologicalbasis of the continuity illusion (Petkov
et al 2007; Sugita 1997).Neurophysiological approachesmay help us to understand the
mechanism of the gap transfer illusion, and they may give clues to understand
the relationship between the perceived continuity of the long glide in the gap transfer
illusion and the perceived continuity in the continuity illusion. Since the event construction model explains the gap transfer illusion in terms of the proximity of onsets
and terminations, we assume that the gap transfer illusion is attributed to neural
phasic responses,such as'onset responsesand offset responses.Also the continuity
illusion can be readily attributed to these responses (Petkov et a\ 2007). In order to
explain the gap transfer illusion, it is necessaryto find neural correlates of the proximity,
and it is necessaryto examine how the onset responsesand the offset responsesare
connected to each other to construct auditory events.
The preference for creating auditory events based upon onsets and terminations
connected with similar spectra and levels may be an example of the Gestalt principle
of similarity. The gap transfer illusion may be a good material to investigate Gestalt
principles in a psychophysicalframework, which is very important to make studies of
auditory organisation more fruitful.
Acknowledgments.
The researchwas supportedby grantsfrom the JapanSocietyfor the Promotion ofScience(19103003
in the fiscalyears2007-2011,20653054
in the fiscalyears2008-2010
and 20330152
in the fiscalyears2008-2012).We thank Kazuo Ueda,JonathanGoodacre,Elvira
P6rez,and three anonymousreviewersfor their valuablesuggestionsand commentson an earlier
versionof the manuscript.
Gap transferillusion
427
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