PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Loudness of ramped and damped sounds that are temporally
shifted across ears
Josef SCHLITTENLACHER1; Robbie ZHAO; Brian C. J. MOORE2
University of Cambridge, UKABSTRACT
In a previous study we have shown that amplitude-modulated sounds are louder when their modulation is outof phase across the two ears than when it is in phase. The level difference required for equal loudness (LDEL)of sounds with diotic presentation and an interaural modulation phase difference of 180° was about 2 dB.
This could be explained by a loudness model where binaural summation lags behind binaural inhibition. The
present study investigated the binaural loudness of ramped and damped sounds in a similar manner. Stimuli
consisted of trains of 1000-Hz tone pulses with linear rise and fall times with ratios of 1:10 (damped sounds)or 10:1 (ramped sounds). Stimuli contained 28 55-ms pulses, 14 110-ms pulses or 7 220-ms pulses, resulting
in a stimulus duration of 1540 ms plus half the pulse duration for the interaurally shifted stimuli. The LDEL
between diotic and interaurally shifted stimuli was close to 0 dB for all of these conditions. For a single 220ms pulse, the LDEL was 1.4 dB for damped sounds, and 3.0 dB for ramped sounds, the diotic sounds being
louder. The difference between a single pulse and a pulse train suggests differences between short-term andlong-term loudness judgments.
Keywords: loudness, time-varying, binaural

1. INTRODUCTION
The loudness of a sound that is presented to both ears is greater than when it is presented to oneear. This effect is called binaural loudness summation. If this summation was perfect in terms ofloudness, the level difference required for equal loudness (LDEL) between a tone that is presentedmonaurally and a tone that is presented diotically would be about 10 dB. However, recent findings
suggest that this LDEL is about 5-6 dB (e.g. (1, 2), see (3, 4) for reviews). The effect of non-perfectbinaural summation has been explained and modelled by binaural inhibition, based on the assumptionthat a sound in one ear reduces the internal response to a sound in the other ear (3, 5).
The perceived loudness of a time-varying sound depends on the duration over which it is judged.
In one loudness model (6), three aspects of loudness are calculated: [A] Instantaneous loudness, whichis calculated from a single very short sample (frame) of the sound and is assumed not to be available
to conscious perception; [B] Short-term loudness, which is the loudness of a short segment of sound,such as a syllable; and [C] long-term loudness, which is the loudness judged over longer durations,such as a sentence. Imaging studies have provided evidence for [A] and [B] at different stage s of theauditory pathway (7, 8). However, it is not known at which stage binaural inhibition and binauralsummation take place. Real-world sounds can differ in both spectrum and time pattern across ears,
and predictions of loudness depend on the sequence of implementation of binaural inhibition andbinaural summation.
Figure 1 shows a block diagram of the Cambridge loudness model for binaural time-varying sounds(9, 10). The model implements binaural inhibition after the calculation of short -term loudness for eachear. In contrast, long-term loudness is calculated from the inhibited short-term loudness for each ear,and this involves an additional stage of temporal smoothing after binaural inhibition has been applied.
With this implementation, the model correctly predicts that amplitude -modulated (AM) sounds whosemodulation phase is shifted by 180° across the two ears have a greater long-term loudness than sounds
1
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js2251@cam.ac.uk
bcjm@cam.ac.uk

with in-phase AM. The LDEL for such sounds depends on the modulation frequency and is up to 2dB.

Figure 1 – Block diagram of the Cambridge loudness model
It has been shown previously that ramped sound (with a slow rise and a fast fall) are perceived as
louder than damped sounds (with a fast rise and a slow fall) when the overall levels of the sounds arematched (11). However, we are not aware of any studies of the loudness of ramped and damped sounds
when the sounds are not identical at the two ears. In the present study we assessed the loudness oftrains of tone pulses with different pulse durations that were presented diotically or shifted by half apulse duration across ears. The pulses were either ramped or damped. The duration of the whole pulse
train was slightly longer than 1.5 s (see section 2.3 for details), probably leading to a decision basedon long-term loudness. Loudness was also assessed for a single pulse with a duration of 220 ms. For
this duration the decision is more likely to be based on short-term loudness.

2. METHOD
2.1 Subjects
Sixteen subjects, aged 18 to 22 years, ten of them male and six female, participated in theexperiment. All of them had normal hearing, with audiometric thresholds not exceeding 20 dB HL
between 125 and 8000 Hz in both ears.
2.2 Apparatus
Stimuli were generated digitally at a sampling rate of 44100 Hz, D/A -converted by an M-Audio
Delta 44 audio interface (Cumberland, RI) and passed through manual attenuators (Hatfield, 2125,Hatfield, UK) to a Sennheiser HD580 headset (Wedemark, Germany).
2.3 Stimuli
Stimuli consisted of tone pulses with durations of 55, 110 or 220 ms. The carrier was a 1 -kHz puretone. The tone pulses had linear rise and fall times with a ratio of 1:10 (damped) or 10:1 (ramped),i.e. 5 ms rise and 50 ms fall, 50 ms rise and 5 ms fall, 10 ms rise and 100 ms fall, 100 ms rise and 10
ms fall, 20 ms rise and 200 ms fall, and 200 ms rise and 20 ms fall. The tone pulses were concatenatedto form a train with a duration of 1540 ms, formed of 28 55-ms pulses, 14 110-ms pulses or seven7689

220-ms pulses. A single 220-ms pulse was also used. All stimuli were presented diotically or shiftedby half a pulse duration across ears. In the latter case, the total stimulus duration w as half a pulse
duration longer.
2.4 Procedure
Subjects compared the loudness of the diotic and shifted sounds for each pulse duration and pulse
shape, resulting in eight runs per subject. A two-alternative-forced-choice task was used. The task was
to decide whether the first or second stimulus was louder. A run consisted of four interleaved tracks,
each using a 1-up/1-down adaptive procedure (12). For two of the tracks, the diotic sound was thestandard stimulus and the shifted sound was the comparison stimulus whose level was varied fromtrial to trial. For the other two tracks, the shifted sound was the standard and the diotic sound was thecomparison. The peak level of the standard was fixed at 70 dB SPL. For each type of standard (dioticor shifted), one track started with a comparison level 10 dB above that of the standard and the otherstarted with a comparison level 10 dB below that of the standard. The order of the standard andcomparison stimuli was random. For each trial, the level of both stimuli was changed by the sameamount, drawn from a uniform distribution between -5 and +5 dB, to encourage subjects to compare
the stimuli within a trial rather than using their long-term memory across trials.
On a given trial, if the comparison was judged as louder than the standard, its level was decreased;otherwise its level was increased. For each track, the change in level was 5 dB until a revers al occurred,
3 dB until a second reversal occurred, and 1 dB thereafter. A run terminated when all tracks reached
the eighth reversal. The level of the comparison was averaged across the last four reversals for eachtrack and then averaged across the four tracks (with the sign adjusted so that the mean reflected thelevel of the shifted sound minus the level of the comparison sound) to yield the LDEL.

3. RESULTS
The results are shown in Figure 2. Circles, connected by a solid line for the pulse -train conditions,show results for damped pulses. Squares, connected by a dashed line for the pulse -train conditions,show results for ramped pulses. The LDELs were between -0.7 and 0.7 dB for the six pulse-train
conditions. For the single 220-ms pulses, the LDEL was positive at 1.4 dB for the damped pulse and
3.0 dB for the ramped pulse, meaning that at equal levels the diotic sound would be louder.

Figure 2 – Level difference required for equal loudness (LDEL) of sounds that were temporally
shifted between the two ears by half a pulse duration and diotic sounds. Circles show means fordamped pulse shapes, squares for ramped pulse shapes, and error bars the standard error of themean. Open and filled grey symbols show predictions of the Cambridge loudness model based onlong-term and short-term loudness, respectively. Negative values indicate that the shifted sounds
would be louder at equal root-mean-square levels.

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The results for the single pulses are close to the predictions based on short-term loudness. The
results for the pulse trains are between the predictions for short-term loudness and long-term loudness,with a tendency to be closer to long-term loudness with decreasing pulse duration.
A two-way 3x2 (duration x pulse shape) within-subjects analysis of variance on the LDEL valuesfor the pulse trains yielded a significant effect of duration, F(2,30) = 5.12, p < 0.05, and a significant
effect of pulse shape, F(1,15) = 5.20, p < 0.05. The LDEL was larger for the longest duration and forthe damped than for the ramped sounds. The interaction was not significant, F(2,30) = 1.16, p = 0.33.
A two-way 2x2 (number of pulses x pulse shape) within-subjects analysis of variance for theconditions with a pulse duration of 220 ms yielded a significant effect of the number of pulses,
F(1,15) = 69.1, p < 0.001. The LDEL was larger for the single pulse than for seven pulses. The effectof pulse shape was not significant, F(1,15) = 1.85, p = 0.19. The interaction was significant,F(1,15) = 11.9, p < 0.01. For one pulse, the LDEL was larger for the ramped than for the damped
sound, while for seven pulses the reverse was the case.

4. DISCUSSION
The loudness of ramped and damped sounds had been found previously to be predicted well by anearly version of the Cambridge loudness model (13). These authors used stimuli with durationsbetween 10 ms and 500 ms and found short-term loudness to predict the results better than long-term
loudness (open symbols without error bars in figure 2), although they argued that long-term loudness
might be better for longer sounds. In the present experiment the model predicts negative LDELs if thesubjects based their estimates on long-term loudness, because binaural loudness summation isimplemented after binaural inhibition, which involves an additional stage of temporal smoot hing of
the inhibited short-term loudness for each ear. In contrast, the short-term loudness for each ear is
calculated prior to the application of binaural inhibition, and this leads to the prediction of a positive
LDEL if loudness estimates are based on short-term loudness (grey symbols without error bars infigure 2). The clearly positive LDEL values for the single 220-ms pulse suggest that subjects usedshort-term loudness for this stimulus. For the pulse train with a total duration of about 1.5 s, the LDEL
values are not clearly positive or negative. A possible reason is that for sequences of tone pulses,
subjects sometimes based their judgments on the loudness of the individual pulses and sometimes on
the overall loudness of the whole sounds, leading to a very small net effect.
Just as ramped and damped sounds differ in loudness in a manner that depends on the duration of
the sounds (13, 14), the LDEL between sounds that were temporally shifted between the two ears anddiotic sounds also depended significantly on pulse shape; the LDEL values were sl ightly larger forthe damped than for the ramped sounds.
The most important findings of the present study are:(a) For a single tone pulse, the LDELs values were positive, indicating that at equal levels thediotic sounds would be louder than the shifted sounds. This result can be explained assumingthat loudness judgments for the single pulse were based on short-term loudness, and thatbinaural inhibition is applied after the determination of short-term loudness, as assumed in theCambridge loudness model (9, 10).
(b) LDEL values for the trains of pulses were close to zero, but increased slightly for the longest
pulse duration. It is possible that for these sounds subjects sometimes base d their judgmentson the loudness of the individual pulses and sometimes on the overall loudness of the wholesounds.

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