![(Color online) Schematic representation of the two experiments conducted in the present study where the duration of rising-and fallingintensity ramps was manipulated in different ways [as indicated by the arrows, a rising ramp taken here, as an example, could be stretched from (1) to (2)]. (a) Experiment 1: The ramps were " stretched " in time while keeping their dynamics constant. (b) Experiment 2: The ramps were stretched in time while keeping their slope constant. A rising ramp is taken as an example here, but the similar operation was realized on falling ramps.](https://www.researchgate.net/profile/Emmanuel-Ponsot/publication/318550014/figure/fig1/AS:519625352978439@1500899746800/Color-online-Schematic-representation-of-the-two-experiments-conducted-in-the-present_Q320.jpg)
Content uploaded by Emmanuel Ponsot
Author content
All content in this area was uploaded by Emmanuel Ponsot on Oct 24, 2017
Content may be subject to copyright.
Global loudness of rising- and falling-intensity tones: How
temporal profile characteristics shape overall judgments
Emmanuel Ponsot,
1,a)
Patrick Susini,
1
and Sabine Meunier
2
1
STMS Laboratory (IRCAM, CNRS, UPMC), 1 place Igor Stravinsky, 75004 Paris, France
2
Laboratoire de M!ecanique et d’acoustique-CNRS, Unit!e Propre de Recherche 7051, Aix-Marseille
University, Centrale Marseille, 4 Impasse Nikola Tesla, CS-40006 Marseille Cedex 13, France
(Received 18 January 2017; revised 19 June 2017; accepted 22 June 2017; published online 19 July
2017)
The mechanisms underlying global loudness judgments of rising- or falling-intensity tones were
further investigated in two magnitude estimation experiments. By manipulating the temporal char-
acteristics of such stimuli, it was examined whether judgments could be accounted for by an inte-
gration of their loudest portion over a certain temporal window associated to a “decay mechanism”
downsizing this integration over time for falling ramps. In experiment 1, 1-kHz intensity-ramps
were stretched in time between 1 and 16 s keeping their dynamics (difference between maximum
and minimum levels) unchanged. While global loudness of rising tones increased up to 6 s, evalua-
tions of falling tones increased at a weaker rate and slightly decayed between 6 and 16 s, resulting
in significant differences between the two patterns. In experiment 2, ramps were stretched in time
between 2 and 12 s keeping their slopes (rate of change in dB/s) unchanged. In this context, the
main effect of duration became non-significant and the interaction between the two profiles
remained, although the decay of falling tones was not significant. These results qualitatively sup-
port the view that the global loudness computation of intensity-ramps involves an integration of
their loudest portions; the presence of a decay mechanism could, however, not be attested.
V
C2017 Acoustical Society of America.[http://dx.doi.org/10.1121/1.4991901]
[JFL] Pages: 256–267
I. INTRODUCTION
Global loudness, which has been defined as the overall
impression of loudness of stimuli varying in loudness across
time (e.g., Susini et al., 2007), is an important psychoacous-
tical variable when dealing with time scales of several sec-
onds. For instance, the industry and the media need to
predict and, therefore, to control, as accurately as possible,
how loud a sound will be perceived. The sound sequences
considered are generally long (at least a few seconds) and
strongly vary in level through time, e.g., the passing-by of an
airplane, an advertisement broadcasted on the radio. Overall
indicators are thus required to evaluate their global loudness,
i.e., listeners’ overall impressions; the primary purpose is
often to control their perceived annoyance, which strongly
relies on this variable (see Dittrich and Oberfeld, 2009).
Psychoacoustical experiments investigating dynamic loud-
ness perception of sound sequences lasting several seconds
have shown that global loudness does not correspond to an
average of momentary loudness, i.e., to the average loudness
experienced during the stimulus, but is rather strongly influ-
enced by the loudest events (e.g., Kuwano and Namba,
1985;Gottschling, 1999;Kuwano et al., 2003;Susini et al.,
2002, 2007). Current indicators of global loudness are all
based on this outcome. In the media, the overall loudness of
a program is simply taken as the integration of its momen-
tary loudness values (predicted by simplified auditory mod-
els), which exceed a certain threshold taken as the mean
loudness value minus ten units (see ITU-R BS.1770, 2006;
EBU-Recommendation, 2011). Other indicators employed in
the industry, such as L
Aeq
, also rely on the assumption that
global loudness could be evaluated by averaging the physical
energy of the stimulus (this issue is discussed in Oberfeld
and Plank, 2011). Even in the context of more basic psycho-
acoustics, Zwicker and Fastl (1999) proposed to use the
maximum value or a certain percentile (e.g., 95th) of the
inferred loudness temporal distribution as a predictor.
Glasberg and Moore (2002) suggested using the peak of the
“short-term loudness” (STL) or the “long-term loudness”
(LTL) time series predicted by their model to estimate the
overall loudness of time-varying sounds. However, recent
studies conducted with very basic sounds have pointed out a
limitation to such assumptions. For instance, it has been
shown that 1-kHz tones increasing linearly in level during 2-
s over a 15-dB dynamics (i.e., range of level variation) are
consistently judged about 3–4 dB louder than their time-
reversed, falling versions, and it was demonstrated that this
asymmetry could not be accounted for by current loudness
models (Ponsot et al., 2015a). It was, in all cases, signifi-
cantly underestimated. Neither the maximum value of STL
or LTL outputs (which is the operation most often consid-
ered for “long” stimuli varying slowly in loudness, e.g., Ries
et al., 2008; see also Moore et al., 2016, for a discussion)
could account for its size.
1
Finally, these results show that,
even with very basic 1-kHz stimuli ramping up or down
in level, global loudness is not simply based on simple
operations (average, maximum) computed on the basis of
short-term or long-term loudness patterns. The mechanisms
a)
Electronic mail: emmanuel.ponsot@ircam.fr
256 J. Acoust. Soc. Am. 142 (1), July 2017 V
C2017 Acoustical Society of America0001-4966/2017/142(1)/256/12/$30.00
that underpin global loudness evaluations of such ramps still
remain undetermined.
Our listening environment contains lots of rising- and
falling-level events lasting a few seconds. Real moving
sound sources (e.g., a car passing by) present increasing
and decreasing level profiles (induced by the approaching
and the receding portions, respectively) and musical
sequences are full of crescendo and decrescendo pas-
sages. It is thus particularly valuable to understand how
intensity dynamics occurring at this time scale are proc-
essed and why asymmetries in global loudness judgments
of simple rising vs falling profiles occur. Focusing on the
perceptual processing of such contours also provide the
possibility to put the present research in the context of the
perception of the dynamics of looming/receding sounds
(Neuhoff, 1998; for a recent review of the literature, see
Olsen, 2014).
The purpose of the present study was twofold: (1) to better
understand the mechanisms underlying the global loudness
evaluation of basic 1-kHz rising- and falling-intensity tones of
several seconds, and (2) to explore to what extent asymmetries
between rising and falling tones are influenced by their tempo-
ral profile characteristics. These closely interrelated issues
were addressed by means of two psychophysical experiments
in which the parameters defining the temporal profiles of these
linear rising and falling ramps of sound level, namely, their
duration,theirslope (i.e., rate of change in dB/s), and their
dynamics (i.e., difference between minimum and maximum
levels in dB), were manipulated to test specific hypotheses
with regard to potential underlying mechanisms.
Most previous studies investigating global loudness of
simple rising and falling sounds at this time scale employed
ramps with the same combination of slope, duration, and
dynamics. Most often, the ramps were 2-s long and covered a
dynamics of 15-dB, thus, resulting in a slope of 7.5 dB/s
(Ponsot et al., 2013;Ponsot et al., 2015a;Ponsot et al., 2015b).
One study examined the effect of the dynamics on the
global loudness of 1.8-s rising ramps (Susini et al., 2010).
For rising ramps having the same maximum level, greater
global loudness estimates were found for ramps with 15-dB
dynamics as compared to those with 30-dB dynamics.
Furthermore, global loudness estimates of these rising ramps
were close but slightly lower than those of constant-intensity
tones presented at their maximum level. To explain these
effects, the authors proposed that global loudness evaluation
of rising ramps might involve a certain integration of its
level-profile over a temporal window located around the
maximum of the stimulus (see Meunier et al., 2010). It is
important to note at this stage that, while this concept of a
temporal integration over the loudest portions of the ramps
might belong to or mirror the same class of phenomena as
do typical temporal integration of loudness in psychoacous-
tics, there are significant divergences between the two. In the
traditional temporal integration literature, the time constants
refer to mechanisms operating at quite short durations
!50–100 ms (e.g., see Buus et al., 1997;Hots et al., 2014).
The temporal integration phenomenon we consider here
likely operates at a much coarser time scale and presumably
takes place in higher-level cognitive stages (we discussed
and illustrated these notions in Ponsot et al., 2016; see, in
particular, Sec. II and Fig. 1). Such a mechanism, which we
will call the integration mechanism throughout this paper, is
consistent, at least qualitatively, with the observation that
when the dynamics of these ramps are decreased while their
maximum level remains the same, a greater amount of
energy is contained under the temporal window and, hence,
global loudness increases. This integration mechanism is
also consistent with the fact that rising ramps are perceived
softer than their maximum level. According to this hypothe-
sis, if the duration of a ramp is increased but its dynamics is
fixed, global loudness should also increase. No experiment
directly tested this assumption with simple rising ramps, but
there is one study that investigated the influence of the dura-
tion on global loudness judgments of time-varying 1-kHz
tones, which consisted of sequences of stationary tones plus
ramps. For sound sequences made of a 3-s constant plateau fol-
lowed by a rising ramp, global loudness was found to increase
gradually when the duration of the ramp increased between 2
and 20 s while its dynamics was kept constant, equal to 20 dB
(see Susini et al., 2007). This result indirectly supports the idea
that a certain integration mechanism might be involved.
In Meunier et al. (2010), it was hypothesized that the
same integration mechanism of the loudest portion would act
with falling ramps: at equal duration, the global loudness of
a falling ramp would decrease when its dynamics is
increased, whereas at equal dynamics, its global loudness
should increase with duration. However, when dealing with
falling-intensity stimuli of a few seconds, there is another
phenomenon that needs to be taken into account. Indeed, a
number of studies observed that global loudness judgments
were greater when the loudness peak was closer to the end of
the sequence (Hellbr€
uck, 2000;Susini et al., 2002;Kuwano
et al., 2003). These authors suggested that this might reflect
a “memory process”: the loudness peak having a smaller
impact on the overall evaluation when its encoding in mem-
ory is further in time; “recency” was proposed as the candi-
date mechanism (Susini et al., 2002). This effect is strongly
related to the “peak-end” rule (Kahneman et al., 1993;
Schreiber and Kahneman, 2000), which has been specifically
introduced and discussed with regard to loudness (Dittrich
and Oberfeld, 2009). In what follows, specifically for down-
ramps, we will thus simply refer to this phenomenon as the
decay mechanism, because it is assumed to downsize the
influence of a loudness peak as a function of the time lapse
between its position and the end of the sound.
2
It is, how-
ever, impossible to tell yet beyond which durations this
mechanism really starts to be involved and what is the typi-
cal rate of decay it consists of. We believe this mechanism
could be partly responsible for the asymmetry observed
between 2-s rising and falling ramps (Ponsot et al., 2015a;
Ponsot et al., 2015b) and that it might emphasize this asym-
metry for longer ramp durations (e.g., 10 s), since the loud-
ness peak of falling tones is then clearly further back away
in time (Susini et al., 2007). Therefore, it could be hypothe-
sized that, when the duration of a falling ramp is increased
while its dynamics is fixed, global loudness judgments result
from the product of two mechanisms: (i) the integration
mechanism, which increases global loudness, and (ii) the
J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al. 257
decay mechanism, which decreases global loudness.
Whether the sum of these two processes leads, in the end, to
an increase or a decrease of global loudness as a function of
the duration can, however, not be predicted. In Susini et al.
(2007), global loudness of sequences containing falling
ramps (of fixed dynamics) followed by constant plateau was
found to remain fairly constant when ramp duration was
increased from 2 to 20 s. However, this result cannot directly
be transposed to the present context, e.g., to suggest that the
two mechanisms have similar weights in the process, as the
presence of a plateau at the end of the sequence might have
significantly affected the integration processes specifically
related to the ramp itself (more than in the case of rising
sequences where the plateau was located at the beginning).
The fact that the two mechanisms might potentially be oper-
ating simultaneously with falling tones can nevertheless be
observed by looking at the evolution of the so-called
“asymmetry” (i.e., the difference of global loudness between
rising and falling sounds) as a function of their duration
when their dynamics are held constant: this asymmetry
should increase. The decay mechanism should also be
observed independently by increasing falling ramps’ dura-
tion while keeping their slope constant. Indeed, the integra-
tion mechanism, which is only influenced by the shape of
the first (loudest) portion of a falling ramp would, when the
slope is unchanged, always provide the same global loudness
quantity whatever the duration of that ramp is. Such a
manipulation should decrease global loudness, directly
reflecting the effect of the decay mechanism.
These hypotheses remain, however, somewhat specula-
tive as they are derived from a small number of studies with
different experimental procedures, which in some cases, did
not use simple rising and falling ramps but more complex
sound sequences. The purpose of the present study was, thus,
to directly address with the same experimental designs the
plausibility that the two proposed mechanisms might be
involved in the global loudness processing of rising and fall-
ing tones. This was examined, in particular, in the context of
direct global loudness judgments using magnitude estimation
tasks. Two psychophysical experiments were designed to
disentangle the two presumed mechanisms by manipulating
the parameters of the ramps (i.e., their slope, duration, and
dynamics), which consisted of 1-kHz stimuli either rising or
falling linearly in level,
3
like those employed in our previous
studies (Ponsot et al., 2015a;Ponsot et al., 2015b). These
manipulations are illustrated in Fig. 1. In experiment 1, the
ramps were “stretched” in time while keeping their dynamics
constant [cf. Fig. 1(a)], resulting in different combinations of
slope and duration. This is similar to what was done in
Susini et al. (2007) with more complex sequences. In this
context, as mentioned above, we hypothesized that (1) global
loudness of rising tones should increase with duration
because of the integration mechanism and (2) global loud-
ness of falling tones should not grow as fast as for rising
tones because both the integration and the decay mechanism
would add. In experiment 2, the ramps were stretched in
time in such a way that their slope was kept constant [cf.
Fig. 1(b)], resulting in different combinations of dynamics
and duration. In that context, we hypothesized that (1) global
loudness of rising tones should not vary with duration
because, as stated earlier, a constant temporal window
located on its loudest portion always integrates the same
amount of energy, and (2) global loudness of falling tones
would decay over time, providing a direct image of the
decay mechanism.
Furthermore, we also wanted to investigate throughout
these two experiments the extent to which asymmetries
between global loudness of rising and falling tones vary with
the manipulated parameters, namely, the slope, the dynamics
and the duration of these ramps. Due to the presumed decay
mechanism operating with falling tones, we were expecting
an increase of the asymmetry with the duration of the time
stretching in both experiments. Finally, the experimental
design also attempted to determine to which extent the
effects of the ramp parameters (slope, duration, dynamics)
on both global loudness judgments and their resulting asym-
metries depend on the mean intensity of the stimuli. Indeed,
we already observed in previous studies that the asymmetry
between rising and falling ramps was significantly reduced
when the maximum level of the stimuli was higher than
80 dB sound pressure level (SPL), an effect that remained
unexplained so far (Ponsot et al., 2015a;Ponsot et al.,
2015b). Thus, in both experiments, ramps were presented in
different intensity-regions, below and above 80 dB SPL. To
complete this investigation, we examined to what extent dif-
ferent global loudness indicators derived from the outputs of
the loudness model of Glasberg and Moore (2002) could
account for the results collected.
II. EXPERIMENT 1
A. Materials and method
1. Participants
Forty-five participants were recruited for this experi-
ment. They were divided into two groups, performing the
experiment under different conditions (see Sec. II A 2
below): group A, 30 participants (15 women, 15 men; age
22–35 years old); group B, 15 participants (8 women, 7 men;
age 18–32 years old). All reported normal hearing. They
gave their informed written consent according to the
Declaration of Helsinki prior to the experiment and were
paid for their participation. The participants were naive with
respect to the hypotheses under test.
FIG. 1. (Color online) Schematic representation of the two experiments con-
ducted in the present study where the duration of rising- and falling-
intensity ramps was manipulated in different ways [as indicated by the
arrows, a rising ramp taken here, as an example, could be stretched from (1)
to (2)]. (a) Experiment 1: The ramps were “stretched” in time while keeping
their dynamics constant. (b) Experiment 2: The ramps were stretched in time
while keeping their slope constant. A rising ramp is taken as an example
here, but the similar operation was realized on falling ramps.
258 J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al.
2. Stimuli
The stimuli were 1-kHz pure tones with various dura-
tions and intensity profiles. The loudness function of each
participant was measured prior to the experiment using 500-
ms constant-intensity tones (presented at ten different levels
equally spaced between 45 and 90 dB SPL). The data col-
lected for these constant-intensity tones were not used in the
paper, except for normalizing the ratings attributed to the
ramps (see Sec. II B). In the experiment, tones with rising-
and falling-intensity profiles were used; their sound level
was linearly varied over 15 dB (i.e., 15-dB dynamics). They
were presented in four regions: R
1
¼[60–75], R
2
¼[65–80],
R
3
¼[70–85], and R
4
¼[75–90 dB SPL]. Participants of
group A were presented with ramps of five different dura-
tions (1, 2, 6, 9, and 12 s); participants of group B were pre-
sented with another set of three durations (4, 8, and 16 s).
The amplitude envelopes of the stimuli were all smoothed
with 10-ms linear rise and fall times.
3. Apparatus
The stimuli were generated at a sampling rate of
44.1 kHz with 16-bit resolution using MATLAB. Sounds were
converted using a RME Fireface 800 soundcard
(Haimhausen, Germany), amplified using a Lake People G-
95 Phoneamp amplifier (Konstanz, Germany) and presented
diotically through headphones (Sennheiser HD 250 Linear
II, Wedemark, Germany). Sound level was calibrated using
a Br€
uel and Kjær artificial ear (type 4153, IEC318, Nærum,
Denmark). Participants were tested in a double-walled (IAC)
sound-insulated booth at Ircam.
4. Procedure
An absolute magnitude estimation (AME) procedure
was used, based on the instructions of Hellman (1982). No
standard was given to the participants. Their task was to give
a number proportional to the global loudness of each sound,
i.e., the overall impression loudness over the total sound
duration (Ponsot et al., 2013;Ponsot et al., 2015a;Susini
et al., 2007;Susini et al., 2010). For each participant, the
experiment was scheduled in one session lasting about one
hour. The measurement of the loudness function was done at
the beginning of the session. After 20 training trials, each
tone was presented 9 times in a “pseudo-random” order to
reduce sequential effects (Cross, 1973), as it was done previ-
ously (see Ponsot et al., 2015a). The experiment continued
with the presentation of rising and falling ramps at various
durations and intensities. A blocked-duration design was
adopted, i.e., each block was made of sounds having the
same duration. Each block consisted of interleaved rising
and falling ramps of equal-duration presented at the four dif-
ferent intensity-regions, as mentioned in Sec. II A 2. Each
stimulus was presented five times. Thus, a total of 200 stim-
uli (2 directions #4 intensity-regions #5 durations #5 repe-
titions) were presented to the participants of group A and a
total of 120 stimuli to the participants of group B
(2 directions #4 intensity-regions #3 durations #5
repetitions). The order of presentation of the blocks was ran-
domly chosen for each participant.
B. Results
For each listener of each group, the average perceived
global loudness of each stimulus was computed using the
geometric mean of all his/her ratings. These mean loudness
estimates were then normalized individually.
4
The data were analyzed separately for each group.
Repeated measures analyses of variance (rmANOVAs;
direction #duration #intensity-region) with univariate
approaches were performed on the logarithm of the normal-
ized loudness ratings accorded to rising and falling ramps
within each group, respectively. The statistical analyses
were conducted using R (R Core Team, 2015). All the tests
were two-tailed and used a probability level of 0.05 to test
for significance. The Huynh-Feldt corrections for degrees of
freedom were used where appropriate. Effect sizes are
reported using partial eta-squared g
p
2
.
The normalized magnitude estimates obtained in each
group are presented in Fig. 2, on a y-log scale and as a func-
tion of the duration of the ramp. Overall, global loudness
estimates of rising tones (!) appeared to be always greater
than (or at least equal to) those given to their time-reversed
versions, i.e., falling tones ("). This was supported by sig-
nificant effects of the direction obtained both for group A
[F(1,29) ¼25.07, p<0.001, g
p
2
¼0.464] and for group B
[F(1,14) ¼12.14, p¼0.004, g
p
2
¼0.464]. Furthermore, the
averaged plots in Fig. 2for both groups A and B showed that
global loudness increased with duration for both ramp direc-
tions, at least until 6 s, but that the speed of this growth
might differ between rising and falling tones. Beyond 6 s,
global loudness tended to remain constant for rising-
intensity tones, whereas it seemed that there might be a
FIG. 2. (Color online) Normalized estimates of global loudness obtained in
experiment 1 in the two conditions (group A on top, who received 15-dB
ramps of 1, 2, 6, 9, and 12 s; group B at bottom, who received 15-dB ramps
of 4, 8, and 16 s) for both rising (!) and falling sounds ("). Results are plot-
ted a y-log axis as a function of the duration of the ramp respective to each
group for the different intensity-regions on the left panels (from R
1
to R
4
)
and averaged on the rightmost panels. Error bars show standard errors of the
mean (SEM) in each configuration.
J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al. 259
slight decrease for falling-intensity tones. The analyses in
group A showed a significant effect of duration [F(4,116)
¼4.70, p¼0.013, g
p
2
¼0.139, ~
e¼0.49] and a significant
duration #direction interaction [F(4, 116) ¼4.60, p¼0.009,
g
p
2
¼0.137, ~
e¼0.61]. In group B, a significant effect of
duration was found [F(2,28) ¼5.82, p¼0.013, g
p
2
¼0.294,
~
e¼0.81] but the duration #direction interaction was only
marginally significant [F(2,28) ¼3.20, p¼0.056, g
p
2
¼0.186,
~
e¼1.15].
To gain further insight into the duration #direction
interaction obtained in group A, multiple post hoc
rmANOVAs were conducted on pairs of adjacent durations
to determine the duration at which this interaction appeared.
When the p-value threshold for significance was corrected
using Bonferonni at the alevel of 0.05 (0.05/4), the interac-
tion between 2 and 6 s was significant [F(1,29) ¼13.47,
p¼0.001, g
p
2
¼0.317], but there were no significant interac-
tions beyond 6 s, which make it impossible to statistically
support the slight decrease that could be observed for falling
tones.
Finally, the overall difference between the curves pre-
sented in each panel (i.e., the asymmetry between rising
and falling tones) was observed to diminish at higher
intensity-regions in group A, as revealed by a significant
direction #intensity-region interaction [F(3,87) ¼5.94,
p¼0.003, g
p
2
¼0.170, ~
e¼0.78]. This interaction could also
be observed in group B (see Fig. 2, bottom) but was not sig-
nificant [F(3,42) ¼1.85, p¼0.160, g
p
2
¼0.117, ~
e¼0.90].
C. Discussion
This first experiment examined how global loudness
judgments of rising and falling ramps of a few seconds
evolve when these sounds are stretched in time such that
their dynamics is kept constant. Global loudness of both ris-
ing and falling sounds was found to increase with duration
until about 6 s. For longer durations from 6 up to 16 s, global
loudness of rising tones reached a constant plateau and a
slight decrease was observed for falling tones. Significant or
marginally significant direction#duration interactions were
thus obtained between the patterns of each profile. It was,
however, not possible to highlight the slight decrease of the
curve observed for falling tones with post hoc analyses; only
the interaction between 2 and 6 s was statistically reliable.
Overall, these results are different to those reported by
Susini et al. (2007), where sequences of 1-kHz tones with
time-varying intensity profiles were employed. In their
study, the stimuli sequences were made of rising or falling
ramps of different durations (from 2 to 20 s) having a fixed
dynamics equal to 20 dB, combined with 3-s constant-inten-
sity plateau presented either before the rising ramp or after
falling ramp. Concerning (plateau-rising) sequences, they
showed that global loudness increased by a fixed amount for
each doubling of duration, whereas we found that the global
loudness of simple rising ramps reached a constant value at
6 s and then remained constant for longer durations, at least
until 16 s. Concerning (falling-plateau) sequences, they
showed that global loudness did not vary significantly with
duration, whereas in the present study, global loudness of
falling tones increased significantly with duration until 6 s.
Whether the differences between the present results and the
results of Susini et al. (2007) can be attributed to the absence
vs presence of a plateau before/after the ramp or whether
they stem from procedural differences cannot be determined.
In the present experiment, we were expecting that the
integration mechanism would increase global loudness of
rising tones and its association with the decay mechanism
would make global loudness of falling tones grow less rap-
idly. Our results only partially supported these hypotheses.
Global loudness of rising tones indeed increased with dura-
tion, as if there was some kind of loudness integration, but
beyond 6 s appeared to “saturate”; a result that cannot—at
first sight—be explained by this integration mechanism.
Indeed, if one considers the area contained in a fixed window
located under the level profile of a linear ramp, this area
should grow logarithmically as a function of the duration of
the “time-stretching” until a certain point corresponding to
the level of a constant-intensity sound. Concerning falling
tones, global loudness also increased with duration, but at a
slower rate, as revealed by a significant direction #duration
interaction found between 2 and 6 s for group A. This might
support our hypothesis that two mechanisms, an integration
mechanism and a decay mechanism, might add up.
However, our results thus indicate that the decay mechanism
plays a significant role only between 2 s and 6 s (i.e., where
the direction #duration interaction was found), whereas we
were rather expecting a somewhat gradual effect as a func-
tion of time. We have no clear explanation for this result, but
it might be possible that the integration mechanism has no
noticeable effect if the slope is small.
It can also be noted that there were differences between
the rating patterns in groups A and B. Although normalized
in the same fashion, the ratings obtained in group B were
overall 63% higher than those collected in group A, showing
that observers of group B used higher numbers. Next, the
size of the effects related to ramp duration was also different
between the two groups (although they had overlapping
loudness functions, on average). We do not have any clear
explanation of these differences, but they might be related to
the contextual differences, as ramp durations were higher in
experiment 1B (4–16 s) than in experiment 1A (1–12 s).
Another outcome of the present experiment concerns
the asymmetry between rising and falling tones: greater
global loudness judgments were obtained for rising ramps
compared to falling ramps at all durations and, as expected,
the size of this asymmetry increased with sound duration.
This increase, which is assumed to be due to the decay
mechanism was visible at all durations above 6–8 s, but it
was only statistically significant between 2 and 6 s. Last, the
asymmetry was found to depend on the intensity-region of
the ramps in Group A. This decrease of the asymmetry in
high intensity-regions was already observed in other studies
on this topic (Ponsot et al., 2015a;Ponsot et al., 2015b), but
its causes still remain undetermined.
The second experiment was designed to further assess
the plausibility of the two proposed candidate mechanisms
using the other experimental design presented in the intro-
duction, i.e., using a time-stretching manipulation where the
260 J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al.
slope of the ramp was preserved. In addition to the ramp stim-
uli, we added constant-intensity tones presented at different
levels and durations (corresponding to the maximum levels
and the durations of the ramps), in order to compare their loud-
ness with the global loudness of the ramps. This also allows us
to control that listeners do not deviate
5
with duration in their
loudness evaluations for sounds lasting several seconds.
III. EXPERIMENT 2
A. Materials and method
1. Participants
Twenty-nine subjects took part in this experiment (13
women, 16 men; age 19–34 years old). All reported normal
hearing. They gave their informed written consent according
to the Declaration of Helsinki prior to the experiment and
were paid for their participation. The participants were naive
with respect to the hypotheses under test.
2. Stimuli
All the stimuli were 1-kHz pure tones. As in experiment
1, 500-ms constant-intensity tones were used to measure the
loudness function of each participant prior to the experiment
(the same levels of presentation were used, equally spaced
between 45 and 90 dB SPL). In the main part of the experi-
ment, tones with constant, rising-, or falling-intensity pro-
files were employed. The constant-intensity tones were
presented at four durations (2, 4, 6, and 12 s) and four levels
(M
1
¼75, M
2
¼80, M
3
¼85, and M
4
¼90 dB SPL).
Different combinations of duration and slope were used to
create an appropriate set of rising- and falling-intensity
tones. Their slope (i.e., absolute rate of change) was either
2.5 dB/s or 5 dB/s. The ramps varying at 2.5 dB/s were pre-
sented at four durations (2, 4, 6, and 12 s) and the ramps
varying at 5 dB/s were presented at three durations only (2,
4, and 6 s) in order to avoid too low (start or end) levels that
would have been induced if the 12-s duration had also been
used. All the ramps were presented with four different maxi-
mum levels (75, 80, 85, 90 dB SPL). Their minimum levels
and, consequently, their dynamics, resulted from the combi-
nations of duration and slope.
3. Apparatus
The apparatus were the same as described in experiment 1.
4. Procedure
The procedure employed in this experiment was similar to
the one described in experiment 1, i.e., an AME procedure
with a blocked-duration design. After the preliminary loudness
function measurement (similar to experiment 1), participants
were presented with longer constant and ramp tones. Each
block consisted of interleaved constant, rising, and falling
ramps of equal duration presented at different levels, as men-
tioned in Sec. III A 2. Each stimulus was repeated three times.
The order of presentation of the four blocks (one for each dura-
tion) was randomly varied between participants. A total of 48
constant-intensity tones (4 levels #4durations#3
repetitions), 96 ramps varying at 2.5 dB/s (4 maximun lev-
els #2directions#4 durations #3repetitions)and72ramps
varying at 5 dB/s (4 maximum levels #2directions#3
durations #3 repetitions) were thus presented to the
participants.
B. Results
The same normalization as in experiment 1 was applied to
the loudness ratings given by each listener. Different
rmANOVAs were conducted to analyze the results in different
ways because the ramps varying at 2.5dB/s and those varying
at 5 dB/s did not exactly share the same set of durations. Since
these multiple analyses were planned prior to the experiment,
uncorrected p-values are reported. To provide the reader a
clear picture of the results obtained with these different analy-
ses, the normalized loudness ratings are presented in Fig. 3
separately for ramps having a slope of 2.5 dB/s (top) and 5dB/
s (bottom), and in Fig. 4for rising (top) and falling (bottom)
ramps. Loudness estimates for constant-intensity tones, which
had the same maximum levels and durations as the ramps, are
superimposed in each panel of Figs. 3and 4.
1. Analysis A: Loudness of constant tones
A first rmANOVA was conducted on the estimates given
to constant tones only. A small increase of loudness estimates
with duration until 6 s could be observed (see Fig. 3), but the
analysis revealed that the effect of duration was not significant
(p>0.05). There was no significant duration#level interaction
(p>0.05). The constant tones are not taken into account in the
analyses that follow, which focus on the effects related to ris-
ing and falling ramps. However, it is important to observe that
the loudness of these constant tones was always greater or at
FIG. 3. (Color online) Normalized estimates of global loudness obtained in
experiment 2 for rising (!) and falling ramps (") whose slope was equal to
2.5 dB/s (top) or 5 dB/s (bottom), plotted as a function of their duration.
Same layout as in previous figures; the data are presented for the different
maximum level of the ramps on the left panels (from M
1
to M
4
), and after an
averaging over these different levels on the rightmost panels. The loudness
estimates obtained for constant-intensity tones having the same level as the
maximum level of the ramp are superimposed in each panel (dashed lines).
Error bars correspond to SEM.
J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al. 261
least equal to the global loudness estimates given to ramps
with the same maximum level (see Fig. 3).
2. Analysis B: Global loudness of rising and falling
ramps varying at 2.5 dB/s
Asecondanalysiswasperformedtospecificallycompare
rising and falling ramps varying at 2.5 dB/s, for which global
loudness estimates are presented on the top of Fig. 3.Greater
estimates were overall obtainedforrisingrampscomparedto
falling ramps, as supported by a significant effect of the direc-
tion [F(1,28) ¼11.39, p¼0.002, g
p
2
¼0.289]. However, as it
can be observed in Fig. 3,thesizeofthisdifferenceappearedto
increase with the duration because the curves took somewhat
different directions. Global loudness judgments of rising tones
slightly increased with duration until 6 s and then reached a pla-
teau, whereas global loudness judgments of falling tones
remained fairly constant with duration and even appeared to
decrease slightly between 6 and 12 s. This was supported by the
fact that there was no significant main effect of the duration
(p>0.05) but a significant direction #duration interaction
[F(3,84) ¼3.94, p¼0.034, g
p
2
¼0.123, ~
e¼0.54]. All these
effects appeared to be similar at the different maximum levels
tested, as supported by no significant interactions between the
maximum level of the ramps and other factors (p>0.05). We
conducted post hoc tests to determine whether the changes
observed with duration for each profile separately (rising/falling)
were significant or not. We found no significant effects of dura-
tion neither for rising tones, nor for falling tones (p>0.05).
3. Analysis C: Global loudness of rising and falling
ramps varying at 5 dB/s
This analysis was concerned with global loudness esti-
mates of ramps varying at 5 dB/s. These data are presented
in Fig. 3(bottom). Overall, similar conclusions to those
obtained with ramps varying at 2.5 dB/s were reached. A sig-
nificant effect of the direction was found [F(1,28) ¼10.92,
p¼0.003, g
p
2
¼0.281]. As on the top of Fig. 3, we could
observe a slight increase of the judgments of rising tones as
a function of duration, and a slight decrease of the judgments
of falling tones with duration. However, neither the effect of
the duration nor the duration #direction interaction were
significant (p>0.05). Last, the overall difference between
rising and falling tones estimates was slightly decreased as
the maximum level of ramp increased; there was a signifi-
cant direction #maximum level interaction [F(3,84) ¼3.14,
p¼0.031, g
p
2
¼0.101, ~
e¼0.96].
4. Analysis D: Global loudness of rising and falling
ramps separately
In order to specifically examine the influence of the
duration on each ramp direction and assess the effect of the
slope on their global loudness judgments, we conducted
additional analyses on rising and falling ramps separately.
Ramps varying at 2.5 dB/s and 5 dB/s were combined for the
set of durations shared between these two groups, i.e., 2, 4,
and 6 s (the 12-s ramps varying at 2.5 dB/s were, thus, not
considered in these analyses). The data separated for rising
and falling ramps are presented in Fig. 4(upper panels,
rising tones; lower panels, falling tones).
First, we analyzed global loudness judgments of rising
ramps lasting 2, 4, and 6 s and varying at 2.5 dB/s or 5 dB/s.
Global loudness estimates of rising ramps varying at 2.5 dB/s
were clearly higher than those given to rising ramps having
the same maximum level and duration but varying at 5 dB/s;
a large and significant effect of the slope supported this
observation [F(1,28) ¼31.92, p<0.001, g
p
2
¼0.533]. There
was no significant effect of the duration (p>0.05), but a sig-
nificant duration #slope interaction [F(2,56) ¼4.57,
p¼0.015, g
p
2
¼0.140, ~
e¼1.06], revealing that the effect of
the duration, although not significant as a main factor, was
different for the two slopes.
Second, we examined the judgments for falling ramps
having the same parameters. Global loudness estimates of
falling ramps varying at 2.5 dB/s were again clearly higher
than those given to falling ramps having the same maximum
level and duration but which varied at 5 dB/s, as supported
by a large and significant effect of the slope [F(1,28) ¼5.94,
p<0.001, g
p
2
¼0.680]. There was no significant effect of
duration (p>0.05) but again, a significant duration #slope
interaction [F(2,56) ¼4.38, p¼0.024, g
p
2
¼0.135, ~
e¼0.83].
C. Discussion
Analyses B and C showed that stretching ramps in time
while maintaining their slope unchanged had no noticeable
influence on global loudness: The effect of duration was not
significant. Therefore, as compared to when the time-
stretching was made at constant dynamics (experiment 1),
where a large main effect of the duration was found, a time-
stretching at constant slope did not strongly affect global
loudness. As discussed in the introduction, this result is com-
patible with the integration mechanism. Moreover, analysis
D showed that the ramps varying at 2.5 dB/s were perceived
FIG. 4. (Color online) Normalized estimates of global loudness collected in
experiment 2 for rising sounds (upper panels) and falling sounds (lower pan-
els). This figure presents, in a different way, the results plotted in Fig. 3to
provide a clearer picture of the influence of the slope on rising and falling
ramps separately, and should be seen as a visual support to analysis D. On
each panel, highest triangles correspond to the estimates given to 2.5 dB/s
ramps (Fig. 3, higher panels) or to 5 dB/s ramps (Fig. 3, lower panels).
Otherwise, the plotting convention is the same as in Fig. 3.
262 J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al.
clearly louder than those varying at 5 dB/s, a result that also
appears to be consistent, at least at a qualitative level, with
the integration mechanism, given that more energy is con-
tained in a similar integration window for ramps varying at
2.5 dB/s as compared to ramps varying at 5 dB/s. The fact
that global loudness of ramps was always below or equal to
the loudness of constant tones presented at their maximum
level also provides support to the integration mechanism.
Although the effect of duration was not significant over-
all, a slight increase in the judgments of rising tones and a
slight decrease in the judgments of falling tones as a function
of duration could be noticed, respectively. This dura-
tion #direction interaction reached significance only for
ramps varying at 2.5 dB/s. It cannot be excluded that other
phenomena are operating when the ramps are stretched in
time at constant slope. In particular, the significant dura-
tion #slope interactions revealed by analysis D suggests that
the effect of the stretching is not the same whether the ramps
vary at 2.5 or 5 dB/s, a result that it is not possible to account
for by the two mechanisms considered in this study.
Overall, these data are not incompatible with our
hypothesis of a decay mechanism involved in global loud-
ness evaluations of long falling ramps, but we were not able
to statistically support it. The fact that the interindividual
variability was large and the range of tested durations
restricted by the current design is undoubtedly a limiting fac-
tor when trying to capture a small and slow-acting effect as
the one considered here.
IV. GENERAL DISCUSSION AND CONCLUSION
A. Summary of experimental findings
In two magnitude estimation experiments, we addressed
whether two mechanisms, which had been proposed as
potential candidates in previous studies, might indeed under-
lie the perceptual computation of global loudness for rising
and falling ramps. The first mechanism under study, called
the integration mechanism, relies on the assumption that the
global loudness of a ramp could be determined by an integra-
tion of its loudest portion over a certain temporal window.
The second mechanism considered here, called the decay
mechanism, is based on the assumption that the output of
this loudness integration is weakened as a function of the
time lapse between the beginning and the end of a falling
ramp, this mechanism being specific to falling ramps.
The plausibility of these two mechanisms was deter-
mined by looking at the extent to which global loudness
judgments of rising and falling tones (with linear level
changes) were influenced by different manipulations of their
parameters, namely, their slope, their dynamics, and their
duration. It should be noted that disentangling perceptual
mechanisms in play with such stimuli by “stretching” their
parameters (slope, duration, and dynamics) is a complex task
because these parameters are not independent; the slope is
indeed equal to the dynamics divided by the duration. In
both experiments, several parameters varied simultaneously
and might, thus, have tainted the results such that it is not
possible to make “clear-cut” conclusions. However, the two
experiments yield various results that allow us to further dis-
cuss the plausibility of the two proposed mechanisms.
Overall, the results obtained in this study provide signif-
icant support to the hypothesis that an integration mecha-
nism might be involved. First, the stretching adopted in
experiment 1 (i.e., stretch in duration keeping ramps’
dynamics unchanged) caused global loudness increase with
duration for both rising and falling ramps, which is consis-
tent with the fact that the energy contained within a fixed
temporal window located around the peak stimulus is
increased. Second, the stretching adopted in experiment 2
(i.e., stretch in duration keeping ramps’ slope unchanged)
led to (1) non-significant effects with respect to duration,
consistent with the fact that the energy contained within a
fixed temporal window remains unchanged, and (2) a large
and significant effect of the slope in experiment 2 both for
rising and falling tones (ramps varying at 2.5 dB/s were
significantly louder than ramps varying at 5 dB/s), consistent
with the fact that less energy is contained in a window
located under ramps having steeper slopes. There are, how-
ever, two departures from this mechanism that can be
noticed: (1) the “saturation” of the estimates of rising tones
beyond 6 s observed in experiment 1 and (2) the slope #du-
ration interaction obtained in experiment 2. As discussed
earlier, since the stretching adopted in experiment 1 induced
both variations in duration and slope at the same time, it
might be possible that another mechanism was involved in
the evaluation of the ramps of long durations and that this
mechanism was responsible for the “saturation” in the judg-
ments beyond 6 s; the ramps had very small slope and could
possibly be assimilated to constant tones. In that sense, the
saturation would finally not be imputable to the integration
mechanism itself. Note that we only examined qualitatively
the extent to which our results agreed with an integration
mechanism; all these results remain to be verified quantita-
tively, for instance, whether loudness integration over a fixed
temporal window of which length is compatible with the rate
of increase observed in experiment 1. The presence of the
decay mechanism was assessed by comparing the estimates
obtained for falling tones with those of rising sounds (for
which only integration is involved). We found small but signif-
icant duration #direction interactions both in experiment 1
and experiment 2 (only for the ramps varying at 2.5dB/s),
consistent with our assumption that a decay mechanism
might play a role. The estimates collected for falling ramps
in experiment 2 presented a small decline as a function of
duration after 6 s but the ramps varying at 2.5 dB/s also
showed an increase between 2 and 6 s; there was no signifi-
cant effect of duration except a significant duration #slope
interaction. As a result, the data collected in the present
study are not incompatible with the idea that a certain decay
mechanism might underlie the processing of falling ramps
of long durations, but its implication could not be statisti-
cally supported. More specifically, the data of experiment 2
suggest that the underlying machinery is not solely com-
posed of the two mechanisms considered here,
6
but that
other mechanisms might be acting or interacting with those,
e.g., by modulating the decay mechanism as a function of
the absolute slope of the ramps.
J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al. 263
Last, global loudness judgments of ramps appear to be,
in addition to their maximum level, primarily guided by their
slope (strong effects of the slope in analysis D, which are
obvious in Fig. 4), much more than by their duration or
dynamics. Besides, the size of the asymmetry between rising
and falling ramps depends on the duration of the ramps
(cf. experiment 1, where asymmetries were increased with
duration) and on their dynamics (cf. experiment 2, where the
asymmetries were reduced for small dynamics). Therefore,
the present study shows that the asymmetry between rising
and falling tones is not specific to the 2-s, 15-dB ramps
employed in previous studies (e.g., Ponsot et al., 2015a;
Ponsot et al., 2015b); it occurs in many other conditions, but
its magnitude depends on the parameters of the ramps.
B. An attempt to predict global loudness directly from
the model of Glasberg and Moore
We evaluated, in particular, the extent to which the
loudness model of Glasberg and Moore (2002) could account
for the results exposed in experiment 1, where the time-
stretching manipulation was assumed to trigger both the inte-
gration and the decay mechanisms. Three basic indicators
directly based on STL and LTL time series of the model out-
puts were examined to see how well they could reproduce
the patterns of observers’ ratings. The first two indicators
considered were the maxima of STL and LTL patterns, i.e.,
STL
max
and LTL
max
, respectively, which we already exam-
ined (Ponsot et al., 2015a;Ponsot et al., 2015b). The third
indicator considered was inspired from the integration mech-
anism hypothesis: We introduced STL
int
, which corresponds
to the average of STL over a fixed temporal window located
around its maximum. Since we had no specific assumptions
concerning the shape of this temporal window, we used a
simple rectangular temporal window whose length was arbi-
trarily chosen equal to 500 ms (in order to roughly account
for the growth of global loudness estimates with duration
obtained in experiment 1, group A). This window was
located so that it started (ended) at the maximum of the STL
pattern of falling (rising) tones. The way these three indica-
tors are computed from STL and LTL outputs, respectively,
is illustrated on the left part of Fig. 5. The global loudness
predictions are presented for various ramp durations, ranging
from 1 to 16 s, in the right panels of Fig. 5.
The rising vs falling asymmetries given by the indicators
proposed to predict global loudness so far, i.e., the maximum
of STL or LTL patterns, considerably underestimate what
was measured by means of various psychophysical experi-
ments. STL
max
and LTL
max
produce only small asymmetries
in the desired direction at short durations
7
(i.e., rising louder
than falling ramps); however, such asymmetries disappear at
longer ramp durations because the influence of the temporal
integration stages is weakened as ramp duration increases.
The growth with duration obtained with STL
max
is negligible,
whereas, as expected, a substantial and logarithmic increase
can be observed with STL
int
. However, STL
int
does not pre-
dict any asymmetries between rising and falling tones.
STL
int
probably provides the best reproduction of the
main trend observed as a function of ramp duration in
experiment 1 (group A): the increase between 1 and 2 s is
comparable to what was measured and the logarithmic
growth well approximates the fact that “saturation” was
observed experimentally beyond 6 s. It is clear that STL
max
is not appropriate to account for the increase with duration.
The integration mechanism we are examining here is better
accounted for by LTL
max
, which shows an increase that
would fit reasonably well the data for rising sounds; but, it
does not do the job for falling sounds. With respect to the
rising vs falling asymmetry, none of these indicators are,
however, able to account for the magnitude of the effect
observed experimentally.
This brief investigation with three simple indicators
derived from the outputs of the model of Glasberg and
Moore (2002) shows that none of them is able to account for
the data collected in experiment 1, group A. The same out-
comes would have been reached if one would have consid-
ered the data of experiment 1 (group B) or experiment 2, and
also using the dynamic loudness model of Chalupper and
Fastl (2002; see Ponsot et al., 2015a). The predictions
derived from these indicators show that a subsequent tempo-
ral integration stage induces the desired growth with dura-
tion observed experimentally. STL
int
computed with a 500-
ms constant is able to produce an increase with duration sim-
ilar to what we obtained with group A. Note that this 500-ms
value is about an order of magnitude higher than the time
constant involved greater than “traditional” experiments on
the temporal integration of loudness. This supports our
hypothesis that the integration mechanism examined here
operates at a much coarser, likely cognitive, time scale.
However, while STL
int
could indeed account for the inte-
gration phenomenon, it cancels at the same time any loudness
difference between up- and down-ramps produced by the auto-
matic gain control (AGC), so that it is not possible to account
both for the integration phenomenon and the asymmetry at the
FIG. 5. (Color online) Different indicators introduced to estimate global
loudness from the outputs of the model of Glasberg and Moore (2002). Both
STL and LTL time series of 1-s ([65–80 dB SPL) rising-intensity (grey lines)
and falling-intensity ramps (black lines) predicted by the model are consid-
ered. (a) STL
max
: using the maximum of the STL. (b) STL
int
: using an aver-
age of STL over a fixed arbitrary 500-ms rectangular integration window
(note that the temporal windows are not to scale for clarity purpose) starting
(ending) at the maximum value of the falling (rising) pattern. (c) LTL
max
:
using the maximum of the LTL. On the right part of the figure, global
loudness predictions based on these different indicators for rising (grey) and
falling (black) ramps of durations ranging from 1 to 16 s are shown.
264 J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al.
same time using STL. LTL (which AGC uses a time constant
of 200 ms) predicts too small of an increase of global loudness
with duration, but is able to amplify the asymmetries between
rising and falling STL patterns. Motivated by the hypotheses
of the mechanisms examined in this paper, we tested various
modifications of the TVL model (Glasberg and Moore, 2002)
for time-varying sounds that would best fit our data and identi-
fied two minimal changes. It appears necessary to (1) signifi-
cantly increase the time-constant of the AGCs to mimic the
integration phenomenon while reinforcing the asymmetry pro-
duced by the model at short ramp durations (such as LTL
does, to a certain extent, but not enough), and (2) add another
decay-like stage, not only to produce the small decline
observed at longest durations for falling ramps but, most criti-
cally, to maintain the asymmetry at longer ramp durations.
Regarding the first point, we observed (not detailed here) that
it was necessary to increase the time constants of the AGCs to
reproduce the growth with duration obtained experimentally at
short durations, but that different values were required to fit
with our different experimental conditions (experiment 1A,
experiment 1B, experiment 2—2.5 dB/s, experiment 2—5 dB/
s). Regarding the second point, it is of note that a decay-like
stage is required to downsize the increase of the falling pattern
that would otherwise superimpose with the rising pattern at
long ramp durations with any integration stage. Indeed, if the
asymmetry is solely driven by the AGC stages, it will inevita-
bly decreased toward zero as the duration of the ramp
increases because the slope of the ramps will thus approach
zero (i.e., the rising and falling patterns will become indistin-
guishable). Taken together, these computational analyses sup-
port our working hypothesis that the temporal integration and
the decay mechanisms considered here do underlie the global
loudness evaluation of rising and falling ramps. However, it is
in our view too preliminary to propose any analytical expres-
sion of these stages before understanding the reasons why dif-
ferent time constants would be needed in different
experimental contexts.
C. Conclusion and perspectives
The data presented in this paper provide the first direct
experimental investigation of the hypotheses raised in previ-
ous studies, that an integration mechanism and a decay
mechanism might be involved in the global loudness evalua-
tion process of rising and falling intensity tones. While these
results qualitatively support the view that global loudness of
intensity-ramps might partly be accounted for by a certain
integration of their loudest portions, the presence of the
decay mechanism could not be demonstrated. Further studies
have to be conducted to directly tackle its implication with
other experimental paradigms.
On a more practical basis, we computed independent
indexes to assess the importance of the effects highlighted in
the different experimental configuration of this study [experi-
ment 1 A, experiment 1B, experiment 2 (ramps 2.5 dB/s),
experiment 2 (ramps 5 dB/s)], in order to help the readers
judge which of the reported effects could be relevant for the
loudness of everyday sounds. These indexes (shown in Fig. 6)
intend to reflect (a) the effects induced by a 5- and 10-dB
change in ramp’s intensity-region (or mean level), (b) the aver-
aged asymmetry between up- and down-ramps, and (c) the
largest change in loudness caused by a variation in duration.
To allow linear comparisons, we took the log-value of the ratio
between the ratings given, respectively, to ramps varying in
intensity-regions 5-dB and 10-dB apart (black bars), to up- and
down-ramps (red bars), and to ramps at the two durations that
received most different ratings (blue bars). Note that these
indexes make use of the same data so they are not indepen-
dent; they should simply be taken as rough, first-order esti-
mates. On average, this analysis shows that the size of the
asymmetry between up- and down-ramps is comparable (or
slightly smaller) to an increase of 5-dB in ramp level, consis-
tent with previous studies (Ponsot et al., 2015a;Ponsot et al.,
2015b). It can also be observed that the change in loudness
caused by ramp duration depends on the context: In experi-
ment 1A, the effect laid between an effect caused by a 5 - and
a 10-dB level increase; in experiment 1B, the effect was simi-
lar to a 5-dB increase in level; in experiment 2 (ramps varying
at 2.5 dB/s), the effect was nearly two times smaller than a 5-
dB increase; in experiment 2 (ramps varying at 5dB/s), the
effect was close to zero. These results show how the loudness
of sounds ramping in level is affected by their parameters
(direction of level change, duration), and which is worth taking
into account when assessing the loudness of everyday sounds
(many natural sounds have very similar level profiles, e.g., a
sound source passing by). In most cases, the effects caused by
these parametric changes are not small and, thus, have to be
considered; most were comparable to a !5-dB increase in
sound level.
The analyses of different indicators based on the outputs
of the model of Glasberg and Moore (2002) show that the
indicators most often used to predict global loudness,
namely, STL
max
, LTL
max
, are not able to reproduce most of
the trends we observed experimentally. In particular, the
increase with duration obtained with the time stretching at
constant dynamics employed in experiment 1 cannot directly
be predicted by taking the maximum of STL or LTL time
series provided by the model. We showed that STL
int
can fit,
FIG. 6. (Color online) Mean values of the indexes reflecting the importance
of the factors manipulated in this study, computed across the four main
experimental conditions (different panels). For each index, all the factors
(except the one the index was based on) were pooled together. Error bars
show SEM across subjects.
J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al. 265
overall, the increase obtained in experiment 1, indicating
that global loudness could be compatible with a certain inte-
gration of STL over a window, which was around 500-ms in
that case (i.e., experiment 1, group A). However, further
analyses have to be undertaken to confirm that the integration
mechanism is indeed involved, and if this is the case, to deter-
mine the shape and the length of such a temporal window, and
to what extent it depends on the experimental context and con-
ditions. Indeed, our results suggest that the size of this integra-
tion window would depend on the ramp parameters or
experimental context. Nevertheless, none of the three indica-
tors considered were able to account for the asymmetries
observed between rising and falling tones and, consequently,
for the fact this asymmetry depends on ramp parameters such
as its dynamics. Therefore, even though an integration mecha-
nism could be part of the global loudness evaluation process of
rising and falling ramps, there are certainly other mechanisms
involved that still remain to be determined.
According to Moore (2014),LTLissupposedtoreflect
“relatively high-level cortical processes and involves memo-
ry,” although the location at which LTL is represented in the
brain has not been examined yet (for a discussion, see
Thwaites et al., 2016). LTL computation involves another
AGC with a long decreasing time constant aiming to reflect
the fact that the overall impression “can persist for several sec-
onds after a sound has ceased” while gently decaying when
the sound is turned off. Here, we show that this is not the case
and that the computation of global loudness from STL or LTL
patterns is more complex than just considering their maximum
value. It is very likely that the processes involved in global
loudness evaluation of rising and falling tones of a few seconds
are presumably part of high-level integration stages not yet
reflected by LTL, which is simply based on a temporal integra-
tion of STL (reflecting the loudness consciously accessible at
any instant). Further psychophysical studies have to be con-
ducted with more complex time-varying sounds before a
model covering the whole set of high-level processes underly-
ing the computation of global loudness could be implemented.
Are such mechanisms specific to loudness evaluation?
There are some studies in the literature indicating that the pro-
cesses examined here in the case of global loudness evaluation
might actually be involved in overall judgments of other types
of sensory information. For example, although the time scale
and the amount of perceptual variation are not the same, the
results obtained for the overall evaluation of increasing and
decreasing sequences of pain yielded similar trends to those
observed in the present study (Ariely and Carmon, 2000). In
particular, increasing sequences are judged as more painful
that decreasing sequences and the slopes of the sequences play
a significant role. Works addressing overall annoyance evalua-
tion of aversive sounds (e.g., Kahneman et al., 1993;V€
astfj€
all,
2004) or the overall evaluation of image quality (Hamberg and
de Ridder, 1999)havebroughttolightimportantprinciples
governing overall evaluation, such as “peak-end” rules and
recency effects, which are often observed in global loudness
judgments of time-varying sounds (e.g., Dittrich and Oberfeld,
2009). Could an integration mechanism be the basis of any
overall evaluation of every rising or falling pattern? Whether
the mechanisms underlying global loudness evaluation are
also involved in the overall evaluations of other sensory attrib-
utes is an aspect that deserves to be specifically addressed in
future studies. It could be particularly fruitful to take a step
back from the specific case of rising and falling level patterns,
and investigate the processing of more complex contours spe-
cifically dedicated to test the decay and the integration mecha-
nisms. One could think of using contours that increase to a
fixed amplitude (or have multiple maximums) and finish at dif-
ferent values so that the maximum does not occur at the end.
One could also vary the position of the maximum in the con-
tour. If the integration mechanism applies, sounds of various
contours but identical maxima should receive similar loudness
judgments. In a similar fashion, one might test the decay
mechanism using V-shaped level contours so that the mini-
mum does not occur at the end. Such investigations should
undoubtedly provide important elements for a better under-
standing of the machinery underlying global loudness process-
ing in a general context.
As pointed out by Ariely (1998): “[…] although this
work examines only one domain of experience (namely pain),
one can speculate that the relationship between momentary
and overall evaluations will apply to other domains as well.”
Reinforcing our knowledge of psychoacoustics with the
investigation of higher-level integration mechanisms related
to general principles of time-varying information processing
would provide important information concerning the mecha-
nisms underlying overall evaluation of dynamic loudness
and, more generally, the mechanisms underlying overall eval-
uation of dynamic sensory events over long time scales.
ACKNOWLEDGMENTS
The authors would like to thank Anne-Laure Verneil for
her help in conducting the experiments. We are particularly
grateful to Robert Teghtsoonian for his comments on an
earlier version of this document. We would also like to
thank Daniel Oberfeld and Stephen Handel for insightful
comments when reviewing this paper. This work was
supported by the project LoudNat funded by the French
National Research Agency (Grant No. ANR-11-BS09-016-
01). Some of the results of this paper were presented at the
30th Meeting of the International Society for Psychophysics,
Fechner Day, in Lund, Sweden, August 2014.
1
One might ask whether taking the average values of STL or LTL outputs
is a better option; this is not the case as this would return even poorer esti-
mates because the averaging operation would dilute the small effects pro-
duced by the asymmetric temporal integration stages (see the discussion in
Ponsot, 2015).
2
One may ask why this decay mechanism would affect falling ramps stronger
than rising ramps. One might compare the decay mechanism to the process
behind time-order errors (TOEs), i.e., the fact that two stimuli compared in a
pair receive different weightings (e.g., Hellstr€
om, 1985). The idea behind
TOEs in successive paired comparison is that the second stimulus is com-
pared with the trace or the memory image of the first one. This trace is inher-
ently fading or disintegrating over time, a phenomenon that is accounted for
by, for example, the sensation weighting model (Hellstr€
om, 1985). In prac-
tice, as the time interval between the two stimuli increases, the weight attrib-
uted to the first stimulus in the judgment decreases given that the uncertainty
of its trace increases (Hellstr€
om and Rammsayer, 2004). Recent results on
temporal loudness weighting of rising and falling ramps showed that observ-
ers exclusively focus on the loudest portions of the sounds for judging their
global loudness, i.e., on the end of rising ramps and the start falling ramps
266 J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al.
(Ponsot et al., 2013). In this context, it is reasonable to assume that the dis-
ruption of the trace is weaker for up-ramps than for down-ramps: While no
sensory stimulation separates the end of a rising ramp from its judgment, the
trace of the starting portion of a falling ramp is disrupted by its continuing
decreasing level. As a result, TOEs (or such related effects) are likely affect-
ing more the judgment of a falling ramp (i) because we integrate a portion
located further in time, and (ii) because this integration is disrupted by the
following part of the stimulus.
3
This parameter manipulation was inspired from studies examining the
influence of these factors to investigate the mechanisms underlying loud-
ness change judgments (Can!
evet et al., 2003;Teghtsoonian et al., 2005).
4
All the ratings given by a listener to both constant tones and ramps were
divided by the mean rating assigned to the 60-dB SPL constant-intensity
tone and multiplied by four. As in previous papers (Susini et al., 2010;
Ponsot et al., 2015a), this normalization intended to match the estimate
attributed to the 60-dB SPL, 1-kHz pure-tone to a value of 4 sones.
However, magnitude estimates normalized in that way are not directly inter-
pretable as sones (according to the standard sone definition) because the
sound level corresponds to the one of a monaural source presented at the
input of the ear canal, not to a sound source frontally presented in free field.
5
The durations employed in this experiment being equal or greater than 1 s,
we are well beyond the durations at which “temporal integration of loud-
ness” occurs, which is generally assumed to be fully completed at 300 ms
(see Rennies et al., 2010;Hots et al., 2014). As a result, the loudness of
constant tones should not be affected by any change of their duration.
6
It is important to note that the analyses and discussions of the present
paper are based on aggregate data. Because substantial interindividual dif-
ferences were observed in the different experiments (not detailed in this
paper), it remains to explore to what extent individual behaviors can be
captured by the mechanisms inferred from the “aggregate observer.”
Indeed, even if the mean trends captured in these experiments comply to
some extent to what one would expect from a given mechanism (e.g., an
integration mechanism), this does not yet constitute a “proof” that observ-
ers were indeed behaving according to this mechanism. Further studies are
necessary to demonstrate that the mechanisms indeed reflect the process-
ing of every observer.
7
The asymmetries produced by the model are the consequence of the two
temporal integration stages employed to derive, first, STL and, second, LTL
from the instantaneous loudness (IL) pattern (see Ponsot et al., 2015a).
Ariely, D. (1998). “Combining experiences over time: The effects of dura-
tion, intensity changes and on-line measurements on retrospective pain
evaluations,” J. Behav. Decis. Making 11(1), 19–45.
Ariely, D., and Carmon, Z. (2000). “Gestalt characteristics of experiences: The
defining features of summarized events,” J. Behav. Decis. Making 13,191–201.
Buus, S., Florentine, M., and Poulsen, T. (1997). “Temporal integration of
loudness, loudness discrimination, and the form of the loudness function,”
J. Acoust. Soc. Am. 101(2), 669–680.
Can!
evet, G., Teghtsoonian, R., and Teghtsoonian, M. (2003). “A compari-
son of loudness change in signals that continuously rise or fall in
amplitude,” Acta Acust. Acust. 89(2), 339–345.
Chalupper, J., and Fastl, H. (2002). “Dynamic loudness model (DLM) for nor-
mal and hearing-impaired listeners,” Acta Acust. Acust. 88(3), 378–386.
Cross, D. V. (1973). “Sequential dependencies and regression in psycho-
physical judgments,” Percept. Psychophys. 14(3), 547–552.
Dittrich, K., and Oberfeld, D. (2009). “A comparison of the temporal weight-
ing of annoyance and loudness,” J. Acoust. Soc. Am. 126(6), 3168–3178.
EBU–Recommendation R 128 (2011). Loudness normalisation and permit-
ted maximum level of audio signals (European Broadcasting Union,
Geneva, Switzerland).
Glasberg, B. R., and Moore, B. C. (2002). “A model of loudness appli-
cable to time-varying sounds,” J. Audio Eng. Soc. 50(5), 331–342.
Gottschling, G. (1999). “On the relations of instantaneous and overall loud-
ness,” Acta Acust. Acust. 85(3), 427–429.
Hamberg, R., and de Ridder, H. (1999). “Time-varying image quality:
Modeling the relation between instantaneous and overall quality,” SMPTE
J. 108(11), 802–811.
Hellbr€
uck, J. (2000). “Memory effects in loudness scaling of traffic noise.
How overall loudness of short-term and long-term sounds depends on
memory,” J. Acoust. Soc. Jpn. (E) 21(6), 329–332.
Hellman, R. P. (1982). “Loudness, annoyance, and noisiness produced by
single-tone-noise complexes,” J. Acoust. Soc. Am. 72(1), 62–73.
Hellstr€
om, A
˚.(
1985). “The time-order error and its relatives: Mirrors of cog-
nitive processes in comparing,” Psychol. Bull. 97(1), 35–61.
Hellstr€
om, A
˚., and Rammsayer, T. H. (2004). “Effects of time-order, inter-
stimulus interval, and feedback in duration discrimination of noise bursts
in the 50- and 1000-ms ranges,” Acta Psychol. 116(1), 1–20.
Hots, J., Rennies, J., and Verhey, J. L. (2014). “Modeling temporal integra-
tion of loudness,” Acta Acust. Acust. 100(1), 184–187.
ITU-R BS.1770. (2006). “Algorithms to measure audio programme loudness and
true-peak audio level,” InternationalTelecommunicationUnion(Geneva,
Switzerland), available online at https://www.itu.int/rec/R-REC-BS.1770/fr.
Kahneman, D., Fredrickson, B. L., Schreiber, C. A., and Redelmeier, D. A.
(1993). “When more pain is preferred to less: Adding a better end,”
Psychol. Sci. 4(6), 401–405.
Kuwano, S., and Namba, S. (1985). “Continuous judgment of level-
fluctuating sounds and the relationship between overall loudness and
instantaneous loudness,” Psychol. Res. 47(1), 27–37.
Kuwano, S., Namba, S., Kato, T., and Hellbr€
uck, J. (2003). “Memory of the
loudness of sounds in relation to overall impression,” Acoust. Sci.
Technol. 24(4), 194–196.
Meunier, S., Susini, P., Trapeau, R., and Chatron, J. (2010). “Global loudness of
ramped and damped sounds,” in 20th International Congress on Acoustics.
Moore, B. C. (2014). “Development and current status of the ‘Cambridge’
loudness models,” Trends Hear. 18, 2331216514550620.
Moore, B. C., Glasberg, B. R., Varathanathan, A., and Schlittenlacher, J.
(2016). “A loudness model for time-varying sounds incorporating binaural
inhibition,” Trends Hear. 20, 2331216516682698.
Neuhoff, J. G. (1998). “Perceptual bias for rising tones,” Nature 395(6698),
123–124.
Oberfeld, D., and Plank, T. (2011). “The temporal weighting of loudness:
Effects of the level profile,” Atten. Percept. Psychophys. 73(1), 189–208.
Olsen, K. N. (2014). “Intensity dynamics and loudness change: A review of
methods and perceptual processes,” Acoust. Aust. 42(3), 159–165.
Ponsot, E. (2015). “Global loudness processing of time-varying sounds,”
Doctoral dissertation, UPMC, p. 39.
Ponsot, E., Meunier, S., Kacem, A., Chatron, J., and Susini, P. (2015b).“
Are rising sounds always louder? Influences of spectral structure and
intensity-region on loudness sensitivity to intensity-change direction,”
Acta Acust. Acust. 101, 1083–1093.
Ponsot, E., Susini, P., and Meunier, S. (2015a). “A robust asymmetry in
loudness between rising- and falling-intensity tones,” Atten. Percept.
Psychophys. 77(3), 907–920.
Ponsot, E., Susini, P., and Meunier, S. (2016). “Loudness processing of
time-varying sounds: Recent advances in psychophysics and challenges
for future research,” in INTER-NOISE and NOISE-CON Congress and
Conference Proceedings, Vol. 253, No. 2, pp. 6437–6442.
Ponsot, E., Susini, P., Saint Pierre, G., and Meunier, S. (2013). “Temporal
loudness weights for sounds with increasing and decreasing intensity
profiles,” J. Acoust. Soc. Am. 134(4), EL321–EL326.
R Core Team (2015). “R: A language and environment for statistical
computing,” R Foundation for Statistical Computing, Vienna, Austria,
available at http://www.R-project.org/ (Last viewed July 6, 2017).
Rennies, J., Verhey, J. L., and Fastl, H. (2010). “Comparison of loudness
models for time-varying sounds,” Acta Acust. Acust. 96(2), 383–396.
Ries, D. T., Schlauch, R. S., and DiGiovanni, J. J. (2008). “The role of temporal-
masking patterns in the determination of subjective duration and loudness for
ramped and damped sounds,” J. Acoust. Soc. Am. 124(6), 3772–3783.
Schreiber, C. A., and Kahneman, D. (2000). “Determinants of the remem-
bered utility of aversive sounds,” J. Exp. Psychol.: General 129(1), 27–42.
Susini, P., McAdams, S., and Smith, B. K. (2002). “Global and continuous loud-
ness estimation of time-varying levels,” Acta Acust. Acust. 88(4), 536–548.
Susini, P., McAdams, S., and Smith, B. K. (2007). “Loudness asymmetries
for tones with increasing and decreasing levels using continuous and
global ratings,” Acta Acust. Acust. 93(4), 623–631.
Susini, P., Meunier, S., Trapeau, R., and Chatron, J. (2010). “End level bias
on direct loudness ratings of increasing sounds,” J. Acoust. Soc. Am.
128(4), EL163–EL168.
Teghtsoonian, R., Teghtsoonian, M., and Can!
evet, G. (2005). “Sweep-
induced acceleration in loudness change and the ‘bias for rising
intensities,’ ” Percept. Psychophys. 67(4), 699–712.
Thwaites, A., Glasberg, B. R., Nimmo-Smith, I., Marslen-Wilson, W. D.,
and Moore, B. C. (2016). “Representation of instantaneous and short-term
loudness in the human cortex,” Front. Neurosci. 10, 183.
V€
astfj€
all, D. (2004). “The ‘end effect’ in retrospective sound quality eval-
uation,” Acoust. Sci. Technol. 25(2), 170–172.
Zwicker, E., and Fastl, H. (1999). Psychoacoustics: Facts and Models
(Springer Science and Business Media, Berlin), Vol. 22.
J. Acoust. Soc. Am. 142 (1), July 2017 Ponsot et al. 267
