 View Online  Export Citation FEBRUARY 02 2026 Time-varying partial loudness of noise burst sequences in stationary noise with a similar level Josef Schlittenlacher ; Agatha R. Cox; Brian C. J. Moore J. Acoust. Soc. Am. 159, 1048–1056 (2026) https://doi.org/10.1121/10.0042387 Articles You May Be Interested In Testing and refining a loudness model for time-varying sounds incorporating binaural inhibition J. Acoust. Soc. Am. (March 2018) On the loudness of low-frequency sounds with fluctuating amplitudes J. Acoust. Soc. Am. (August 2019) Influence of interaural time differences on loudness for low-frequency pure tones at varying signal and noise levels Proc. Mtgs. Acoust. (August 2017) 18 February 2026 10:42:45 https://pubs.aip.org/asa/jasa/article/159/2/1048/3378462/Time-varying-partial-loudness-of-noise-burst https://pubs.aip.org/asa/jasa/article/159/2/1048/3378462/Time-varying-partial-loudness-of-noise-burst?pdfCoverIconEvent=cite javascript:; javascript:; javascript:; https://orcid.org/0000-0001-7071-0671 https://crossmark.crossref.org/dialog/?doi=10.1121/10.0042387&domain=pdf&date_stamp=2026-02-02 https://doi.org/10.1121/10.0042387 https://pubs.aip.org/asa/jasa/article/143/3/1504/609577/Testing-and-refining-a-loudness-model-for-time https://pubs.aip.org/asa/jasa/article/146/2/1142/663720/On-the-loudness-of-low-frequency-sounds-with https://pubs.aip.org/asa/poma/article/30/1/050004/908562/Influence-of-interaural-time-differences-on https://servedbyadbutler.com/redirect.spark?MID=188841&plid=3318326&setID=1044502&channelID=0&CID=1578727&banID=524059810&PID=0&textadID=0&tc=1&rnd=5518874329&scheduleID=3474304&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&mt=1771411365700246&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Fasa%2Fjasa%2Farticle-pdf%2F159%2F2%2F1048%2F20888316%2F1048_1_10.0042387.pdf&request_uuid=5a61aebc-d170-4e52-81dc-c96de3136206&hc=7bf3ec77fbb188cec997512ed06440b2d4080a24&location= Time-varying partial loudness of noise burst sequences in stationary noise with a similar level Josef Schlittenlacher,1,a) Agatha R. Cox,1 and Brian C. J. Moore2 1Department of Speech, Hearing and Phonetic Sciences, University College London, London WC1N 1PF, United Kingdom 2Cambridge Hearing Group, Department of Psychology, University of Cambridge, Cambridge CB2 3EB, United Kingdom ABSTRACT: Loudness increases with increasing duration up to 200ms after sound onset. This temporal integration is well documented in quiet but less understood in the presence of other sounds and for very short durations. The present study investigates the temporal integration of partial loudness for bursts of noise in the presence of equally intense background noise. Level differences required for equal loudness between a reference burst duration of 20ms and target burst durations of 1, 2, 5, and 10ms were obtained using a 1-up/1-down staircase procedure in the laboratory and online for burst repetition rates of 5, 10, and 20Hz and for rectangular and Hann shaped bursts. All results showed that the short duration bursts were perceived as louder than expected from the temporal integration of energy. The difference was equivalent to a change in level up to 6.7 dB and was larger for higher burst repetition rates. The difference was higher when using abrupt onsets and offsets for both target and reference compared to bursts with a Hann window shape. Differences between experiments conducted in the laboratory and online were small (up to 1.2 dB) but were statistically significant. VC 2026 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1121/10.0042387 (Received 20 August 2025; revised 25 December 2025; accepted 13 January 2026; published online 2 February 2026) [Editor: Pavel Zahorik] Pages: 1048–1056 I. INTRODUCTION Most noise regulations quantify the impact of a noise source by specifying a level in decibels that must not be exceeded when measured in a quiet test environment. This is an approach that does not always correspond to human perception. The commonly used A-weighted equivalent sound level (LAeq) is based on the average sound intensity over long measurement periods. Some variations of the metric, like the day-night-average sound level [Sec. 3.19 in ANSI/ASA (2013)], the community noise equivalent level [Sec. 3.20 in ANSI/ASA (2013)] or the day-evening-night average sound level (European Union, 2002) add penalties based on the time of day but still do not take into account the distribution of intensity during the measurement period. The latter, however, is important in many real environ- ments, where noise sources are often similar in level to the noisy environments in which they occur, for example in cities. A stationary sound whose intensity is consistently below that of the background noise will have a lower impact on human perception than an overall equally intense but time-varying sound whose peak intensity is well above that of the background noise some of the time. This differ- ence in human loudness perception in the presence of back- ground sounds is considered by the concept and models of partial loudness (e.g., Glasberg and Moore, 2005). The pre- sent study investigates the partial loudness of sequences of short noise bursts in roughly equally intense background noise, i.e., with the signal and background at about the same LAeq—a scenario similar to that of rotorcraft in urban cities, with a focus on the temporal characteristics of the noise bursts. For simultaneous sounds with a similar spectrum, such as a pure tone and narrowband noise centred at the same fre- quency, the tone is essentially inaudible for signal-to-noise ratios (SNRs) smaller than about �3 dB (e.g., Glasberg et al., 1984; Zwicker, 1954). The exact value varies some- what between individuals and depends on frequency. Moore et al. (1997) modelled the masking effect within each audi- tory filter for the average normal-hearing listener assuming a “threshold” SNR of �3 dB for center frequencies above 500Hz and progressively higher “threshold” SNRs with decreasing frequency below 500Hz, the threshold SNR reaching about 10 dB at 50Hz. Experiments on the loudness of signals presented in broadband noise showed that loud- ness grew rapidly with increasing level once the threshold value was exceeded, and for SNRs exceeding about 15 dB, the partial loudness of the signal in noise became similar to that of the signal in quiet (Zwicker, 1963; Stevens and Guirao, 1967; Houtgast, 1974). Thus, partial masking occurs over only a small range of SNRs, and a small change in sig- nal level can lead to a rather large change in loudness (see also, for example, Schroeder et al., 1979). When a pure tone or complex tone acts as the background and a noise is the target, the SNR at the masked threshold is somewhat lower than when the tone is the target and the noise thea)Email: j.schlittenlacher@ucl.ac.uk 1048 J. Acoust. Soc. Am. 159 (2), February 2026 VC Author(s) 2026. ARTICLE................................... 18 February 2026 10:42:45 https://orcid.org/0000-0001-7071-0671 https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.1121/10.0042387 mailto:j.schlittenlacher@ucl.ac.uk http://crossmark.crossref.org/dialog/?doi=10.1121/10.0042387&domain=pdf&date_stamp=2026-02-02 background, but the growth of partial loudness with increas- ing level above the masked threshold is about equally steep (Hellman, 1972; Gockel et al., 2002, 2003). All of these studies have used stationary sounds, except for the modulations inherent to narrowband noise. For time- varying sounds, duration has an important influence on loud- ness. In quiet, the loudness of a sound grows with increasing duration up to 150 to 200ms (e.g., Scharf, 1978). This effect is known as temporal integration. Some studies reported shorter “critical durations” above which loudness reaches its final value, for example 65ms for noise bursts (Miller, 1948). For durations longer than the critical duration, loud- ness does not grow further with increasing duration. Pollack (1958) reported a critical duration of 100ms for noise bursts presented one per second, but his data showed considerably shorter critical durations for sequences with more bursts per second, for example 10ms for nine bursts per second. Studies measuring reaction time, which is thought to be gov- erned by similar neural processes to loudness and decreases progressively with increasing loudness, have shown a criti- cal duration of 40ms for pure tones (Schlittenlacher and Ellermeier, 2015). For durations shorter than the critical duration, the increase in loudness with duration has often been approxi- mated with a simple model such that an increase in level of 3 dB has the same effect as a doubling of duration, as if energy was integrated over time (e.g., Pollack, 1958; Zwicker, 1974). This has the convenient effect for simple metrics such as the LAeq that the metric captures the effects of temporal integration, although only for durations shorter than the critical duration and not taking into account effects such as the dependence of temporal integration on absolute level (Florentine et al., 1996). In this study, temporal inte- gration, measured as the level difference required for equal loudness (LDEL) between 5-ms and 200-ms sounds, was about 10 dB near threshold but almost 20 dB at moderate sound pressure levels (SPLs) (about 65 dB). More complex loudness models incorporate temporal integration towards the end of the processing chain, i.e., at a higher level of the auditory pathway. The Cambridge loud- ness models (e.g., Glasberg and Moore, 2002; Moore et al., 2016) distinguish between instantaneous loudness, short- term loudness for judgments of short segments such as a syllable, and long-term loudness for judgments of longer segments, such as a sentence. Instantaneous loudness is thought to be a stage involved in forming the loudness per- cept, but it may not be directly perceived. Areas in the brain that track the instantaneous loudness of speech stimuli have been identified using magnetoencephalography (Thwaites et al., 2016; Thwaites et al., 2017). Instantaneous loudness is calculated using time frames (windows) whose durations are chosen to be as short as possible while achieving the desired spectral resolution. The window sizes range from 2ms for high frequencies to 64ms for low frequencies. For signals shorter than this, the windows act like smoothers and effectively integrate intensity. Short-term loudness is calcu- lated from instantaneous loudness using a function resembling an automatic gain control circuit with an attack time constant of 22ms. The attack time constant determines the rate of increase in loudness with duration; the temporal build-up corresponds to that of a first-order system [see Glasberg and Moore (2002) for details]. Long-term loudness is calculated from short-term loudness using a similar circuit but with an attack time constant of 99ms. When a sound is abruptly turned on, the predicted loudness builds up over a duration equal to about two to three times the respective time constant, plus the time associated with previous steps, since the build-up of long-term loudness is in series with the build-up of short-term loudness. Relatively little is known about the temporal integration of partial loudness. On the one hand, one could argue that if temporal integration is governed by high-level processes, partial loudness may build up over time in the same way as loudness in quiet. On the other hand, one may argue that since the auditory system is already excited by the back- ground sound, the loudness of any further sound presented at a suprathreshold level may build up more quickly than for that sound presented in quiet. Florentine et al. (1998) com- pared the loudness of tones with equivalent rectangular durations of 5ms and 200ms. When the tones were pre- sented in broadband noise with a level of 60 dB SPL, the LDEL of the two tones was about 15 to 20 dB for all audible levels of the tone. This is smaller than the LDEL of about 25 dB for a 60-dB-SPL tone in quiet and similar to the LDELs found near absolute threshold and for very high lev- els in quiet. The LDELs of Florentine et al. (1998) quanti- fied the total amount of temporal integration but did not give information about the time course of temporal integra- tion. Specifically, they did not measure temporal integration over the first few milliseconds following the onset of a sound, which may be important for impulsive sounds. Richards (1977) measured temporal integration of partial loudness for a 1-kHz tone with durations from 10 to 640ms, using several tone and masker levels. For most conditions, his results were fitted well by two straight lines, with a more rapid growth of loudness for durations up to 80ms than for higher durations. A peculiarity of the results was that tempo- ral integration continued for durations up to at least 640ms, even in quiet. For a 60-dB-SPL tone in a 50-dB-SPL noise, temporal integration was similar to that in quiet and similar to that expected from intensity integration, i.e., the growth of loudness with duration corresponded to accumulating the sound’s energy over time. The present study was intended to contribute to knowl- edge about the temporal integration of partial loudness for very short sounds (noise bursts) using burst durations up to 20ms. Since purely temporal aspects of sound are usually produced with high precision with any hardware, most of the experiments were performed online, but one experiment was repeated in the laboratory to quantify possible differ- ences between online and laboratory measurements. LDELs were estimated between bursts with durations of 1, 2, 5, and 10ms and bursts with durations of 20ms, using burst repeti- tion rates of 5, 10, and 20Hz. Abrupt onsets and offsets J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. 1049 https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 https://doi.org/10.1121/10.0042387 were used to produce these short durations. A final experi- ment was conducted to investigate differences between rect- angularly shaped bursts and Hann-window shaped bursts. All experiments used an SNR of 0 dB, which is of particular interest for predicting community acceptance of a new noise source with a level similar to that of existing noise sources. If the level of a new noise source was much higher than that of existing noise sources, it would likely be judged as a major nuisance; if its level was much lower, and it was masked by the ambient noise to a large extent, its low loud- ness would likely be tolerated. The temporal sequence of noise bursts resembled the repetition of bursts produced by rotorcraft, and the results may guide the sound design of helicopters, drones, or electric vertical takeoff and landing vehicles (“flying taxis”) regarding the shaping of their over- all temporal envelope. II. METHOD Five experiments were conducted in total, four of them online. Experiments 1a and 1b used the same stimuli and almost identical methods but were conducted in the labora- tory and online, respectively. Experiments 1 to 3 differed in burst frequency, with ten bursts per second for experiment 1, five bursts per second for experiment 2, and 20 bursts per second for experiment 3. Experiment 4 investigated if employing rise and fall times rather than abrupt onsets and offsets of the bursts had an effect on the LDEL. Each participant took part in only one experiment, so burst repeti- tion rate and location were studied between-subjects. Experiment 3 was conducted in 2021, and preliminary results were presented at Inter-noise (Schlittenlacher and Moore, 2021). All other experiments were conducted in 2024 and 2025. A. Participants Twenty participants completed each experiment, except for experiment 1a, which was completed by sixteen partici- pants. The participants for experiment 1a were recruited on campus. Nine participants for experiment 3 were recruited via a university website. All other participants were recruited via the “Prolific” platform (prolific.com). Participants tested in the laboratory were checked to have normal hearing (better than 20 dB hearing level) in both ears. The online participants self-reported having no hearing loss and no hearing difficulties. Nobody participated in more than one experiment. All participants were reimbursed for their time. Sexes and ages of the participants are shown in Table I. B. Stimuli The background sound was taken from a recording of an urban highway. Due to the high amount of traffic, it was rather stationary. It was bandpass filtered with cutoff fre- quencies of 250 and 4000Hz using a sixth-order Butterworth filter. This was done to ensure a frequency range that could be reproduced by consumer hardware in online experiments. Two seconds were cut from the record- ing and 20-ms raised cosine rise and fall times were applied. This segment was “frozen,” i.e., the same for all trials and experiments. Figure 1 shows its average spectrum (left panel) and waveform and envelope, the latter obtained through half-wave rectification and 50-Hz low-pass filtering (right panel). To confirm that the background sound was TABLE I. Age and sex of the participants for each experiment. Experiment Female Male Age range (years) Mean age (years) 1a 12 4 19–61 32 1b 10 10 27–64 40 2 12 8 20–60 41 3 11 9 20–52 29 4 7 13 21–73 37 FIG. 1. Characteristics of the background sound. The left panel shows the average spectrum of the frozen background sound as used in the experiments (blue line) and from its recording before bandpass filtering (black dashed line). The right panel shows the waveform of the background sound and its enve- lope (blue line), obtained through half-wave rectification and 50-Hz low-pass filtering. 1050 J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 http://prolific.com https://doi.org/10.1121/10.0042387 stationary, its short-term loudness level was calculated using the model of Moore et al. (2018) and analyzed from 200ms after the onset (to disregard the growth of calculated loud- ness after the onset of the sound) to the end, using a root mean square level of 65 dB SPL. The short-term loudness level ranged between 80.2 phon and 82.4 phon with a mean of 81.4 phon and a standard deviation of 0.4 phon. The target sounds were bursts cut from a synthetic noise that had the same magnitude spectrum as the background sound but random and thus different phases of the compo- nents. The noise was synthesized to have a low crest factor (so-called “low-noise” noise) using the method described by Moore et al. (2004) and parameters (except for the desired spectrum) used by Moore et al. (2018). This was done to minimize the chance of waveform clipping in the online experiments. Note that the low-noise property depends on the specific choice of component phases for the entire broad- band signal. In the auditory system, the broadband signal is filtered into multiple narrow bands, and this destroys the “low-noise” property [for details, see Chap. 1 in Moore (2014)]. The noise bursts had durations of 1, 2, 5, 10, or 20ms and were presented in burst sequences with a total duration of 1600ms and burst rates of 5, 10, or 20Hz. Odd- numbered bursts were cut from the synthetic noise. Even numbered bursts were the same as the preceding bursts except for a phase shift of 180 degrees. This was done to avoid any overall offset of the mean amplitude from zero. The sequence of bursts was presented simultaneously with the background sound, starting 200ms after the background sound started. In experiments 1 to 3, the bursts had abrupt onsets and offsets. In experiment 4, half of the stimuli had bursts with raised-cosine shaped rise and fall times that were half of the stimulus duration each, i.e., their waveform was multiplied with a Hann window that had the same dura- tion as each burst. The other half of the stimuli had bursts with abrupt onsets and offsets. C. Apparatus Experiment 1a was conducted in the laboratory. Stimuli were generated and presented via MATLAB (The Mathworks, Natick, MA), an RME (Haimhausen, Germany) Hammerface sound card, and Sennheiser (Wedemark, Germany) HD580 headphones, which have a diffuse-field response and produce 95 dB SPL for a 1-V 1000-Hz sinusoi- dal input, as measured in KEMAR dummy head (GRAS Sound and Vibration, Holte, Denmark). Participants sat in a double-walled sound-attenuating booth. The SPL of the ref- erence stimuli was set to 65 dB SPL. Experiments 1b to 4 were conducted online. Participants were asked to wear headphones and to use a desktop computer or laptop. Stimuli were presented via a web browser with code written in JavaScript and the Web Audio API. For setting the refer- ence level, participants were asked to play a female speech sound from the LibriSpeech corpus (Panayotov et al., 2015) at a loudness typical for speech and not to change the system settings thereafter. The speech sound was a sentence that lasted six seconds and was repeated until the participant clicked a button to continue. The root-mean-square (RMS) level of the reference stimuli was the same as the RMS level of that speech stimulus. D. Procedure All experiments measured the LDEL between a refer- ence stimulus that had noise bursts with a duration of 20ms and a target stimulus that had shorter bursts. The sequences of bursts were presented in the urban background sound whose level was kept constant at 65 dB SPL (laboratory, experiment 1a) or the reference level determined by the speech sound (online, experiments 1b to 4). LDELs were determined with a two-interval, two-alternative forced- choice task in which the participants indicated which of the two helicopter-like sounds, i.e., noise burst sequences, was louder. Four LDELs were determined for each condition: Either the level of the 20-ms bursts was varied or the level of the shorter bursts was varied. The variable sound started at an RMS level either 10 dB higher or 10 dB lower than the RMS level of the background sound. The RMS level of the fixed sequence of bursts was always equal to the level of the background sound. After each response, the level of the noise bursts in the variable sound was changed in a 1-up/1- down procedure (Levitt, 1971) until eight reversals occurred. The step sizes were 5 dB for the first two reversals, 3 dB for the next two reversals, and 1 dB for the remaining four reversals. The mean level at the last four reversals was used to estimate the LDEL. In experiments 1 to 3, the target sounds had burst dura- tions of 1, 2, 5, and 10ms. The repetition rate of the bursts was 10Hz in experiment 1, 5Hz in experiment 2, and 20Hz in experiment 3. In experiment 4, the target sound always had a burst duration of 2ms, i.e., sequences of 2-ms bursts were compared to sequences of 20-ms bursts. The burst rep- etition rates were 5 and 20Hz, and the bursts either had abrupt onsets and offsets or their envelopes were multiplied by a Hann window, thus also resulting in four conditions. Table II gives an overview of all conditions. The combination of burst duration, burst repetition rate, and shape of burst onsets and offsets resulted in four condi- tions in each experiment. Since four LDELs were measured for each condition, there were four up-down tracks per con- dition, resulting in sixteen tracks in each experiment. The experiments were divided into blocks, which were run in a pseudo-random order and between which participants were encouraged to take breaks. Each experiment lasted about 40–45min on average. Experiments 1b, 2, and 3 differed only in the repetition rate and participants. Experiments 1a and 1b differed in whether the experiment was done in the laboratory or online and in one aspect of the procedure: In experiment 1a, the four tracks for a single condition were interleaved, i.e., presented in one block with the software randomly choosing which of the four tracks was presented on the next trial. In the online experiments, a block con- sisted of one track. Thus, there were four blocks in J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. 1051 https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 https://doi.org/10.1121/10.0042387 experiment 1a (the four conditions) and sixteen blocks (four conditions times four tracks) in all other experiments. E. Analysis Unless stated otherwise, LDELs are expressed as the RMS level of the sequence with the shorter bursts minus the RMS level of the sequence with the 20-ms bursts; silent intervals between bursts were included in the RMS calcula- tion. Thus, a negative LDEL indicates that the sequence with the shorter pulses needed less overall energy than the sequence with longer pulses to give equal loudness. The energy across the whole sequence of 1.6 s rather than the power of a single burst was used to allow a direct compari- son with noise evaluation metrics that also average the energy across the whole duration of measurement. For example, an LDEL of �8 dB between a sequence with 1-ms bursts and a sequence with 20-ms bursts would indicate that the sequence with 1-ms bursts needed 8 dB less energy for equal loudness but the power of a single 1-ms burst was 5 dB higher than that of a 20-ms burst since the 20-ms bursts accumulated energy during 20 times as much time (10log10(20)¼ 13 dB). In the rest of this paper, the term energy is used to refer to the energy during the whole 1.6 s of the burst sequence, and the term burst power to refer to the power that is present during a single burst. To allow an easier comparison to studies that used burst power as the measure, all figures contain a second panel with the same data but with the LDELs expressed as the level difference between the noise bursts themselves. All data from a participant were excluded from the analysis when the four LDELs for any condition differed by more than 20 dB. This limit was chosen because it was the difference between starting values of the up-down tracks and random clicking without listening would result in a dis- crepancy between tracks of that order of magnitude. This led to the exclusion of one participant for experiment 1a, four participants for experiment 1b, four participants for experiment 2, three participants for experiment 3, and three participants for experiment 4. A within-subjects analysis of variance (ANOVA) was computed for each experiment. This was a one-way ANOVA with factor burst duration for experiments 1 to 3 and a two-way ANOVA with factors window shape and rep- etition rate for experiment 4. An additional ANOVA with additional between-subjects factor location was computed for the combined data of experiments 1a and 1b to estimate the effect size of the difference between laboratory and online data collection. III. RESULTS The results of experiments 1a and 1b are shown in Fig. 2. Average LDELs based on the RMS levels of the whole sequences (left panel) ranged from �3.4 dB for 1-ms target bursts to �1.3 dB for 10-ms target bursts for experi- ment 1a and from �4.6 dB to �0.4 dB for the online data from Experiment 1b. A two-way ANOVA showed a signifi- cant effect of duration, F(3,87)¼ 30.1, p< 0.001, g2p ¼ 0.509, no significant effect of location, F(1,29)¼ 0.428, p¼ 0.518, g2p ¼ 0.015, but a significant interaction between the two factors, F(3,87)¼ 3.51, p¼ 0.019, g2p ¼ 0.108. Together with the descriptive results, this indi- cates that the effect of duration on the LDEL based on RMS level of the sequence was a little greater for the online data and conversely a little smaller based on the burst levels. In other words, for the shortest duration, temporal integration was somewhat closer to that expected from integration of intensity in the laboratory than in the online experiment. Separate one-way ANOVAs for each experiment yielded a significant main effect of duration in both cases, F(3,42)¼ 7.08, p< 0.001, g2p ¼ 0.336 for experiment 1a and F(3,45)¼ 26.4, p< 0.001, g2p ¼ 0.638 for experiment 1b. The results for the burst sequences with repetition rates of 5Hz (experiment 2, red line with circles in Fig. 3) and 20Hz (experiment 3, blue line with squares in Fig. 3) showed similar patterns. For a burst duration of 1ms, the LDEL based on the whole sequence was �3.3 dB for the repetition rate of 5Hz and �6.7 dB for the repetition rate of 20Hz. Overall, the LDELs became more negative (left panel) or smaller (right panel) with increasing burst repeti- tion rate. One-way ANOVAs based on the whole sequence yielded significant main effects of duration: F(3,45)¼ 20.0, p< 0.001, g2p ¼ 0.571 for experiment 2 and F(3,48)¼ 85.6, p< 0.001, g2p ¼ 0.843 for experiment 3. The LDELs for the Hann-windowed bursts conformed more closely to integration of energy than for the bursts with abrupt onsets and offsets but were still negative (exper- iment 4, Fig. 4, left panel). The LDELs were more negative for the higher burst repetition rate. For the Hann-windowed bursts, the rise and fall times were shorter for the 2-ms bursts than for the 20-ms bursts since the window length equaled the burst duration. Experiment 4 replicated the results obtained in the previous experiments for the 2-ms bursts with rectangular envelopes, with LDELs (based on TABLE II. Overview of experimental conditions. Experiment Location Burst durations (ms) Burst repetition rate (Hz) Burst onsets and offsets 1a Lab 1, 2, 5, 10 10 Abrupt 1b Online 1, 2, 5, 10 10 Abrupt 2 Online 1, 2, 5, 10 5 Abrupt 3 Online 1, 2, 5, 10 20 Abrupt 4 Online 2 5, 20 Abrupt, Hann window 1052 J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 https://doi.org/10.1121/10.0042387 the whole sequence) of �1.9 dB for the 5-Hz repetition rate (experiment 2: �1.4 dB) and �4.4 dB for the 20-Hz repeti- tion rate (experiment 3: �4.9 dB). A two-way within-sub- jects ANOVA yielded significant main effects of window shape, F(1,16)¼ 14.6, p¼ 0.001, g2p ¼ 0.477, and repetition rate, F(1,16)¼ 18.4, p< 0.001, g2p ¼ 0.535, and a significant interaction, F(1,16)¼ 6.60, p¼ 0.021, g2p ¼ 0.292. The results of all experiments were compared with pre- dictions of a model for partial loudness (Glasberg and Moore, 2005; but using the time constants of Moore et al., 2018). Figure 5 shows the participants’ LDELs (abscissa) plotted against the predicted LDELs (ordinate) based on three different measures: The maximum of the long-term partial loudness, which is used to estimate the overall loud- ness of a sound sequence (Glasberg and Moore, 2002; Moore et al., 2016); the mean of the short-term partial loud- ness, which was used by Glasberg and Moore (2005) to esti- mate partial loudness; and the maximum of the instantaneous partial loudness as an extreme without any temporal integration except for the window size of the Fourier transforms. Clearly, none of the measures gave accurate predic- tions. The LDELs predicted using the mean of the partial short-term loudness and the maximum of the long-term par- tial loudness differed by less than 1 dB. This is not surpris- ing because the attack time constants for both short-term and long-term loudness are longer than the durations of the bursts used here, so both types of loudness were still build- ing up when a burst ended. The predictions were close to the values expected from integration of energy (0 dB in the left FIG. 2. LDELs of 20-ms reference bursts and target bursts with durations from 1 to 10ms, for a 10-Hz burst repetition rate (experiment 1). Red circles and blue squares denote means across participants and runs from the laboratory (experiment 1a) and online (experiment 1b), respectively. Error bars denote 61 standard deviation. The left panel shows LDELs based on the RMS level of the whole sequence, while the right panel shows LDELs based on the level of the noise bursts themselves. The dashed line in a given panel represents the 0-dB (no difference) line of the other panel. For example, for the left panel the dashed line represents 0-dB difference in Lpeak (or burst level). FIG. 3. LDELs for 20-ms reference bursts as a function of target burst duration. Red circles and blues squares show mean results for 5-Hz (experiment 2) and 20-Hz (experiment 3) repetition rates. The black line shows the mean results for a 10-Hz repetition rate (experiment 1b) for comparison. Otherwise, as Fig. 2. J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. 1053 https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 https://doi.org/10.1121/10.0042387 panels of Figs. 2 to 4) but slightly positive, implying slightly slower temporal integration. For the fastest temporal integration process assessed here, the maximum value of the instantaneous partial loud- ness, the predicted LDELs were more negative than the obtained LDELs and were close to expectations based on the burst power. For experiment 1, for example, the pre- dicted LDELs based on the whole sequence were �10.7, �7.9, �4.3, and �1.7 dB for burst durations of 1, 2, 5, and 10ms, respectively. The predicted values were similar for the same burst durations in experiments 2 and 3, since the window sizes of the fast Fourier transform mostly included only a single burst for all repetition rates. The results in Fig. 5 suggest that temporal integration of partial loudness for short, repeated bursts is faster than predicted by long-term loudness, short-term loudness, or energy integration. Using the loudness model, a better fit to the present data might be obtained by assuming an addi- tional temporal integration process applied to instantaneous loudness, with an attack time shorter than that used to esti- mate short-term loudness. However, that is beyond the scope of the current paper, since any change in model parameters must not be based on data for impulsive noise bursts alone. IV. DISCUSSION All experiments showed that a simple integration of energy over time, as it is used by various noise evaluation metrics, did not capture the LDEL values for short burst FIG. 4. LDELs for 2-ms target bursts and 20-ms references bursts for each burst shape. Red circles and blues squares show mean results for the 5-Hz and 20-Hz burst rates, respectively. Otherwise, as Fig. 2. FIG. 5. LDELs obtained in all experiments versus predicted LDELs. Blue symbols show LDELs predicted from the maximum of the long-term partial loud- ness, red symbols show LDELs predicted from the mean of the short-term partial loudness, and black symbols show LDELs predicted from the maximum instantaneous partial loudness. Squares show results of experiment 1a (10-Hz burst repetition, laboratory), circles those of experiment 1b (10-Hz burst repe- tition, online), triangles those of experiment 2 (5-Hz burst repetition), plus signs those of experiment 3 (20-Hz burst repetition), and � characters those of experiment 4 (burst shapes). 1054 J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 https://doi.org/10.1121/10.0042387 durations. The deviation of experimental results from pre- dictions based on energy integration was up to 6.7 dB for bursts with abrupt onsets and offsets and the fastest repeti- tion rate (see Fig. 3, left panel). The negative LDELs based on the level of the whole sequence indicate that the temporal buildup of loudness was faster than expected from energy integration. However, it was not instantaneous, shorter burst durations still being less loud than longer burst durations at equal burst power and LDELs not being as negative as would be predicted from instantaneous loudness. Comparable effects of repetition rate have been found for loudness in quiet: the loudness of short bursts of noise increased with repetition rate from 0.3 to 50Hz (Garrett, 1965). The increase was apparent even for low burst rates, i.e., from 1 to 3Hz. This effect might be modelled by chang- ing the release time for short-term loudness. However, to cover the low rates investigated by Garrett, a release time constant close to that for long-term loudness [750ms in Moore et al. (2018)] would be needed. The set of available results thus suggests that the attack time—or build up—of short-term loudness may be faster for short repeated sounds, but the release time—or decay of loudness after a sound event—may be less dependent on the specific sound or even be similar to that for long-term loudness. The Cambridge models of loudness (Glasberg and Moore, 2002; Moore et al., 2016) reflect the concept that the loudness of time-varying sounds cannot be characterized by a single value. Rather, there may be several aspects of loud- ness, such as the momentary loudness of a segment of sound lasting a few hundred ms such as a syllable (short-term loud- ness) and the loudness of a longer sound such as a sentence (long-term loudness). To estimate these different aspects of loudness, the models incorporate a set of time constants, representing different temporal-integration processes. It is possible that a third aspect of loudness is applicable for reg- ular and predictable but very short bursts of sound, as used in the present study. Modelling this may require the use of a very short attack time but with a longer release time to account for integration across bursts and to account for the finding that the LDEL for the 1-ms bursts became more neg- ative with increasing repetition rate. The present experiments used stimuli with the same long-term spectrum for the background and target sounds. This ensured that the LDELs resulted largely from the tem- poral properties of the sounds. However, it may have been more difficult for the listeners to separate the target from background than would be the case for sounds with distinct spectra. The impact of the background being included in the loudness assessment was mitigated by using the same back- ground level in both intervals of the task and by the instruc- tions to judge the loudness of the “helicopter-like” sounds. This instruction might have introduced a bias if participants had a negative attitude towards helicopters. However, this bias would have occurred for both intervals, with no or lim- ited effect on the LDEL. Consider next the effect that the abrupt onsets and off- sets had on the present results. Typically, such abrupt changes in level cause a spectral spread and increase loud- ness. In the present experiments, this effect was mitigated by using the same ramps for the target and the reference and by using a broadband noise carrier, although there may have been some spectral spread outside the passband below 250Hz or above 4000Hz. Experiment 4 showed a statisti- cally significant effect of burst shape, with smaller LDELs for the Hann-windowed bursts. However, the overall pattern was the same as for the abruptly gated bursts. In particular, the LDELs based on the whole sequence were still negative, more so for the higher burst rate. The higher LDELs associ- ated with abrupt onsets are important to consider for highly impulsive sounds such as rotors, sonic booms, or a jackham- mer. Impulsive sounds have often been reported to lead to higher psychoacoustic annoyance (e.g., Torija et al., 2022; Torija and Nicholls, 2022). This is consistent with the results of experiment 4, which suggest that impulsive onsets lead to faster temporal integration and thus higher loudness for short bursts. Another possible explanation for the fast temporal inte- gration found in the present study is that the auditory system was already excited by the background at the time of burst presentation. With a background noise at a level similar to that of the bursts, the total loudness before burst onset was not much less than that of noise and target together. It is possible that some of the neural activity caused by the back- ground was perceptually assigned to the burst, increasing the loudness of the burst and leading partial loudness to build up very quickly in the first few milliseconds. The few decibels of additional temporal integration in the first few milliseconds is comparable to the difference found by Florentine et al. (1998) between the temporal integration of a 60 dB SPL tone in quiet and in the presence of an equally intense masker. The largest difference between the LDELs obtained online and in the laboratory in experiment 2 occurred for the 1-ms bursts, with LDELs of �4.6 dB (online) and �3.4 dB (laboratory; see Fig. 2). The 1.2-dB difference is somewhat larger than the 0.5-dB difference obtained between different conditions online that were replicated in experiment 4. Apart from the headphones used, the difference may come from the use of different populations. Participants in the lab- oratory were primarily young students, which resulted in a lower average age by eight years. Furthermore, the hearing of the laboratory participants was verified as being normal using calibrated equipment. For the online participants, nor- mal hearing was self-reported on the day of the experiment and earlier on the recruitment platform. There may have been a small effect of absolute level, although it is likely that, on average, online participants used a level close to 65 dB SPL. It is unlikely that the less quiet environment online had an effect since the background noise level was high enough to mask many everyday sounds. Even though the interaction with location was statistically significant, the effect size of 1.2 dB was rather small and the overall pattern of the laboratory and online results was similar. Thus, we think that online experiments are suitable for studying trends J. Acoust. Soc. Am. 159 (2), February 2026 Schlittenlacher et al. 1055 https://doi.org/10.1121/10.0042387 18 February 2026 10:42:45 https://doi.org/10.1121/10.0042387 in loudness perception when sounds are compared to a refer- ence, differ only in their temporal characteristics, and are presented in background noise. V. CONCLUSIONS (1) Temporal integration of partial loudness for very short noise bursts was larger than would be expected from integration of energy. The effect was equivalent to a level difference of 6.7 dB for 1-ms bursts compared to 20-ms bursts. (2) Although the partial loudness of short bursts of noise built up more rapidly than expected from integration of energy or calculated using short-term partial loudness, partial loudness still took some time to build up. The LDEL values were smaller in absolute magnitude than would be expected from burst power or calculated instantaneous loudness. 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