Influence of Late Reverberation and Echoes on
Rhythmic Drum Playing

Joris Agator, Sølvi Ystad, Mitsuko Aramaki, Adrien Vidal, Richard

Kronland-Martinet

► To cite this version:

Joris Agator, Sølvi Ystad, Mitsuko Aramaki, Adrien Vidal, Richard Kronland-Martinet. Influence of Late Reverberation and Echoes on Rhythmic Drum Playing. The 17th International Symposium on Computer Music Multidisciplinary Research, Nov 2025, Londres (Grande Bretagne), United Kingdom. 10.5281/zenodo.17498178. hal-05424325

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# Influence of Late Reverberation and Echoes on Rhythmic Drum Playing

Joris Agator¹, Sølvi Ystad¹, Mitsuko Aramaki¹, Adrien Vidal¹, and Richard Kronland-Martinet¹

Aix Marseille Univ, CNRS, PRISM, Marseille, France agator@prism.cnrs.fr

**Abstract.** Musical interpretation is influenced by the acoustics of the room in which musicians perform, though studies are not unanimous about the way acoustical parameters affect musical interpretation. Instead of considering the influence of the global and complex acoustics of a room, the present study focuses on a simpler model. A previous study showed the impact of a single echo on the tempo. This study completes the model by adding a basic synthetic late reverberation. An experimental protocol in which participants were asked to play a rhythmic pattern while hearing an echo and a reverberation was set up for this purpose. The results reveal that the echo has an influence on the tempo produced by the participants: when the delay of the echo is shorter than the inter onset interval of two notes, people tend to accelerate. If the delay is longer, people tend to slow down. However, the reverberation time has no influence on the tempo. This study is a second step to understand musical adaptations to an acoustic environment in the case of rhythmic reproduction.

**Keywords:** rhythm reproduction; echo; synthetic late reverberation; musical interpretation; auditory perception

## 1 Introduction

The acoustic environment, and in particular reverberation, plays an important role in a musical context, both for the listener experience and for the performing musician. Numerous studies have investigated the way musicians adapt their interpretation to the response of the room in which they are performing. However, at present there is no model for predicting how musicians adapt their performance according to the acoustic feedback and the musical piece they are playing. Developing such a model could be of interest when conceiving architectural elements of new concert halls and might also be useful for musical rehearsals to prepare musical performances in specific acoustic environments. Different adaptations of interpretation have been observed, such as the intensity among pianist

<figure><img src="image_2.png" /></figure>

<footnote>All rights remain with the authors under the Creative Commons Attribution 4.0 International License (CC BY 4.0).</footnote>

<footnote>Proc. of the 17th Int. Symposium on Computer Music Multidisciplinary Research, London, United Kingdom, 2025</footnote>
when the reverberation time increases [2], or the extent of violists' vibrato [11]. Luizard *et al.* (2019) [8] showed that singers have individual strategies for adapting to real or virtual acoustics.

Apart from these examples, most studies have focused on the influence of the acoustic environment on the tempo of the performance, in particular the influence of the reverberation time [3, 1, 5, 9, 10]. However, results differ from one study to another. Bolzinger *et al.* (1994) [3] did not observe any variation on the tempo in their studies. More recently, Berg (2019) [1] and Fischinger *et al.* (2015) [5] found that musicians tend to slow down when the reverberation time increases, but Schärer Kalkandjiev *et al.* (2013) [9] equally observed that a professional musician in concert conditions also slows down with a short reverberation time. The same study also revealed that an important early acoustical support (i.e. the ratio of the energy reflected in the first 100ms to the direct sound) could lead to a decrease in the tempo. A later study made by Schärer Kalkandjiev *et al.* (2015) [10], showed that the tempo was influenced both by the reverberation time and the paces of the music. Slow pieces were played with an even lower tempo in acoustics with large reverberation time, while fast pieces were played with an increased tempo, suggesting that the reverberation time alone cannot explain the adaptation of the musicians. Thus, both the music and the acoustical environment in all their aspects (and not only the reverberation time) have an influence on the performers' behavior.

In a previous study, (currently under review), we observed the effect of a single echo on the tempo of the reproduction of a rhythm pattern. The results revealed that when the echo delay is a little shorter than the note inter onset interval (IOI), i.e. the time between the onsets of two consecutive events, then the participants tended to accelerate. On the contrary, when the echo delay was slightly longer than the next note, they slowed down. In the first study, the model of room impulse response was very simplistic, we now wish to test another parameter of room acoustic to complexify our model. Therefore, we decided to study the reverberation time, as it is the most common parameter the studies on the link between musical interpretation and the acoustic environment. Our model was then composed of one echo and a synthetic late reverberation

In this study, we decided to concentrate on the temporal aspect of the adaptation. We established an experimental protocol similar to the one of the first study with a simple rhythmic reproduction task, which consisted of playing a rhythmical pattern with either a gradually added echo, a reverberation, or both. The idea of using only a rhythmic pattern was to eliminate any kind of melodic or frequential influence on our results. We hypothesized that the reverberation time would have an influence on the tempo of the participants, as observed in the literature [3, 1, 5, 9, 10]. However, we hypothesized that the echoes would have a stronger effect on the tempo than the reverberation. If this was the case, it could explain the differences in musicians' adaptation observed in certain studies. To test these hypotheses, we decided to ask participants to play the rhythmic pattern multiple times with an imposed tempo at the beginning. An echo, a late reverberation, or both, with different values for the delay or the reverberation
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Rhythmic pattern used in the experiment, consisting of a group of 4 notes and a group of 2 notes. Each group is composed of short notes with IOI of 250ms, except the last notes which lasted for 500ms. The total duration of the pattern is 2s.</figcaption></figure>

time across trials was used. We tested three delays for the echo, and four values for the reverberation time.

The paper is structured as follows. Section II presents the detailed protocol with the used stimuli, and it also describes the processing, recording and analysis of the data. The results are presented in Section III, and discussed in Section IV, leading to some preliminary conclusions on how the echo and the late reverberation could influence the tempo.

# 2 Methods

## 2.1 Stimuli

The rhythmic pattern chosen for this experiment was made of a group of four notes followed by a group of two notes (Fig. 1). This pattern was used by Finney et al. (2002) [4] in a study on delayed auditory feedback, from which this protocol was inspired. Finney et al. (2002) [4] showed that this pattern was the most sensitive to sound feedback changes among others. Furthermore, this pattern was simple enough for non-musicians to take part in the experiment.

To keep the rhythmic pattern playable by people regardless of their musical experience, we chose a slower tempo and adapted the echo delay to the IOI present in the rhythm. We therefore imposed a starting tempo of 120bpm (an IOI of 500ms for each pulse) on the participants. With this tempo the IOI between the last note of each group and the first note of the following group (i.e. notes 4 and 6) was 500ms. These notes will be called long notes as opposed to the other notes which have an IOI of 250ms (i.e. notes 1, 2, 3 and 5) that will be called short notes in the following (Fig. 1). The whole duration of the rhythmic pattern (notated *D*) was 2000ms.

Three values of echo delay ($\delta$) were chosen: 230ms, 250ms, and 270ms. Those delays were the most influential in our previous study. A fourth condition, with no echo, was also added (called 0ms in the following) (Fig. 2 a). In the case of the 250ms echo, the delay of the echo and the short IOI were the same, meaning that the echo will be heard while the participants play the following note (Fig. 2 c). The situations of 230ms and 270ms were symmetrical with respect to the short IOI. The echo was heard respectively 20ms before and after the following
<figure><img src="image_4.png" /><figcaption>Fig. 2. Temporal representation of the rhythmic pattern with the echoes. Notes played by the participants are represented with filled circles and echoes with hollow circles in different conditions: a) 0ms, b) 230ms, c) 250ms, d) 270ms. e) represents the attenuation of the different reverberation used on the first note of the pattern in this example</figcaption></figure>

note (Fig. 2 b and d). With those values, we are clearly in presence of echoes as the participants will hear two distinct events. It should be noted that, these values of delays do not correspond to any real situation as they are far too long; the effects observed in this study can therefore not be directly related to the adaptation of musicians with the real acoustics. Further studies are required to link the results of this experiment to real acoustics.

For the reverberation time we decided to synthesize a late reverberation. Our model was quite simple: a white noise with an exponential attenuation.

$$IR = wn(t) \times \exp(-\frac{\alpha}{20} \times ln(10) \times \frac{t}{RT}) \quad (1)$$

With *wn* the white noise, *α* the attenuation in dB, and *RT* the desired reverberation time. This gave us an impulse response that was then convolved with the audio. We used a white noise, so the impulse response was neutral towards the frequency, and would only slightly modify the timbre.

Four values of reverberation time *RT* were chosen: 250ms, 500ms, 1s, and 2s. A condition without reverberation was also added. Those times were selected as they would, respectively, cover a short note, a long note, half the pattern, or
the whole pattern (Fig. 2 e). We decided to use a 20dB attenuation so the times
could be compared to those in the literature which are for a 60dB attenuation
between 0.41s [9] and 5.91s [5]. In our case, for a 60dB attenuation our values
ranged between 0.750s and 6s. The echo previously described was also convolved
with the reverberation.

## 2.2 Instruction and Protocol

To ensure that participants played the rhythm at the initial tempo, the principle of synchronization-continuation was used [12]. Participants were asked to play in synchrony with a reference created digitally, and then to keep on playing at the same speed when the reference stopped. The synchronization sound corresponded to the pattern played five times with a hi-hat sound, which differed from the sound produced by the participants. Participants were asked to listen to the first pattern and then synchronize with the four following ones. During this phase, which lasted for 10s, there was no echo, so that the participant could concentrate on reproducing the rhythm at the correct tempo.

This part was then followed by a 4s phase, during which the feedback changed with growing intensity. At the beginning of this phase there was no synthesized feedback, while at the end its intensity equaled the intensity of the impact sound. We supposed that if the feedback changed abruptly, we might have observed a lot of errors in the pattern reproduction while our aim was to observe the adaptation of participants to the audio feedback.

The last phase, during which the echo was at its maximum intensity, lasted for 30s. Theoretically, 15 repetitions of the pattern should be played during this phase, as their duration is 2s. This was the phase during which we analyzed the evolution of the participants’ performance in the presence of the echo, the late reverberation, or both.

Although changes in tempo were expected, we decided to use a fixed temporal duration of one minute for the trial. This decision was made to ensure that no bias was introduced for shorter or longer trials. Also, we could not count the number of patterns in real time either, and therefore we could not dynamically adapt the duration of each trial.

In total, each trial lasted for 44s and a bip indicated its end. A continuous progress bar indicated where the participants were in the trial. At the end of each trial the participants were then invited to press a button on a screen to start the next trial. A delay of 2s was added between this action and the beginning of the reference sound to allow the participants to prepare for the next trial.

To correctly study the interactions between reverberation time and echo, we decided to study all the couples of reverberation times and echo delays leading to twenty conditions (5RT × 4δ) Each condition was repeated twice, leading to a total of forty trials for each participant. We decided to limit the number of repetitions, echo delay values and reverberation times in order to reduce the effect of fatigue among the participants, especially among non-musicians. The order of the forty trials was randomized for each participant. The trial number with respect to the total number of trials was displayed on the computer screen.
A training session was provided ahead of the test so that the participants could familiarize themselves with both the rhythmic pattern and the device. During this session, the participants performed the same task three times as in the main experiment: one without echo nor reverberation, one with an echo of 260ms, one with a reverberation time of 1s. In the instructions, participants were asked to play the rhythm "the best they could". To avoid bias, neither echo nor reverberation time were mentioned in the instructions. Participants were only told that the sound feedback would change.

## 2.3 Apparatus

Participants were asked to tap the rhythm with a drumstick held in their dominant hand, on a MIDI pad (BopPad by Keith McMillen). They were asked to tap forcefully to make sure they reached the detection threshold of the pad. The impact sound was captured with a microphone (Røde NT5) situated beneath the pad. The signal was then digitized with an audio interface (RME Fireface UCX) with buffer size of 64 samples. The sounds were played to the participants through open headphones (Sennheiser HD650).

The sound heard by the participants was consequently a combination of three sounds: 1) the direct impact sound naturally produced by the drumstick on the pad; 2) the same sound captured by the microphone digitized and played through the headphones (to make sure that the participants perceived the direct sound correctly); and 3) the audio feedback – reverberation, echo or both – played through the headphones. No drum sample was played to the participants. If we consider the strike on the pad as the initial time of our system ($t = 0$), the direct sound is then heard 2ms after the strike (the ears of the participant being at approximately 70cm of the pad). The sound replicated by the computer is heard 8ms after the strike, or 6ms after the direct sound. Note that because the microphone was beneath the pad, the numerical sounds were phase shifted by $\pi$ with respect to the direct sound.

The experiment was done inside an audiometric cabin, meaning that no other sound or room effects could bias the measurement. The values of the reverberation times of the audiometric cabin are reported in Table 1

<table><caption>**Table 1.** Reverberation times of the audiometric cabin by octave bands.</caption><thead><tr><th>band (Hz)</th><th>31.5</th><th>63</th><th>125</th><th>250</th><th>500</th><th>1k</th><th>2k</th><th>4k</th><th>8k</th><th>16k</th></tr></thead><tbody><tr><td>RT<sub>60</sub> (s)</td><td>0.77</td><td>0.68</td><td>0.22</td><td>0.14</td><td>0.06</td><td>0.04</td><td>0.05</td><td>0.05</td><td>0.07</td><td>0.08</td></tr></tbody></table>

The numerical echo, the reverberation, as well as the recordings of the MIDI data (time and velocity) and the course of the experiment were processed with the Max/MSP software. The delay of the echo was controlled with the spat5 library using the delay object [7]. The real-time convolution was done with the HISSTools Impulse Response Toolbox (HIRT).
## 2.4 Participants

Twenty participants, mean age 32.6 years (standard deviation 10.3), twelve women, took part in the experiment. Half were musicians, among which none were drummers. None of the participants had self-reported hearing problems. Each participant signed a consent form.

## 2.5 Data Processing

All the data processing was done in python, using numpy, scipy and pandas libraries. The MIDI data of each impact was recorded. This data contained two kinds of information: the elapsed time between the start of the trial and the impact, and the MIDI velocity equivalent to the force of the impact. The IOIs were calculated from the time intervals between each impact. In certain cases, the information of a single impact was transmitted twice by the MIDI device. The participants may also have made rebounds with the drumstick, which led to unwanted notes to be deleted. We considered that such unwanted notes had an IOI of less than 100ms. If any intended hit below 100ms was produced after the previous one, we assumed that it was an error in the pattern reproduction as it was far from any of the theoretical IOI of the pattern. Even for non-expert drummers, it would have been quite complicated to produce intended hits within 100ms after the previous one as this delay corresponds to a very fast playing tempo. For each of these notes, we deleted the second impact responsible for this very short IOI. The new note IOI was then recalculated. We attribute the symbol *d* to the correct IOIs. It appears that the presence of rebounds is subject specific and does not correlate to their musical experience or the situation they are playing.

To determine the produced tempo, we had to ensure that participant played the correct pattern. If a participant had improvised a rhythm, we could not have compared it to other participants, nor to the other note he or she played. To identify patterns, we detected long and short notes. A threshold of 375ms, median value between 250ms and 500ms, was used to separate long and short notes. This separation threshold seems sufficiently far from the IOIs, so if a participant accelerated or decelerated, long and short notes could still be correctly separated. Short notes were associated with the character “s”, and long notes with “l”. This gave us a string for each trial of “s” and “l” which reflected the rhythm played by the participants. Within these strings, the pattern “ssslsl” (corresponding to a single rhythmic pattern) could be isolated and identified as patterns correctly played by the participants. For each pattern we calculated the total duration (named *D*) by adding the IOI of each note of the pattern.

Having identified the correctly played patterns, we could then deduce the number of patterns played incorrectly by the participants. This error $\epsilon$ was obtained from the difference between the theoretical number of patterns that participants should have played and the number of correctly played pattern. We calculated this error only for the last 30s of each trial, with a theoretical number
of 15 patterns. This error could also take negative values, meaning that more patterns were played than the theoretical number.

Concerning the MIDI velocity, we normalized the value as there was a great variability between participants and between trials. The normalization was done for each participant by dividing the MIDI velocity by the mean MIDI velocity value of each participant.

## 2.6 Statistical Analyses

The independent variables of our study were the echo delay $\delta$, the reverberation time $RT$, the repetition $rep$, and if the participant was musician $M$. Four dependent variables were considered: the pattern duration $D$, the IOI between each note $d_i$, the normalized MIDI velocity $v$, and the error $\epsilon$. The pattern duration provides information on how participants globally adapted their tempo. The IOI of each of the six notes allow for a more precise analysis on how the pattern was distorted. The MIDI velocity reveals whether the intensity of playing is influenced by the echo or the reverberation time as observed by Bolzinger et al. (1992) [2]). Finally, the error tells us if some situations cause greater disturbance than others. In the following sections, only the results on pattern duration will be presented. As a trial was composed of several patterns, that varied with no clear tendency or consistency across trials, we decided to focus on the mean value for each variable (except $\epsilon$). In this way, we obtained single values for each trial representing the global adaptation for each participant to the different situations. The mean value is also a robust indicator, regardless of the correctness of the participants' performances. However, it does not give us any information on the participants' adaptation during the trial. Other descriptors, such as the derivative of the pattern duration across a trial, did not give any clear results, and therefore will not be presented in this article.

To test our hypothesis we used a non-parametric test called Manova.RM [6]. This test allowed us to test our multiple factor experiment even if the data did not follow a particular distribution. Our results were further refined with Conover-Friedmann post-hoc test on the significant factors identified

## 3 Results

<table><caption>**Table 2.** Results of the Manova.rm analyse. $\delta$ is the echo delay, $RT$ the reverberation time, $rep$ the repetition, and $M$ if the participant was a musician</caption><thead><tr><th>Factors</th><th>δ</th><th>RT</th><th>δ:RT</th><th>rep</th><th>δ:rep</th><th>RT:rep</th><th>δ:RT:rep</th><th>M</th></tr></thead><tbody><tr><td>p-value</td><td>&lt;0.001</td><td>0.144</td><td>0.194</td><td>0.424</td><td>0.204</td><td>0.759</td><td>0.603</td><td>0.043</td></tr><tr><td>Factors</td><td>δ:M</td><td>RT:M</td><td>δ:RT:M</td><td>rep:M</td><td>δ:rep:M</td><td>RT:rep:M</td><td>δ:RT:rep:M</td><td></td></tr><tr><td>p-value</td><td>0.103</td><td>0.658</td><td>0.784</td><td>0.179</td><td>0.103</td><td>0.846</td><td>0.227</td><td></td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Boxplot of the pattern duration according to a) the echo duration and b) the reverberation time. The 2000ms value corresponds to the case in which participants played the rhythm at the correct initial tempo of 120bpm. The 1840ms (respectively 2160ms) dotted line is drawn in comparison with the echo delays of 230ms (respectively 270ms) as it corresponds to the expected value if short note IOIs were 230ms (respectively 270ms). The stars represent the results of post-hoc tests with ****: p < 0.001</figcaption></figure>

Table 2 shows the p-values for the different interactions between our factors. The echo delay alone $\delta$ has a significant influence. The musicianship of the participant seems to also have a significant influence, but as the p-value is near the 0.05 threshold, the influence of this factor is limited.

Figure 3 a) shows the boxplot of the mean duration of patterns for the last 30 seconds of the 20 participants according to the echo delay $\delta$. The mean of the pattern duration ranged from 1.944s for the echo delay of 230ms to 2.013s for the echo delay of 270ms. We can notice that participants have generally accelerated with respect to the initial tempo, even when there was no echo (mean pattern duration of 1.968s) The results of Conover-Friedman post-hoc test are represented in Figure 3. The 230ms delay gives us a significantly shorter pattern, while the situation of 270ms gives us a significantly longer pattern. The 250ms delay does not give significant result in comparison with the case without echoes.

Figure 3 b) shows the boxplot of the mean duration of patterns. The mean pattern duration ranged from 1.969s for the case without reverberation to 1.985s for the case of 1s of reverberation time. If we can observe a small increase in the pattern duration with the increase of reverberation time – except for the 2s case – these differences are not significant.

# 4 Discussion

The results obtained in this study support the ones found in our first study. First we observe that the echo has an influence on the tempo. When the echo is before the next note, participants accelerated, and when it is after the next note, they
slowed down. However, if in the first study people were consistent around the initial tempo of 120bpm (short IOIs of 250ms), in the present study they have generally accelerated. For example in the case of no echo, the mean value was 1.968s. In spite of this global shift, if we compare the 230ms and 270ms cases to the 0ms, we observe the same variations as in the previous study.

The first hypothesis of this experiment was that the reverberation time would influence the tempo. However, the results obtained here do not support this hypothesis. It appears that the reverberation time does not significantly influence the tempo of the participants. Also, while, in previous studies, an increase in reverberation time resulted in a decrease in tempo [1, 5], participants tended to accelerate with the longest reverberation in our case. This could be related to the study of Schärer Kalkandjiev et al. (2015) [10] or the study of Bolzinger et al. (1992) [2] where no change in the tempo was observed with the different reverberation times.

Therefore, our second hypothesis, that echoes have a stronger influence on the tempo than the reverberation time, seems verified. Hence, the variations observed in studies [1, 5, 9, 10] could be explained by audible echoes or reflections that are perceptually compelling. However, a limit in this comparison is the difference between the instrument used. In our study we decided to us a percussive sound, with a rapid decay, while in the previous studies, they used instruments with longer note duration, such as voice or choir [1, 5], piano [2, 3], organ [1], or orchestral instruments [1, 9, 10]. One could expect different results depending on the instruments used. For example, with self-sustained instrument, such as violins, altos, cellos, brasses and organs, the echo could be "lost" in the note played, implying that it is no longer heard, and then would have no influence on the playing. Therefore, further studies are required to fully draw the comparison with the result obtained in our study with our simplistic model, to the ones observed in real life scenarios.

The musical experiences of the participant has a small influence on our results. If we a significant difference between musician and non musician in our experiment, this factor has no interaction with any of the other independent variable. This is interpreted as musician and non-musician were influenced in the same way by the echo and the reverberation.

Lastly, the high p-value for the repetition factor *rep* shows that participants were very consistent from a trial to another.

# 5 Conclusion

This article is the sequel of a previous study in which we showed that the presence of a single echo could influence the tempo when playing a rhythmic pattern. In order to complexify the model of the first study, we added a synthetic late reverberation with variable reverberation time. This study confirms the result of the previous study, that the relation between the echo delay and the note IOI have an influence on the tempo. However, while many of the studies observed an influence of the reverberation time on the tempo, it is not the case here. Our
reverberation model with the rhythmical pattern used and the percussive sound,
showed no influence of the reverberation time on the tempo.

It would further be of interest to interrogate how our model behaves in the
case of other instruments or more melodic contexts. The use of sustained sounds
for instance, could imply different interactions between the notes played, the
echo and the reverberation. More investigations are required to fully understand
how a musician would play a certain piece given the acoustic environment.

## Acknowledgments

This work was carried out as part of the HARMONIE project of the PEPR
ICCARE. It was supported by the French National Research Agency (ANR-23-
PEIC-0002) under the France 2030 program.

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