Bachelor’s Thesis, 15 ECTS
Programme in Cognitive Science, 180 ECTS Spring term 2019
Supervisor: Guy Madison
EXPLORING THE LIMITS OF
BEAT TEMPO WITH AN
ILLUSION OF INFINITE
TEMPO CHANGE IN A
METRICAL PATTERN
Mattias Widengren
Abstract
Humans have the ability to synchronise with sounds divided by equal intervals and predict when the next sound is coming, as opposed to reacting to them. By creating a pulse within ourselves based on these recurrent sounds we are able to, for instance, play music and dance. A stable pulse can be maintained accurately even without external stimuli for up to about two seconds. Previous research showed that this limit could be extended to about eight seconds if the pulse was supported by a sound pattern with a facilitating temporal structure, which also seemed to be slowing down infinitely. The present study used the same type of multi-level pattern, but with longer playing time and stricter instructions for the participants. Just as in the seminal study the participants had to hit a drumstick against a drum pad according to their inner representation of the pulse when hearing the stimuli, for both increasing and decreasing tempi. In addition, the present study featured four different rates of tempo change. The results showed that the produced time interval could be extended to around 16 seconds for decreasing tempo with the slowest rate of change.
Keywords: Music, multi-level pattern, pulse, beat, time. Abstrakt
Människor har förmågan att synkronisera med ljud separerade av lika långa tidsintervaller och förutse när nästa ljud kommer, istället för att bara reagera på dem. Genom att skapa en inre puls baserad på dessa återkommande ljud kan vi till exempel spela musik och dansa. En stabil puls kan upprätthållas även utan externa stimuli i upp till omkring två sekunder. Tidigare forskning visade att denna gräns kunde förlängas till omkring åtta sekunder om pulsen stöddes av ett ljudmönster med en underlättande temporal struktur, som också verkade sakta ner i oändlighet. Den aktuella studien använde sig av samma typ av stimuli, men med längre speltid och striktare instruktioner till deltagarna. Precis som i den första studien var deltagarnas uppgift att slå en trumstock mot en trumplatta baserat på deras inre representation av pulsen när dom hörde stimulit, för både ökande och avtagande tempo. Dessutom så innehöll den aktuella studien fyra olika grader av tempoändringar. Resultaten visade att det producerade tidsintervallet kunde ökas till nästan 16 sekunder för avtagande tempo med den långsammaste graden av ändring.
EXPLORING THE LIMITS OF BEAT TEMPO WITH AN ILLUSION OF INFINITE TEMPO CHANGE IN A METRICAL PATTERN
Rhythmic music consists of events pieced together to form complex temporal patterns. The most basic feature of such patterns is that they have at least one level that is isochronous, which means that all intervals are equal. This is typically the level at which listeners perceive the “beat” in the music, which is very important for organising the often complex stream of sound events in the listener’s mind (e.g., Madison & Merker, 2002). People have the ability to synchronise with this beat and predict the time of future events within the beat, as opposed to reacting to them. In fact, even new-born infants demonstrate the ability to perceive the beat (Winkler, Háden, Ladinig, Sziller, & Honing, 2009). The typical way to predict when future beats are going to occur is by attributing an isochronous pulse to some level in the metrical structure of the music. The pulse is actually created by the mind as a means to cognitively organise time-regular sequences (Fitch, 2013).
The purpose of the present study is to demonstrate the subjective nature of this pulse, and to measure across how long intervals the pulse can be maintained, when supported by a metrical structure, as in music. Is there a limit to how long the intervals can be for people to still maintain their inner representation of the metrical structures they hear? There is reason to believe that there is such a limit, because it has, for example, been shown in previous studies that the pulse becomes considerably less stable, and can even break down, for durations above about two seconds (e.g., Madison, 2001; Mates, Radil, Müller, & Poppel, 1994). In these studies, the participants were however not presented to a stimulus with a metrical structure, which means that they had nothing to support their perceived pulse to. A seminal study by Madison (2009) did however show that people could maintain a pulse and successfully synchronise with intervals as far as eight seconds apart, when supported by a metrical sound structure. In other words, when supported by a whole pattern of layered temporal levels, the duration between the perceived pulses could be extended considerably (Madison, 2009). We do not know though if eight seconds is really the upper limit to how long people can maintain the pulse, because of limitations in the experimental design, which will be approached further on. There is also a lower limit between 100 and 200 ms, below which both perception and production of sequences are less temporally precise (Hibi, 1983).
Since the pulse is subjective it can be manipulated, and this fact was exploited to create an illusion of infinite tempo-change (Madison, 2009). The tempo-change illusion is based on the fact that listeners base their pulse on an active cognitive process, and that this process is strongly influenced by the previous context. It has been found that when hearing a beat, the brain elicits a sustained periodic EEG response tuned to the beat frequency. An additional frequency tuned to the corresponding metric interpretation of this beat has also been observed (Nozaradan, Peretz, Missal & Mouraux, 2011). These findings suggest that there is some neural activity that represents and organizes beat and meter when hearing rhythmical stimuli.
That previous study did however only feature five revolutions of the pattern, which meant it only played for about three minutes. It is unlikely that participants arrived at the upper limit of their ability in that short a time. In order to better assess the limit, the present study will have longer playing time, with more revolutions, which gives the participants opportunity to follow the pattern for a longer time. Moreover, in the original study, the instructions did not specify for how long the participant should attempt to follow the tempo change, so it is possible that individual factors determined if they followed through or switched to a faster (or slower) level in the metrical pattern, something which typically occurred through doubling and quadrupling the tempo (or dividing it by two or four in the case of increase tempo).
In the present study the participants are asked to follow the tempo-change for as long as they can muster, without switching to a faster (or slower) level. In other words, they are asked to not double or quadruple the tempo (or divide it by two or four), which will give room for ultimately perceiving a very fast or slow pulse. Although, as previously said, even in the seminal study a few individuals produced as long intervals as up to eight seconds, but the results do not say what would have been the limit of their performance.
Just as in the seminal study it is expected that the participants will follow the tempo changes they are hearing, but this time give them more time to actually reach the boundary of their respective subjective pulse. Because of the fact that the participants this time around will receive stricter instructions and be exposed to the stimuli for a longer time it seems reasonable to expect that they could produce longer intervals than the aforementioned eight seconds. Moreover, it is expected that the participants produce as short intervals for increasing tempo as in the previous study, which was around 100 ms. Shorter than that should not be possible due to sensori-motor limitations when producing the actual hits.
Method Participants
The study included 16 participants (6 women, 10 men, M = 34.4 years of age, age range 19–54 years). One participant had to be excluded due to an obvious misunderstanding of the instructions, so the final sample consisted of 15 people. The participants constituted a convenience sample and varied substantially in their musical background and musical abilities. Three participants had been playing an instrument systematically for at least 15 years, four participants had played an instrument for at least one year but less than 15 years, and the remaining eight participants had played an instrument for either less than a year or not at all. Worth noting though is that all participants did the same tests, no matter which category they belonged to. The categorisations were created only to be able to distinguish the results according to previous musical experience.
Instruments and Materials
An AlesisDM5 drum module connected via a Roland MPU-401 MIDI interface to a PC computer with custom designed software was used to present the stimuli and record the beats from the participants. The stimuli were produced and played in real-time through Peltor HTB7A headphones. The responses were registered via hits with a drumstick against a RolandPD-85 drum pad.
Stimuli
session 16 trials. Twelve of the total 24 trials consisted of one condition without tempo change, called static. The purpose of the static pattern was to have the option to analyze the participant’s preferred tempo, something that was not done in this study. All patterns with tempo change were played for a predetermined number of revolutions, no matter how many hits the participant produced. The basic principles of the multi-level pattern are illustrated in Figure 1 (see figure caption).
Figure 1. Illustration of a multi-level pattern with a length of 384 sound events and decreasing intervals. Each sound is represented by a dot, which are connected with lines only to highlight their relative position. Each level is manifested by the canonical position on the y-axis, while the exact position represents the absolute loudness. The average time between the sounds is 49 ms, which means that the whole pattern takes 19.2 s to complete. The figure shows only the last 3 s of the first revolution and the first 3 s of the second revolution, in order to highlight the boundary when the pattern repeats. The time between the sounds is slowly increased from 36 to 62 ms, as seen in the increasing distance between the dots along the x-axis, which becomes particularly evident by comparing the longer intervals before the boundary to the longer intervals after the boundary. The gradual change in loudness masks the boundary, in the sense that level 2 before the boundary has the same loudness as level 3, and this shift is true for all levels.
static trials in succession, and in order to provide the same training and experience to all participants in preparation for the second session. All conditions in the second session appeared in a randomized order. The reason was to eliminate order effects and thus be able to draw firm causal conclusions about the effects of the conditions. Pilot testing determined the number of revolutions of the tempo-change patterns and were optimized for each condition in order to allow for maximal tempo-following behavior while at the same time avoiding them being overly taxing and boring. The reason for using a lot of different conditions was to give the participants as good chances as possible to produce “extreme” intervals, whether it was short or long intervals. Not knowing beforehand which condition would be the most successful for this cause, it was deemed best to have many variations. This choice also brought the possibility to compare behaviors and results between conditions within the same participant. Table 1 lists all conditions used in the experiment. The longest trial stretched over more than 5 minutes and the shortest was less than 30 seconds long.
Table 1.
All conditions used in the experiment
Session Condition Order Revolutions Pattern length Direction of change 1 1 1 U
∞
0 1 2 2 6 768 + 1 3 3 U∞
0 1 4 4 6 384 + 1 5 5 U∞
0 1 6 6 4.5 768 - 1 7 7 U∞
0 1 8 8 4.5 384 - 2 1 Random U∞
0 2 2 Random 7.5 768 + 2 3 Random U∞
0 2 4 Random 7.5 384 + 2 5 Random U∞
0 2 6 Random 5.5 768 - 2 7 Random U∞
0 2 8 Random 5.5 384 - 2 9 Random U∞
0 2 10 Random 7.5 192 + 2 11 Random U∞
0 2 12 Random 7.5 96 + 2 13 Random U∞
0 2 14 Random 5.5 192 - 2 15 Random U∞
0 2 16 Random 5.5 96 -Procedure
The participant sat down in a chair in front of the drum pad, with the drumstick in the preferred hand and headphones on. First, it started with a practice round, so the experimenter could see that the participant had understood the instructions. The participant’s task was to hit the drumstick against the drum pad according to the pulse perceived from the sound pattern in the headphones. After that, the experimenter left the room and the participant started the experiment. The experiment consisted of two sessions. After the first session was completed there was a short break where the participant received new instructions for the second session. Because the instructions for the second session were revealed after the end of the first session, it could not influence the participants’ behavior during the first session.
The first session had no explicit instructions about how to approach the task, except that the participant should find the beat and hit the pad once for every perceived beat, in a way that felt natural. Although this was not mentioned in the instructions, this led participants to for example double or quadruple the hitting tempo (or slowing down the same amounts) when it became so fast or slow that it felt uncomfortable or unnatural. The first session consisted of eight trials with different lengths, tempo-change rate, and direction of change (slowing down or speeding up). All the different conditions are listed in Table 1. The first session started with a static pattern, that is, without any tempo change. It continued until the participant had hit 15 hits on the drum pad, after which it stopped. The third, fifth and the seventh trials were identical to the first one.
The instructions for the second session specified that the participant should try to follow the perceived tempo change for as long as possible without changing to a different level (e.g. doubling/quadrupling etc. the hitting tempo) in the sound pattern. The instructions for the second session are included in the Appendix. The second session consisted of 16 trials. After the second session was done the participant came out of the room and answered a few questions about their experience of the experiment and about their musical training and experience. These questions are not reported in detail here, because they were included merely to clarify if the participants had experienced any problems and were comfortable with the experience. All in all, the experiment took around 50 minutes to complete per participant.
Design
The study employed a repeated-measures experimental design, with beating behaviour as the dependent variable, and instructions, rate of tempo change, and direction of tempo change as independent variables. The only thing that differed between participants was the order of the conditions they were exposed to in the second session.
Results
eyes closed during the whole experiment. In other words, this participant simply ignored the stimuli, and therefore the data cannot be used.
These numerous and rather complex data will be described in several ways, in order to comprehensively convey their relevant aspects. In general, I will begin with a more fine-grained level of description, and gradually aggregate data so as to more directly address the hypotheses.
The hypotheses are specifically concerned with the effect of the illusion, that is, how far participants are able to follow it to extremely short or long intervals. The most important part of the data is therefore in the end of each sequence, or, in the case of participants’ switching between levels, in the end of each bout of responses just before switching. Because it is very hard and sometimes impossible to determine if a series of responses follow the same level in the multi-level pattern, I decided to simply extract the shortest IRIs in the decreasing interval conditions, and the longest IRIs in the increasing interval conditions. These IRIs will definitely reflect the limit performance of the participants, while ignoring whether they are consecutive or not. To this end, I selected the ten shortest IRIs in each decreasing condition. For the increasing conditions I selected the five longest IRIs, because these naturally differ much more than the short ones, so it makes less sense to aggregate these. When intervals are short, participants naturally produce many more in the same amount of time that the multi-level pattern is presented. The numbers of responses were 16,650 for decreasing and 8,089 for increasing intervals, having removed the outlier participant and all responses from the static conditions.
The means across the ten selected decreasing intervals are plotted for all different conditions and for each participant in Figure 2. As can be seen, the results did not differ that much between the two sessions. On the other hand, looking at the means across the five selected increasing intervals, there was quite a big difference between the two sessions, as can be seen in panel B. This is explained by the new instructions for session 2 having a bigger impact for the increasing intervals than the decreasing intervals. Two participants were able to produce mean intervals of over 11 seconds in the second session. The same participants produced mean intervals of only around 2 to 3 seconds in the first session.
The most striking aspect of the results is the huge individual variation. Some participants follow decreasing intervals to less than 200 ms, and other only to around 600 ms. Some participants follow increasing intervals to a mean of around 11 s, across the five longest IRIs, while can only muster a mean of around 3 s. In fact, participants 13, 14, and 15 seem to have misunderstood the task, or are unable to perceive the pulse.
Figure 3. Individual extreme IRIs for all participants as a function of direction of tempo change
Finally, Figure 4 shows the effect of the instructions, across all participants but separately for each level of musical experience. This division was made because I noted a tendency for more musically experienced participants to follow the tempo change longer, and also to follow the instructions more accurately. What we see is no effect at all of instructions for the decreasing intervals, regardless of musical experience. Apparently, this condition took participants to their limit very quickly and efficiently, such that there was no room for improvement in the face of instructions to follow longer. However, the instruction to follow the pattern longer had a very large effect, with an approximate 70 percent increase, which was even larger for the most experienced group, at more than 100 percent.
Figure 4. Mean IRIs in milliseconds (on the y axis) created by the participants in respective
category of musical experience (on the x axis) in both decreasing and increasing conditions.
Discussion
The question of how long intervals that can really be produced when listening to these types of patterns is a hard one to answer. What can be seen from these results is though that we seem to have reached close to the boundary of what most people are able to produce, because the participants did not produce longer and longer intervals the whole way through one pattern. Instead we could see that most participants probably lost their inner representation of the pulse somewhere in every trial and had to start over producing shorter intervals. To really know what the limit could be though it is recommended to replicate the study with more participants. Other alterations that can be made are to have fewer conditions. In the present study many different conditions were used to be able to compare results and behavior between the conditions. However, if fewer conditions would be used, even longer patterns with more revolutions could be added, to try to get even closer to the limit of perceivable sustained pulse. There will always be a limit to how much useful data one participant can produce in one sitting, because of different reasons such as getting tired (both mentally and physically), losing focus or simply getting bored. In theory one could assume that participants can sit for hours and listen to the patterns and hit the drum pad, but in reality, their focus will be reduced after a while. The ethical aspects must be taken into consideration, and the design of the experiment should be one that does not exhaust its participants.
Another way to expand the design for future research is to use the categories I created for musical experience in a broader way. The three categories were (0) no experience or less than a year playing an instrument, (1) intermediate, 1-14 years of playing an instrument, and (2) experienced, having played an instrument for 15 years or more, as seen in Figure 4. In the present study some signs of possibly intriguing results could be seen when looking at them grouped in this way. Since one of the three categories only included three participants and another one only four participants it is not reasonable to draw any conclusions from the results though. However, it can be interesting to look at the data and discuss the results in a hypothetical way as if the same results would be seen in a bigger sample. An interesting aspect of the results is that the most experienced musicians created the longest intervals in session 2 but the other way around in session 1. As previously stated, because of too few participants in each group, it could just as well be a coincidence. It could however also be that, when choosing for themselves, experienced musicians prefer shorter intervals to keep their representation of the pulse more precise. When asked to “hold out” for as long as possible they may have the ability to extend this representation and keep it over longer periods of time if needed.
Reference list
Fitch, W. (2013). Rhythmic cognition in humans and animals: distinguishing meter and pulse perception. Frontiers in Systems Neuroscience. 7:68. doi:10.3389/fnsys.2013.00068 Hibi, S. (1983). Rhythm perception in repetitive sound sequence. Acoustical Society of
Japan, 4(2). 83-95.
Madison, G., & Merker, B. (2002). On the limits of anisochrony in pulse attribution.
Psychological Research, 66, 201–207. https://doi.org/10.1007/s00426-001-0085-y
Madison, G. (2001). Variability in isochronous tapping: higher order dependencies as a function of inter tap interval. Journal of Experimental Psychology: Human Perception and
Performance, 27, 411–422.
Madison, G. (2009). An auditory illusion of infinite tempo change based on multiple temporal levels. PLoS ONE, 4(12): e8151. doi:10.1371/journal.pone.000815
Mates, J., Radil, T., Miiller, U., & Poppel, E. (1994). Temporal integration in sensorimotor synchronization. Journal of Cognitive Neuroscience, 6, 332-340.
Nozaradan, S., Peretz, I., Missal, M., & Mouraux, A. (2011). Tagging the neuronal entrainment to beat and meter. The Journal of Neuroscience, 31, 10234-10240.
Winkler, I., Háden, G., Ladinig, O., Sziller, I., & Honing, H. (2009). Newborn infants detect the beat in music. PNAS, 106(7), 2468–2471. https://doi.org/10.1073/pnas.0809035106 World Medical Association. (2013). Declaration of Helsinki: Ethical principles for medical
Appendix – Instructions for session 2 (in Swedish)
Du kommer igen att höra både korta och mycket långa ljudsekvenser, och din uppgift är fortfarande att ”slå takten” på en trumplatta till din upplevda puls baserat på vad du hör i lurarna.
Återigen kommer tempot ibland ändras i ljudsekvensen, och då ska du fortfarande försöka synkronisera till den puls du upplever. Din uppgift nu är alltså precis samma som i första sessionen, dock med skillnaden att du denna gång inte bör byta mellan olika typer av
"mellanrum" (t.ex från helnoter till halvnoter eller tvärtom) mellan slagen. OBS! Det betyder ändå att du ska "följa med" i tempoändringarna du hör!
Alltså, lyssna till ljudsekvensen, försök synkronisera dina slag med den upplevda pulsen och följ den pulsen så länge du kan, även genom tempoändringarna.
När du hör den melodiliknande sekvensen och skärmen blir blå igen är testet slut och du kan komma ut ur båset för att svara på några korta frågor om din upplevelse.
