Metrical Accents Do Not Create Illusory Dynamic Accents

Metrical accents, which are said to arise from perception of a beat in a rhythm, confer subjective prominence to events that fall on the beat. Does that mean the metrically accented events are perceived as physically more prominent (e.g., louder or longer) than other events? A recent study requiring participants to detect small physical changes in melodies having a subjectively imposed beat (Repp, 2010) suggested a negative answer. The present study used a much simpler beat induction paradigm to revisit this issue. Following a brief isochronous induction sequence, musically trained participants heard two probe tones, one of which, or neither of which, fell on the projected beat. The task was to compare the two probe tones with regard to their relative loudness, which was varied systematically. The results showed that some participants judged an on-beat probe tone to be relatively louder than an off-beat tone, but only when the second probe tone fell on the first beat following the induction sequence and the beat tempo was relatively fast. Because this result was also obtained when all but the last induction tone were omitted, it probably reflects a rhythmic grouping accent (Povel & Essens, 1985) rather than a metrical accent. Therefore, the study provides no evidence that a metrical accent creates a phenomenal dynamic accent. Repp et al.: Metrical accents and loudness 3 When a rhythmic structure gives rise to perception of a regular beat (“tactus”), the on-beat positions in the resulting metrical hierarchy are considered “strong” or “metrically accented” (Lerdahl & Jackendoff, 1983). This means that auditory events falling on the beat are subjectively more prominent than those not falling on the beat, even though they may not differ in their physical properties. Induction of a beat can give rise to overt periodic movements such as foot tapping and engages brain areas involved in motor control even when overt movement is absent (Grahn & Brett, 2007; Grahn & Rowe, 2009). Beat induction also creates expectations of hearing auditory events in temporal on-beat positions (Snyder & Large, 2005), and it focuses attention on these positions (Large & Jones, 1999). As a result, it is theoretically possible that metrically accented events are actually perceived to be physically different from metrically unaccented events: Their increased subjective prominence may result in illusory increases in their subjective loudness or duration that in turn reinforce their prominence. Alternatively, the increased subjective prominence conveyed by metrical accentuation may be purely cognitive or motoric, leaving the perception of auditory event properties unaffected. A recent study (Repp, 2010) addressed this issue empirically. In each trial, musically trained participants heard an isochronous melody composed of 12 tones, played twice in succession with legato articulation. In the second presentation, depending on the experimental condition, one of the 12 tones was louder, softer, longer, or shorter than the other tones, and the task was to identify this changed tone. The deviant tone could fall either on or off the beat of the melody. The melody had a 6/8 (2 × 3) meter, which was Repp et al.: Metrical accents and loudness 4 prescribed by music notation displayed on a screen, and it started on the beat. Consequently every third note was metrically accented. Three different melodies were created from the same sequence of pitches by shifting the starting pitch, in order to separate effects of pitch structure from effects of meter. The results of this study provided no evidence of perceptual biases indicating that tones on the beat were perceived as louder or longer than notes off the beat. The results did indicate, however, that participants paid more attention to tones on the beat because sensitivity to deviations in loudness or duration was increased in those positions. The data of that study were rather complex because the effects of meter were overlaid on pronounced effects of pitch structure and serial position. Also, the metrical structure was somewhat labile because the imposed meter sometimes conflicted with metrical cues contained in the pitch structure. Therefore, the results can hardly be considered definitive. The purpose of the present study was to introduce a much simpler paradigm to re-address the specific question of whether metrically accented tones sound louder than metrically unaccented tones. Instead of a subjectively imposed meter, a simple beat was induced by an isochronous sequence of tones, which was followed by two probe tones whose relative loudness had to be judged. Four experiments were conducted, and author BHR piloted additional experiments on himself (described in an Appendix). The four experiments aimed to investigate whether an on-beat probe tone is perceived as louder than an off-beat probe tone and whether that effect depends on the beat period (Experiment 1), whether it extends beyond a silent beat following the induction tones (Experiment 2), whether it depends on the number of induction tones Repp et al.: Metrical accents and loudness 5 (Experiment 3), and whether it is influenced by patterns of accentuation in the induction tones (Experiment 4). Methods Participants The participants were nine graduate students from the Yale School of Music (3 men, 6 women, ages 21-27), who were paid for their efforts. They all played their primary musical instruments (piano (2), violin, viola (2), flute, trombone, harp, guitar) at a professional level, having studied them for 10-24 years. All were regular participants in rhythm perception and production experiments in author BHR’s laboratory. Author BHR also ran himself in all experiments, but his data were not included (see Appendix). Materials and equipment Figure 1 shows a schematic diagram of the paradigm. A short sequence of induction tones (also referred to as “beats” here) with a constant inter-beat interval (IBI) was followed by two probe tones (T1, T2). The probe tones were separated by an interval equal to half the IBI and followed the final induction tone after an interval equal either to the IBI, or three fourths of the IBI, or half the IBI. Consequently, either T1 coincided with the next projected beat (“T1 on beat”), or neither tone coincided with that beat (“Off beat”), or T2 coincided with it (“T2 on beat”). Insert Figure 1 here Repp et al.: Metrical accents and loudness 6 All tones had a piano timbre and a nominal duration of 40 ms. Induction tones had the pitch C4, whereas probe tones had the pitch D4. All induction tones had the same intensity (MIDI velocity of 60). The two probe tones had five possible intensity relationships, one of which was equality (MIDI velocities of 60/60). The other four pairs of MIDI velocities were 54/66, 57/63, 63/57, and 66/54. These differences between T1 and T2 are approximately equal to -3, -1.5, 1.5, and 3 dB, respectively (Repp, 1997). The tones were produced by a Roland RD-250s digital piano under control of a program written in Max/MSP 4.0.9 that ran on an Intel iMac computer. The combination of three probe tone phases and five intensity relationships yielded 15 trials. In each of the four experiments reported here, there was a third variable with three levels, which increased the number of different trials to 45. A random sequence of these 45 trials made up one trial block, and each experiment consisted of five such blocks. In Experiments 1 and 2, the third variable was IBI duration: 400, 600, or 800 ms. In Experiment 1, the probe tones were timed as shown in Figure 1. In Experiment 2, the probe tones occurred near the second projected beat, with the first projected beat being silent. In other words, the probe tones followed the final induction tone with delays of 2*IBI, 1.75*IBI, or 1.5*IBI. In Experiments 3 and 4, the IBI was fixed at 400 ms. In Experiment 3, the third variable was the number of induction tones: 1, 4, or 7. In Experiment 4, there were again four induction tones and the third variable was their relative loudness. They were either of equal intensity (MIDI velocity of 60), or the first and third tones were louder (MIDI velocity of 72) while the second and fourth tones were Repp et al.: Metrical accents and loudness 7 softer (MIDI velocity of 48), or the reverse. The intensity difference amounted to about 6 dB (Repp, 1997). Procedure Each experiment took about 25 minutes. Experiments 1 and 2 were conducted in one 1-hour session, and Experiments 3 and 4 in another 1-hour session, about six weeks later. Their order was not counterbalanced. Participants sat in front of the computer and listened over Sennheiser HD280 pro headphones at a comfortable intensity. After the task had been explained, they started the first trial in a block by clicking on a virtual button on the screen. On the screen the question “Which of the two probe tones was louder?” was displayed. Below the question was an array of seven virtual response buttons that increased in size from the center outwards. The large button on the left was labeled ”First”, the large button on the right was labeled “Second”, and the small button in the middle was labeled “??”. Participants were instructed to click the button whose size reflected their confidence in the response. Then they clicked another virtual button to start the next trial. At the end of a block of trials, participants saved their data in a file. Analysis The seven response levels were scored as -3 (T1 definitely louder than T2) to 3 (T2 definitely louder than T1). These relative loudness ratings were averaged across the five repetitions of each trial (i.e., across blocks) and analyzed in repeated-measures ANOVAs with Greenhouse-Geisser correction where appropriate. Repp et al.: Metrical accents and loudness 8 Results Experiment 1 The purpose of Experiment 1 was to see whether there is any effect of probe tone phase at all, and whether that effect depends on the beat period (IBI). If probe tones falling on the beat are perceived as louder, then ratings should be highest for “T2 on beat”, intermediate for “Off beat”, and lowest for “T1 on beat”. In addition, of course, ratings should increase as the actual intensity of T2 relative to T1 increases. The results are shown in Figure 2. Relative loudness ratings increased with the T2 – T1 intensity difference, as expected, but probe tone phase seemed to have an effect only at the shortest IBI. A 3 (IBI) × 3 (phase) × 5 (intensity) ANOVA naturally yielded a highly significant main effect of intensity and also an IBI × Intensity interaction, F(8, 64) = 4.37, p = .015, because the response functions differed somewhat in shape for the three IBI durations. However, the main effect of phase, F(2, 16) = 4.21, p = .066, and the IBI × Phase interaction, F(4, 32) = 2.91, p = .090, both fell short of significance. In a separate two-way ANOVA on the IBI = 400 ms condition, the main effect of phase still did not reach significance, F(2, 16) = 4.20, p = .059. Inspection of individual results revealed substantial individual differences, with some participants showing large effects of phase at IBI = 400 ms, but others showing no effect whatsoever. Insert Figure 2 here Repp et al.: Metrical accents and loudness 9 Experiment 2 The purpose of Experiment 2 was to investigate whether there was any effect of phase at the second projected beat, assuming there is an effect at the first beat. (The results of Experiment 1, conducted in the same session, were not yet known.) There was no trace of any effect of phase; the average response functions coincided almost exactly at each of the three IBIs. Experiment 3 With the results of Experiment 1 now known, the purpose of Experiment 3 was to follow up the (albeit rather inconsistent) effect of phase at IBI = 400 ms and to see whether it depends on the number of induction tones. If the effect is due to beat induction and metrical accentuation, then it should disappear when all but the last induction tone are omitted. If the number of induction tones is increased from four to seven, however, the effect of phase might increase, due to stronger beat induction. If the effect decreases with seven induction tones, that too could be taken as evidence for beat induction: Since a beat tempo of 400 ms IBI is relatively fast, it could be that the real tactus has a period of 800 ms, in which case the probe tones would fall around a weaker beat after seven induction tones than after four (assuming the odd-numbered induction tones constitute the tactus; Brochard et al., 2003). The results are shown in Figure 3. Surprisingly, there were similar effects of phase in all three induction-tone conditions. In the ANOVA, where the third variable was now number of induction tones, the main effect of phase was significant, F(2, 16) = Repp et al.: Metrical accents and loudness 10 15.39, p = .002, and interacted with intensity, F(8, 64) = 4.31, p = .012, due to somewhat different shapes of the response functions for the different phases. However, it did not interact with number of induction tones, F(4, 32) = 1.76, p = .201. Moreover, the effect of phase was asymmetric, being almost entirely due to the “T2 on beat” condition. The results for the “T1 on beat” condition did not differ significantly from the “Off beat” condition, as was confirmed in a separate ANOVA, F(1, 8) = 1.89, p = .207. Insert Figure 3 here Experiment 4 The purpose of Experiment 4 was to ascertain whether dynamically accenting two beats (either 1 and 3 or 2 and 4) in a sequence of four induction tones makes any difference. Assuming that such accentuation induces a tactus or higher-level beat with a period of 800 ms, and given that the probe tones occurred around the fifth beat (the first projected beat), accenting beats 1 and 3 should enhance the effect of probe tone phase, whereas accenting beats 2 and 4 should decrease it, if the effect is due to metrical accentuation. (Results of Experiment 3 were not known at that point.) The results are shown in Figure 4. There seemed to be again an asymmetric effect of phase, as one should expect because Experiment 4 was conducted in the same session as Experiment 3, and the no-accents condition was identical with the four-induction-tones condition In Experiment 3. Relative to the no-accents condition, the effect of phase seemed enhanced in the 1-3 accentuation condition, but not reduced in the 2-4 accentuation condition. The results of the ANOVA (with accent as the third variable) did Repp et al.: Metrical accents and loudness 11 not support these visual impressions, however. The main effect of phase was not significant, F(2, 16) = 1.38, p = .281, nor was the interaction of accent and phase, F(4, 32) = 0.986, p = .378. Besides the obviously significant main effect of intensity, only the main effect of accent reached significance, F(2, 16) = 5.49, p = .043, due to higher scores overall in the 1-3 accentuation condition. There were large individual differences, with the apparent effect of phase being mainly due to three individuals who showed huge effects, while most others showed little or no effect. Insert Figure 4 here Discussion The present study introduced a simple psychophysical paradigm with which to test the hypothesis that an induced beat affects the perceived loudness of a tone that coincides with it. The results suggest that it does not. This conclusion is based on the following considerations. Experiment 1 showed that an effect of probe tone phase, if any, occurred only at the fastest beat tempo. According to our hypothesis, however, beat induction should have occurred at all three beat tempi, especially at IBI = 600 ms, which according to some studies (e.g., Parncutt, 1994) is close to the preferred beat tempo. Experiment 2 showed no effect of phase when the probe tones occurred near the second projected beat, following a silent beat. This is contrary to our hypothesis, although it is possible that a projected beat rapidly loses power or precision (cf. Janata & Paroo, 2006). Repp et al.: Metrical accents and loudness 12 Experiment 4 showed the effect of phase to be idiosyncratic and not reliably affected by accentuation of alternate induction tones. Thus it provided no support for our hypothesis either. Experiments 1, 2, and 4 used four induction tones, and it is possible that this number was not sufficient to induce a beat. However, the results of Experiment 3 suggest that this was not the problem: The effect of probe tone phase, which was statistically reliable only in this experiment, did not change when seven induction tones were presented. The crucial result of this experiment, however, was that a similar effect of phase was obtained after only a single induction tone. A single tone cannot possibly induce a beat. However, it could be argued that, because the single-induction-tone trials occurred in the context of other trials that had four or seven induction tones, and because the IBI was fixed at 400 ms, participants expected a beat to occur 400 ms after the single induction tone. To the extent that beat induction is equivalent to the generation of temporal expectations, this argument could account for the results. There is an alternative explanation, however, which takes into account the fact that the effect of phase was asymmetric, being almost entirely due to T2 occurring on the beat (Experiments 1, 3, 4). The explanation also considers that the effect of phase occurred only at a relatively fast tempo (IBI = 400 ms; Experiment 1) and only on the first projected beat (Experiment 2). When T2 was on the beat, T1 and T2 followed the last induction tone with short inter-onset-intervals of 200 ms, which resulted in a tight rhythmic group (see Figure 1). It is known from the research of Povel and Essens (1985) that in a rhythmic group of three or more tones, the first and last tones are perceived as accented. This accent is called grouping accent, and it is independent of metrical accent. Repp et al.: Metrical accents and loudness 13 Moreover, there is some evidence that a tone with grouping accent is perceived as louder than a tone without grouping accent (Povel & Okkerman, 1981; see also Repp, 2005). Here, when T2 occurred on the beat, it also carried a grouping accent because of its group-final position, whereas T1 did not carry a grouping accent, being wedged between the final induction tone and T2. When T1 occurred on the beat, or when both probe tones were off beat, a longer interval (400 or 300 ms) intervened between the final induction tone and T1, which prevented grouping of the probe tones with the final induction tone. In that case, T1 and T2 formed a two-tone group by themselves, and although the second tone in such a group tends to be perceived as accented, this tendency may not have been pronounced at the particular interval durations employed here (cf. Povel & Okkerman, 1981). It should have led to T2 being judged as louder than an equally intense T1 when T1 fell on the beat, but there was no indication of such a bias in the data (see Figures 24). It is plausible that grouping accent is relatively stronger in a three-tone group than in a two-tone group, which has no medial tones for the outer tones to contrast with. The strength of rhythmic grouping naturally decreases with temporal separation, which explains why effects of phase occurred only at a relatively fast beat tempo (Experiment 1), and not at all after a long silent interval (Experiment 2). The number of preceding induction tones (Experiment 3) is irrelevant to grouping of tones that occur in rapid sequence. We consider it likely, therefore, that the effects of probe tone phase we have found reflect grouping accent, not metrical accent. This conclusion is also consistent with the findings of Repp (2010), which indicated that metrical accents do not generate perceptual biases in loudness or duration judgments. Repp et al.: Metrical accents and loudness 14 The pronounced individual differences remain puzzling. Why did some participants show a large effect of phase, whereas others did not show any effect at all? The latter, incidentally, seemed to be the ones with the relatively better rhythmic skills, as judged informally from various earlier experiments in which they had participated. Two possibilities suggest themselves: One is that the phase effect, when it occurred, was due to rhythmic grouping but that participants not showing the effect did not group the probe tones with the final induction tone, perhaps because of their pitch difference. The other possibility is that rhythmic grouping was not the cause of the phase effect, after all, but that participants showing the effect either showed a real effect of metrical accent on perceived loudness or conflated metrical accent (of which, as musicians, they were naturally aware) with loudness in their judgments. In other words, they may have been judging relative prominence or accentedness rather than loudness as such (see also the Appendix). In either case, the fact that some participants showed no effects of phase is evidence that the loudness of the probe tones can be perceived veridically, which suggests that metrical accent at least has no obligatory effect on perceived loudness, but more likely has no effect at all. Repp et al.: Metrical accents and loudness 15 Acknowledgments This research was supported by National Science Foundation grant BCS-0924206. Address correspondence to Bruno H. Repp, Haskins Laboratories, 300 George Street, New Haven, CT 06511-6624, USA. E-mail: [email protected] Repp et al.: Metrical accents and loudness 16 Appendix: Personal Observations of Author BHR The experimental paradigm used here was inspired by rhythmic stimuli employed in a study by Abecasis et al. (2009). These authors investigated electromagnetic brain responses to identical tones that were either metrically accented or metrically unaccented but had the same grouping accent because they occurred second in a two-tone group. The critical tones (indicated here by underlining) occurred in a cyclically repeated xxoxxoxo sequence (x = tone, o = silence), which was intended to induce a beat (indicated here by bold face) that fell on the first tone of the first two-tone group but on the second tone of the second two-tone group (i.e., xxoxxoxo). The authors found that metrical accentuation of a group-final tone resulted in a larger brain response. I had an opportunity to listen to these sequences when visiting coauthor RB in the spring of 2010. To my ears, the rhythm was metrically unstable: Sometimes I heard it as intended, with the beat alternately on the first and on the second tone of successive twotone groups, but at other times I always heard the beat falling on the second tone, which resulted in a temporally irregular beat (3+3+2) and seemed to be irreversible unless I took a break from listening. I am mentioning this not to cast doubt on results obtained with these stimuli, but to suggest that grouping accent (which tends to favor the second tone in two-tone groups) was strong enough to compete with a preference for temporal regularity of the beat, at least in my perception. In the present study, I simplified this paradigm by preceding a single two-tone group with an isochronous induction sequence. As is my habit, I ran myself through each Repp et al.: Metrical accents and loudness 17 experiment before running my regular group of musicians, and I also explored several additional conditions. My coauthors also ran themselves in some of the experiments. My first run through Experiment 1 yielded huge, symmetric (i.e., deviating in both directions from the “off beat” baseline) effects of probe tone phase at all three IBI durations, with only a slight decrease as IBI duration increased. I was excited by these results because the paradigm seemed to “work,” yet puzzled because the large effect of metrical accentuation conflicted with the negative results of my previous study (Repp, 2010). My excitement was soon tempered, however, by pilot results from coauthors RB, who showed only a small effect of phase (and only when T1 > T2), and JRI, who showed no effect at all. I then ran myself through Experiment 2 and found no effect of phase, just as in the group results. Clearly, whatever had caused the effects for me in Experiment 1 did not extend to the second projected beat. (Much later, coauthor EP ran herself in Experiment 2, and she did seem to show a small effect of phase, which remains a singular result.) I then ran myself in a version of Experiment 1 in which T1 and T2 were separated by only one fourth of the IBI, to see how good my temporal resolution at the first projected beat was. With these stimuli I obtained effects similar to the group results in Figure 2, with a clear effect of phase at IBI = 400 ms and much smaller effects (if any) at the two longer IBIs. This could be attributed to poorer temporal resolution at the longer IBIs. At this point I realized that my large effects of phase in my first run through Experiment 1 may have been due to the way I phrased the instructions to myself. For me, the question on the screen said “Which of the two probe tones was more accented?” In Repp et al.: Metrical accents and loudness 18 judging relative accentedness, I may have conflated metrical accent with loudness (i.e., dynamic accent). From this point on, I displayed the question that said “louder” rather than “accented” (as in the instructions to the musician participants) and made efforts to focus my attention specifically on the relative loudness of the tones. With these new self-instructions, I ran myself in a version of Experiment 1 which had the original IBI/2 separation of T1 and T2, but with IBIs of 400, 800, and 1200 ms. I obtained a very clear, symmetric effect of phase at IBI = 400 ms, though it was smaller than in my first run, perhaps due to my new focus on relative loudness. At IBI = 800 ms, the phase effect was much reduced (also relative to my first run), and at IBI = 1200 ms it was barely present. This could again be attributed to increasing temporal uncertainty about the projected beat. Next I ran myself in a version of Experiment 3 in which the number of induction tones was 3, 4, or 5, to see whether it mattered whether the probe tones fell on an even or an odd beat (cf. Brochard et al., 2003). It did not matter: I showed a clear, slightly asymmetric effect of phase in all three conditions. However, there was a new effect: I showed a strong bias to rate T1 as louder than T2. This seemed like an effect of grouping accent, but it was unexpectedly favoring T1. (The group results also showed a tendency in that direction—see the “off beat” condition for T2 – T1 = 0 in Figures 2, 4, and 4—but my bias was much stronger.) My next venture was Experiment 4. The accentuation of induction tones did not seem to make any difference for me. I again showed clear effects of phase, with an asymmetry resembling that shown in Figure 4, though less pronounced. A bias favoring T1 was also present. Coauthor EP also ran herself and showed very large, asymmetric Repp et al.: Metrical accents and loudness 19 effects of phase, with the largest effect when induction tones 1 and 3 were accented (cf. Figure 4), and the smallest effect when induction tones 2 and 4 were accented. She also showed a bias in favor of T1. Next I ran myself in the version of Experiment 3 that the group of musicians received, with 1, 4, or 7 induction tones. I showed the largest phase effect with 4 tones, but also effects with 1 and 7 tones. The effects were fairly symmetric, but a bias favoring T1 was still present. EP ran herself, too, and showed large asymmetric effects of phase with 1 and 4 tones, a small effect with 7 tones, and a bias in favor of T1. I followed this with a version of the experiment with 1, 2, or 3 induction tones. Here the effects of phase were a good deal smaller for me, but they seemed to increase with the number of induction tones. This result is consistent with the suggestion that there may be projection of a beat even from a single induction tone when there is a constant IBI in the experiment: With fewer induction tones overall and thus less exposure to the IBI, such projection would be weakened. My bias favoring T1 was still present. After a break of about 6 months, I returned to this project for some further explorations. In what might have become Experiment 5, I introduced subdivisions between the induction beats. Three tones with pitches G4, E4, and D4 were repeated four times in an isochronous sequence, followed by another G4. Thus there were five induction beats (G4), with triple subdivision of the four IBIs. The probe tones occurred around the first projected beat, and their separation from the last induction beat was IBI/3. There were three IBI durations: 450, 600, and 750 ms. With this design, and after a long break, I failed to obtain a clear effect of phase at any IBI. My bias in favor of T1 also had largely disappeared. Repp et al.: Metrical accents and loudness 20 My final explorations were inspired by the work of Phillips-Silver and Trainor (2007, 2008) and Trainor et al. (2009), which had also partially motivated my earlier study (Repp, 2010). As I discussed there, the results of these authors could be interpreted as indicating that tones accompanied by head movement (but not by leg movement) are perceived as louder, due to engagement of the vestibular system and its potential interaction with auditory perception. The question now was: Would engaging the vestibular system by head nodding with the beat create (or enhance) an effect of probe tone phase? I repeated the last experiment, nodding my head in synchrony with beats 3, 4, 5, and 6, where the last beat was the projected one, so that the on-beat probe tone was also accompanied by a head nod. I repeated this experiment once, to be sure of the results. Then I ran myself one last time, this time tapping my foot instead of nodding my head. In all three runs I obtained moderately sized effects of phase, where previously I had obtained none. The effects did not seem to depend on IBI duration. These results were encouraging in that moving with the beat seemed to have had an effect for me. However, there was no difference between head nodding and foot tapping, contrary to what the hypothesis of vestibular engagement would predict. Moreover, the prolonged head nodding had some aftereffects: I felt dizzy for the rest of the day and even the next day. This may have been due to my age, but I thought the experiment was potentially causing discomfort and decided not to collect data from musicians. Now that I am retired, I leave it to younger and more intrepid researchers to pursue similar lines of research. Repp et al.: Metrical accents and loudness 21 References Abecasis, D., Brochard, R., del Rio, D., Dufour, A., & Ortiz, T. (2009). Brain lateralization of metrical accenting in musicians. Annals of the New York Academy of Sciences, 1169, 74-78. Brochard, R., Abecasis, D., Potter, D., Ragot, R., & Drake, C. (2003). The “ticktock” of our internal clock: Direct brain evidence of subjective accents in isochronous sequences. Psychological Science, 14, 362-366. Grahn, J. A., & Brett, M. (2007). Rhythm and beat perception in motor areas of the brain. Journal of Cognitive Neuroscience, 19, 893-906. Grahn, J. A., & Rowe, J. B. (2009). Feeling the beat: Premotor and striatal interactions in musicians and nonmusicians during beat perception. Journal of Neuroscience, 29, 7540-7548. Janata, P., & Paroo, K. (2006). Acuity of aditory images in pitch and time. Perception & Psychophysics, 68, 829-844. Large, E. W., & Jones, M. R. (1999). The dynamics of attending: How people track timevarying events. Psychological Review, 106, 119-159. Lerdahl, F., & Jackendoff, R. (1983). A generative theory of tonal music. Cambridge, MA: MIT Press. Parncutt, R. (1994). A perceptual model of pulse salience and metrical accent in musical rhythms. Music Perception, 11, 409-464. Phillips-Silver, J., & Trainor, L. J. (2007). Hearing what the body feels: Auditory encoding of rhythmic movement. Cognition, 105, 533-546. Repp et al.: Metrical accents and loudness 22 Phillips-Silver, J., & Trainor, L. J. (2008). Vestibular influence on auditory metrical interpretation. Brain and Cognition, 67, 94-102. Povel, D.-J., & Essens, P. (1985). Perception of temporal patterns. Music Perception, 2, 411-440. Povel, D.-J., & Okkerman, H. (1981). Accents in equitone sequences. Perception & Psychophysics, 30, 565-572. Repp, B.H. (1997). Acoustics, perception, and production of legato articulation on a computer–controlled grand piano. Journal of the Acoustical Society of America, 102,1878–1890. Repp, B. H. (2005). Rate limits of on-beat and off-beat tapping with simple auditory rhythms: 2. The role of different kinds of accent. Music Perception, 23, 167–189. Repp, B. H. (2010). Do metrical accents create illusory phenomenal accents? Attention, Perception, & Psychophysics, 72, 1390-1403. Snyder, J. S., & Large, E. W. (2005). Gamma-band activity reflects the metric structure of rhythmic tone sequences. Cognitive Brain Research, 24, 117-126. Trainor, L. J., Gao, X., Lei, J.-J., Lehtovaara, K., & Harris, L. R. (2009). The primal role of the vestibular system in determining musical rhythm. Cortex, 45, 35-43. Repp et al.: Metrical accents and loudness 23 Figure Captions Fig. 1. Schematic diagram of the experimental paradigm. Vertical bars indicate tones. The grey bar indicates the projected beat when it does not coincide with a probe tone. IBI = inter-beat interval. Fig. 2. Results of Experiment 1: Relative “T2 > T1” loudness ratings as a function of T2 – T1 intensity difference, with standard error bars, for three IBI durations. Fig. 3. Results of Experiment 3: Relative “T2 > T1” loudness ratings as a function of T2 – T1 intensity difference, with standard error bars, for 1, 4, or 7 induction tones. Fig. 4. Results of Experiment 4: Relative “T2 > T1” loudness ratings as a function of T2 – T1 intensity difference, with standard error bars, for three accent conditions. Repp et al.: Metrical accents and loudness 24 Fig. 1 !""""""""!""""""""!""""""""!" !""""""""!""""""""!""""""""!""""""""!"""""""""" !""""""""!""""""""!""""""""!""""""""""" !"""!" !"""!" ! ! #$%&'()$"*+,&+$'+" -.)/+"0)$+1" 02"