Distortions in Reproduction of Two-Interval Rhythms: When the “Attractor Ratio” Is Not Exactly 1:2

Repp, Bruno H.; London, Justin; Keller, Peter E.

doi:10.1525/mp.2012.30.2.205

Cited by 29 publications

(34 citation statements)

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“…If these deviations of the intersections from the 1:3:2 attractor were statistically reliable (we did not assess this), they would suggest an attractor in the vicinity of 1:3:2 whose interval ratios are not simple. In studies of musicians' production and perception of two-interval rhythms, Repp et al (2011Repp et al ( , 2012 recently found that the attractor deviated significantly from 1:2. Similar deviations from simple-ratio attractors for three-interval rhythms thus are conceivable.…”

Section: Discussionmentioning

confidence: 99%

“…Even highly trained musicians tapping in synchrony with an exact auditory rhythm template show these distortions, which thus seem to be almost unavoidable. Recent investigations have suggested that the attractor for musicians is not exactly 1:2 but slightly larger, whereas it is often smaller than 1:2 for nonmusicians (Repp, London, & Keller, 2011, 2012. The reasons for these deviations from the exact simple (i.e., small-integer) ratio are not yet fully understood.…”

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confidence: 97%

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Systematic Distortions in Musicians’ Reproduction of Cyclic Three-Interval Rhythms

2012

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In a classic study, Fraisse (1956) demonstrated that sequences of four sounds defining three different interval durations exhibit characteristic distortions in reproduction: The two more similar intervals tend to be assimilated to each other, resulting in a rhythm containing just two interval durations. The present study examined whether highly trained musicians (including percussionists) are able to perform such rhythms accurately in a synchronization-continuation tapping paradigm. Eleven rhythms, a subset of those used by Fraisse, were presented cyclically at his original tempo and also at a slower tempo. The musicians produced significant rhythm distortions, though they were smaller than those observed by Fraisse and not always assimilative. They were relatively larger at the fast than at the slow tempo and occurred in both synchronization and continuation. In contrast to Fraisse’s data, the most variably reproduced target rhythm was the one in which the two longer intervals were identical. The pattern of distortions suggested attraction towards ideal rhythms in which all three interval durations are different, representing metrical categories with nominally simple interval ratios (some permutation of 1:2:3) that were probably activated by the cyclic presentation of the rhythms. However, these attractors themselves seemed to be somewhat distorted, perhaps reflecting the simultaneous presence of a nonmetrical attractor that differentiated two interval categories regardless of ratio, as observed by Fraisse.

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Section: Discussionmentioning

confidence: 99%

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confidence: 97%

Systematic Distortions in Musicians’ Reproduction of Cyclic Three-Interval Rhythms

2012

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“… 1 In a synchronization task, Repp et al (2011) observed non-integer ratios around 44% to be significantly distorted toward 33%, which may be a range effect, given repeated exposures and attempts to synchronize with patterns featuring subdivisions nearer to 33% in that experiment (see also Repp et al, 2012). In addition to the present study, others have observed ratios around 43% distorted toward 50% (e.g., Snyder et al, 2006).…”

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confidence: 91%

To the beat of your own drum: Cortical regularization of non-integer ratio rhythms toward metrical patterns

Motz

Erickson

Hetrick

2013

Brain and Cognition

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Humans perceive a wide range of temporal patterns, including those rhythms that occur in music, speech, and movement; however, there are constraints on the rhythmic patterns that we can represent. Past research has shown that sequences in which sounds occur regularly at non-metrical locations in a repeating beat period (non-integer ratio subdivisions of the beat, e.g. sounds at 430 ms in a 1000 ms beat) are represented less accurately than sequences with metrical relationships, where events occur at even subdivisions of the beat (integer ratios, e.g. sounds at 500 ms in a 1000 ms beat). Why do non-integer ratio rhythms present cognitive challenges? An emerging theory is that non-integer ratio sequences are represented incorrectly, “regularized” in the direction of the nearest metrical pattern, and the present study sought evidence of such perceptual regularization toward integer ratio relationships. Participants listened to metrical and non-metrical rhythmic auditory sequences during electroencephalogram recording, and sounds were pseudorandomly omitted from the stimulus sequence. Cortical responses to these omissions (omission elicited potentials; OEPs) were used to estimate the timing of expectations for omitted sounds in integer ratio and non-integer ratio locations. OEP amplitude and onset latency measures indicated that expectations for non-integer ratio sequences are distorted toward the nearest metrical location in the rhythmic period. These top-down effects demonstrate metrical regularization in a purely perceptual context, and provide support for dynamical accounts of rhythm perception.

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“…Phase space plots of durational structure in rhythmic patterns. One iteration (column i), and three iterations with random noise (similar overlaid polygons, column ii) and accelerando (similar smeared polygons, column iii) (Repp, London, & Keller, 2012). The number of edges in a polygon describes the number of IOIs in the temporal sub-pattern, in this case: two notes of alternating length (row A); repeating patterns of length three (B), four (C), and five (D) IOIs.…”

Section: Limitationsmentioning

confidence: 99%

Visualizing and Interpreting Rhythmic Patterns Using Phase Space Plots

Ravignani

2017

Music Perception

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Structure in musical rhythm can be measured using a number of analytical techniques. While some techniques—like circular statistics or grammar induction—rely on strong top-down assumptions, assumption-free techniques can only provide limited insights on higher-order rhythmic structure. I suggest that research in music perception and performance can benefit from systematically adopting phase space plots, a visualization technique originally developed in mathematical physics that overcomes the aforementioned limitations. By jointly plotting adjacent interonset intervals (IOI), the motivic rhythmic structure of musical phrases, if present, is visualized geometrically without making any a priori assumptions concerning isochrony, beat induction, or metrical hierarchies. I provide visual examples and describe how particular features of rhythmic patterns correspond to geometrical shapes in phase space plots. I argue that research on music perception and systematic musicology stands to benefit from this descriptive tool, particularly in comparative analyses of rhythm production. Phase space plots can be employed as an initial assumption-free diagnostic to find higher order structures (i.e., beyond distributional regularities) before proceeding to more specific, theory-driven analyses.

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Distortions in Reproduction of Two-Interval Rhythms: When the “Attractor Ratio” Is Not Exactly 1:2

Cited by 29 publications

References 28 publications

Systematic Distortions in Musicians’ Reproduction of Cyclic Three-Interval Rhythms

Systematic Distortions in Musicians’ Reproduction of Cyclic Three-Interval Rhythms

To the beat of your own drum: Cortical regularization of non-integer ratio rhythms toward metrical patterns

Visualizing and Interpreting Rhythmic Patterns Using Phase Space Plots

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