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Detectability of uneven rhythms H.H. Schulze Philipps Universität Marburg Fachbereich Psychologie

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Uneven rhythms The metrum is not divided into equal temporal intervals Example: 3:4,4:5,6:7 In turkish music these rhythms are called limping rhythms (aslak).

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Questions What is the threshold for detecting unevenness? How does it depend upon the period of the pulses and the length of the sequence? Does it depend upon the ear to which the sound is presented? Does it improve with training?

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Conditions Number of Periods (1,2,3,4) Ear (left,right) Period (200ms,300ms,400ms,500ms) Session(1,2)

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subjects 29 Subjects Psychology students 26 play an instrument

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Stimuli

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Method Two alternative forced-choice uneven vs even The five different periods were randomized from trial to trial The adaptive method of Kaernbach was used with five parallel staircases with random switching

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Kaernbachs adaptive Method Rule: After a correct response decrease level by 1 step after an incorrect response increase the level by 3 steps the procedure converges to a level with p- correct of.75

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Examples of individual data The following figures show the threshold of the detectability as a function of the number of periods for three subjects. Lines with the triangular symbol are for the first session. Lines with a circle symbol are for the second session. The color codes the ear condition.

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Individual Parameters Fitting a linerar model for the threshold function with period as a factor and nbeats as a covariate. The following figure shows the individual parameters and confidence intervals for all subjects. The intercept reflects the threshold for nperiod = 1 The coefficients of nbeats reflect the decrease of the threshold with the number of periods presented. The coefficients of period are for the dummy coded period variable

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Mean data

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Mean data nbeats

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Period Effect

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Session effect

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Ear effect

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Summary of statistical analysis Significant effects of period, number of beats and session No effect of ear

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Multiple look prediction for improvement The multiple look prediction of SDT is that the threshold is inverse proportional to the square root of the number of periods. Assumptions: 1.the internal observations in each event are independent random variables 2.The detectability index is proportional to the relative shift of the uneven beat. Predictions for mean data are shown in

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Mean data and multiple look prediction

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Conclusions There is large interindividual variability for the thresholds of detectability. Webers law does not hold. The thresholds are lowest for the 500ms conditions. The ear to which the rhythms are presented does not have any effect on the discriminability of the stimuli. With training the sensitivity to unevenness can be improved The improvement with the number of periods presented is less than expected by a simple multiple look model of SDT in the mean data, but the estimation of individual parameters of the threshold function still has to be done.

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