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Temporal control mechanism in equaled interval tapping.

Subjects who were at intermediate levels of musical performance made equaled interval tapping in several tempos. The temporal fluctuation for the tapping was observed and analysed. The power spectrum of the fluctuation showed a critical phenomenon at around a frequency which corresponds to the period of 20 taps, for all tempos and all subjects, i.e., the slope of the spectrum was flat or had a positive value in the high frequency region above the critical frequency but it increased as the frequency decreased in the low frequency region below the critical frequency. Moreover, auto-regressive models and Akaike's information criterion were introduced to determine the critical tap number. The order of the best auto-regressive model for the temporal fluctuation data was distributed around 20 taps. These results show that the memory capacity of 20 taps governs the control of equaled interval tapping. To interpret the critical phenomenon of 20 taps with the memory capacity of the short term memory, the so called magic number seven, a simple chunking assumption was introduced; subjects might have unconsciously chunked every three taps during the tapping. If the chunking assumption is true, when subjects consciously chunk every seven taps, the memory capacity of taps should shift to about 50 taps. To test if the assumption is true or not, subjects made a three-beat rhythm tapping and a seven-beat rhythm tapping with equaled intervals. As a result, the memory capacity for these accented tappings were also estimated as 20 taps. This suggests that the critical phenomenon cannot be explained by the chunking assumption and the magic number seven, rather this finding suggests that there exists a memory capacity of 20 taps and this is used for equaled interval tapping.