Comparison of Different Calculation Methods of Effective Duration (τ_e ) of the Running Autocorrelation Function of Music Signals

This paper discusses methods to calculate the eff ective duration τ_e of the running autocorrelation function (ACF) of music signals. The iterative method is newly proposed and compared with the methods of previous studies. The index R, describing the accuracy of the τ_e regression, is also introduced. The iterative method was found to improve the accuracy of the τ_e regression for orchestral music signals with a wide variation of ACF envelopes. The resulting τ_e is discussed with reference to music tempo; the τ_e value increased as the music tempo decreased. Also, a longer inter-onset interval led to a long τ_e value and staccato results in a short τ_e value.