On the use of the instantaneous frequency to understand phenomena in polyphonic piano sounds

Abstract

The extraction of amplitudes and frequencies of partials from musical tones have been developed over the past ten years in order to carry out statistical studies on spectral parameters [Ando, J. Acoust. Soc. Am. 94, 37–45 (1993)] and/or to measure the frequency ratios of spectral components [Brown, J. Acoust. Soc. Am. 99, 1210–1218 (1996)]. This paper presents a study of the temporal evolution of the amplitude and frequency of piano sounds’ partials in order to take into account the eventual frequential fluctuations in the identification method of polyphonic piano sounds developed by the authors [Rossi and Girolami, J. Acoust. Soc. Am. 100, 2842 (1996)]. The notion of analytical signal and instantaneous frequency is used to find the characteristics of beats appearing in the evolution of the amplitude of single notes and single notes’ partials. In the case of polyphonic piano sounds, pertubations in the temporal evolution of frequency and amplitude of a given partial, due to the presence of a close partial belonging to another note, are presented.