An analysis of music sound by a 12 even-tempered discrete wavelet

Abstract

Music sounds are analyzed using a 12 even-tempered wavelet based upon the variable-density perfect translation invariance complex discrete wavelet transform (VD-PTI-CDWT) which divides an octave frequency band into 12 filter banks of equivalent width. Music chords generated from different sound sources thus analyzed are represented as scalogram and in 3 dimension (3D) graph over time-frequency domain. The scalogram representation provides information corresponding to the western music notation and accords with human's cognition for pitch of the music sound whereas 3D graph representation is capable of providing more detail sound information. We further apply the method to Specmurt analysis in order to estimate the fundamental frequency distribution of polyphonic music sound. The polyphonic sound of C 4, G 4, D 5, A 5 in scientific notation generated with saw-tooth wave tone is successfully filtered out its overtones to provide the fundamental frequency distribution.