The Modulation Scale Spectrum and its Application to Rhythm-Content Description

In this paper, we propose the Modulation Scale Spectrum as an extension of the Modulation Spectrum through the Scale domain. The Modulation Spectrum expresses the evolution over time of the amplitude content of various frequency bands by a second Fourier Transform. While its use has been proven for many applications, it is not scale-invariant. Because of this, we propose the use of the Scale Transform instead of the second Fourier Transform. The Scale Transform is a special case of the Mellin Transform. Among its properties is "scale-invariance". This implies that two timestretched version of a same music track will have (almost) the same Scale Spectrum. Our proposed Modulation Scale Spectrum therefore inherits from this property while describing frequency content evolution over time. We then propose a specific implementation of the Modulation Scale Spectrum in order to represent rhythm content. This representation is therefore tempo-independent. We evaluate the ability of this representation to catch rhythm characteristics on a classification task. We demonstrate that for this task our proposed representation largely exceeds results obtained so far while being highly tempo-independent.