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.

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In this paper, a novel approach for the computation of a pitch salience function is presented. The aim of a pitch (considered here as synonym for fundamental frequency) salience function is to estimate the relevance of the most salient musical pitches that are present in a certain audio excerpt. Such a function is used in numerous Music Information Retrieval (MIR) tasks such as pitch, multiple-pitch estimation, melody extraction and audio features computation (such as chroma or Pitch Class Profiles). In order to compute the salience of a pitch candidate f , the classical approach uses the weighted sum of the energy of the short time spectrum at its integer multiples frequencies hf . In the present work, we propose a different approach which does not rely on energy but only on frequency location. For this, we first estimate the peaks of the short time spectrum. From the frequency location of these peaks, we evaluate the likelihood that each peak is an harmonic of a given fundamental frequency. The specificity of our method is to use as likelihood the deviation of the harmonic frequency locations from the pitch locations of the equal tempered scale. This is used to create a theoretical sequence of deviations which is then compared to an observed one. The proposed method is then evaluated for a task of multiple-pitch estimation using the MAPS test-set.

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