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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Swing is a typical long-short rhythmical pattern that is mostly present in jazz music. In this article, we propose an algorithm to automatically estimate how much a track, a frame of a track, is swinging. We denote this by swing ratio. The algorithm we propose is based on the analysis of the auto-correlation of the onset energy function of the audio signal and a simple set of rules. For the purpose of the evaluation of this algorithm, we propose and share the “GTZAN-rhythm” test-set, which is an extension of a well-known test-set by adding annotations of the whole rhythmical structure (downbeat, beat and eight-note positions). We test our algorithm for two tasks: detecting tracks with or without swing, and estimating the amount of swing. Our algorithm achieves 91% mean recall. Finally we use our annotations to study the relationship between the swing ratio and the tempo (study the common belief that swing ratio decreases linearly with the tempo) and the musicians. How much and how to swing is never written on scores, and is therefore something to be learned by the jazzstudents mostly by listening. Our algorithm could be useful for jazz student who wants to learn what is swing.

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