Universal patterns in sound amplitudes of songs and music genres

Abstract

We report a statistical analysis over more than eight thousand songs. Specifically, we investigate the probability distribution of the normalized sound amplitudes. Our findings seems to suggest a universal form of distribution which presents a good agreement with a one-parameter stretched Gaussian. We also argue that this parameter can give information on music complexity, and consequently it goes towards classifying songs as well as music genres. Additionally, we present statistical evidences that correlation aspects of the songs are directly related with the non-Gaussian nature of their sound amplitude distributions. In recent years, studies of complex systems have become widespread among the scientific community, specially in the statistical physics one [1][2][3][4][5]. Many of these investigations deal with data records ordered in time or space (i.e., time series), trying to extract some features, patterns or laws that may be present in the systems studied. This approach has been successfully applied to a variety of fields, from physics and astronomy [6] Music is a well known worldwide social phenomenon linked to the human cognitive habits, modes of consciousness as well as historical developments [14]. In the direction of music's social role, some authors investigated collective listening habits. For instance, Lambiotte and Ausloos [15] analyzed data from people music library finding audience groups with the size distribution following a power law. They also investigated correlations among these music groups, reporting non-trivial relations [16]. In another work, Silva et al.[17] studied the network structure of the song writers and the singers of Brazilian popular music (mpb). There is also an interest in the behavior of music sales [18] as well as in the success of musicians [19][20][21].Despite these cultural aspects, songs form a highly organized system presenting very complex structures and long-range correlations. All these features have attracted the attention of statistical physicists. In a seminal paper, Voss and Clarke [22] analyzed the power spectrum of radio stations and observed a 1/f noise like pattern. They also showed that the correlation can extend to longer or shorter time scales, depending on the music genre. Hsü and Hsü[23] investigated the changes of acoustic frequency in Bach's and Mozart's compositions, finding self-similarity and fractals structures. In contrast, they report no resemblance to fractal geometry [24] for modern music. Fractal structures have also been reported in the study of sequences of music notes [25], where Su and Wu [26] suggest that the multifractal spectrum can be used to distinguish different styles of music. In this brief literature review, we see that special attention was paid to the fractal structures of music, correlations and power spectrum analysis. However, much less attention has been paid to the understanding of the amplitude distribution. This last point has been noted by Diodati and Piazza[34]. In their work, they investigated the distribution of t...

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