Zipf's law in short-time timbral codings of speech, music, and environmental sound signals

Timbre is a key perceptual feature that allows to discriminate between different sounds. Timbral sensations are highly dependent on the temporal evolution of the power spectrum of an audio signal. In order to quantitatively characterize such sensations, the shape of the power spectrum has to be encoded in a way that preserves certain physical and perceptual properties. Therefore, it is common practice to encode shorttime power spectra using psychoacoustical frequency scales. In this paper, we study and characterize the statistical properties of such encodings, here called timbral code-words. In particular, we report on rank-frequency distributions of timbral code-words extracted from 740 hours of audio coming from disparate sources such as speech, music, and environmental sounds. Analogously to text corpora, we find a heavy-tailed, Zipfian distribution with exponent close to one. Importantly, this distribution is found independently of different encoding decisions and regardless of the audio source. Further analysis on the intrinsic characteristics of most and least frequent code-words reveals that the most frequent code-words tend to have a more homogeneous structure. We also find that speech and music databases have distinctive code-words while, in the case of the environmental sounds, this database-specific code-words are not present. Finally, we find that a Yule-Simon process with memory provides a reasonable quantitative approximation for our data, suggesting the existence of a common simple generative mechanism for all considered sound sources. Our results provide new evidence towards understanding both sound generation and perception processes and, at the same time, they suggest a potential path to enhance current audio-based technological applications by taking advantage of knowledge about the found distribution. URL http://dx.plos.org/10.1371/journal.pone.0033993 [5] Source URL: https://www.iiia.csic.es/en/node/53956 Links [1] https://www.iiia.csic.es/en/bibliography?f[author]=185 [2] https://www.iiia.csic.es/en/staff/joan-serr%C3%A0 [3] https://www.iiia.csic.es/en/bibliography?f[author]=186 [4] https://www.iiia.csic.es/en/bibliography?f[author]=187 [5] http://dx.plos.org/10.1371/journal.pone.0033993