Zipf's Law in Short-Time Timbral Codings of Speech, Music, and Environmental Sound Signals

Abstract

Timbre is a key perceptual feature that allows discrimination 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 short-time 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 specific, 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.

Large-Scale Analysis of Zipf’s Law in English Texts

“…This pattern (1) has been found across different languages, literary styles, time periods, and levels of morphological abstraction [2,5,6]. More fascinatingly, the same law has been claimed in other codes of communication, as in music [7] or for the timbres of sounds [8], and also in disparate discrete systems where individual units or agents gather into different classes [9], for example, employees into firms [10], believers into religions [11], insects into plants [12], units of mass into animals present in ecosystems [13], visitors or links into web pages [14], telephone calls to users [15], or abundance of proteins (in a single cell) [16]. The attempts to find an explanation have been diverse [3,15,[17][18][19][20][21][22][23][24], but no solution has raised consensus [20,25,26].…”

Note Onset Deviations as Musical Piece Signatures

“…Noticeably, the fits yielded exponents in the ranges provided by [9]. Since, as mentioned, we only wanted to have an impression of the behavior of , we did not pursue more robust power law fitting strategies such as the ones followed in our previous work [45], [46] or elsewhere [47], nor did we consider more advanced techniques for determining the existence of long-range correlations such as the ones employed, e.g., in [9], [39].…”

Music Positioning and Annotation For Television Videos

“…Each music extracts two music pieces' fingerprints and matches in two stages: lookup and minimum-distance matching. The music annotation database contains a lookup table(LUT) with all possible 32 bit sub-fingerprints as an entry [3]. All the same 32-bit sub-fingerprints are indexed and pruning.…”