The Rarity of Musical Audio Signals Within the Space of Possible Audio Generation

TL;DR

This paper analyzes the extreme unlikelihood of white noise signals producing music-like audio, providing mathematical bounds and implications for algorithmic music generation and machine learning's potential to explore musical space.

Contribution

It introduces a mathematical framework to quantify the rarity of music signals within the space of all possible audio signals, informing future algorithmic and machine learning music systems.

Findings

Music-like signals are exceedingly rare within the space of all possible audio signals.

Mathematical bounds on the probability of white noise producing music-like signals are established.

The results suggest a vast, largely unexplored space of potential music signals for machine learning to discover.

Abstract

A white noise signal can access any possible configuration of values, though statistically over many samples tends to a uniform spectral distribution, and is highly unlikely to produce intelligible sound. But how unlikely? The probability that white noise generates a music-like signal over different durations is analyzed, based on some necessary features observed in real music audio signals such as mostly proximate movement and zero crossing rate. Given the mathematical results, the rarity of music as a signal is considered overall. The applicability of this study is not just to show that music has a precious rarity value, but that examination of the size of music relative to the overall size of audio signal space provides information to inform new generations of algorithmic music system (which are now often founded on audio signal generation directly, and may relate to white noise via such machine learning processes as diffusion). Estimated upper bounds on the rarity of music to the size of various physical and musical spaces are compared, to better understand the magnitude of the results (pun intended). Underlying the research are the questions `how much music is still out there?' and `how much music could a machine learning process actually reach?'.