’’1/f noise’’ in music: Music from 1/f noise

Abstract

The spectral density of fluctuations in the audio power of many musical selections and of English speech varies approximately as 1/f (f is the frequency) down to a frequency of 5×10−4 Hz. This result implies that the audio-power fluctuations are correlated over all times in the same manner as ’’1/f noise’’ in electronic components. The frequency fluctuations of music also have a 1/f spectral density at frequencies down to the inverse of the length of the piece of music. The frequency fluctuations of English speech have a quite different behavior, with a single characteristic time of about 0.1 s, the average length of a syllable. The observations on music suggest that 1/f noise is a good choice for stochastic composition. Compositions in which the frequency and duration of each note were determined by 1/f noise sources sounded pleasing. Those generated by white-noise sources sounded too random, while those generated by 1/f2 noise sounded too correlated.