The Temporal Statistics of Musical Rhythm across Western Genres: An Amplitude Modulation Phase Hierarchy Model

Statistical learning by the human brain plays a core role in the development of cognitive systems like language and music. Both music and speech have structured inherent rhythms, however the acoustic sources of these rhythms are debated. Theoretically, rhythm structures in both systems may be related to a novel set of acoustic statistics embedded in the amplitude envelope, statistics originally revealed by modelling children’s nursery rhymes. Here we apply similar modelling to explore whether the amplitude modulation (AM) timescales underlying rhythm in music match those in child-directed speech (CDS). Utilising AM-driven phase hierarchy modelling previously applied to infant-directed speech (IDS), adult-directed speech (ADS) and CDS, we test whether the physical stimulus characteristics that yield speech rhythm in IDS and CDS describe rhythm in music. Two models were applied. One utilized a low-dimensional representation of the auditory signal adjusted for known mechanisms of the human cochlear, and the second utilized probabilistic amplitude demodulation, estimating the modulator (envelope) and carriers using Bayesian inference. Both models revealed a similar hierarchically-nested temporal modulation structure across Western musical genres and instruments. Core bands of AM and spectral patterning matched prior analyses of IDS and CDS, and music showed strong phase dependence between slower bands of AMs, again matching IDS and CDS. This phase dependence is critical to the perception of rhythm. Control analyses modelling other natural sounds (wind, rain, storms, rivers) did not show similar temporal modulation structures and phase dependencies. We conclude that acoustic rhythm in language and music has a shared statistical basis.