Hierarchical temporal structure in music, speech and animal vocalizations: jazz is like a conversation, humpbacks sing like hermit thrushes.

Humans talk, sing and play music. Some species of birds and whales sing long and complex songs. All these behaviours and sounds exhibit hierarchical structure-syllables and notes are positioned within words and musical phrases, words and motives in sentences and musical phrases, and so on. We developed a new method to measure and compare hierarchical temporal structures in speech, song and music. The method identifies temporal events as peaks in the sound amplitude envelope, and quantifies event clustering across a range of timescales using Allan factor (AF) variance. AF variances were analysed and compared for over 200 different recordings from more than 16 different categories of signals, including recordings of speech in different contexts and languages, musical compositions and performances from different genres. Non-human vocalizations from two bird species and two types of marine mammals were also analysed for comparison. The resulting patterns of AF variance across timescales were distinct to each of four natural categories of complex sound: speech, popular music, classical music and complex animal vocalizations. Comparisons within and across categories indicated that nested clustering in longer timescales was more prominent when prosodic variation was greater, and when sounds came from interactions among individuals, including interactions between speakers, musicians, and even killer whales. Nested clustering also was more prominent for music compared with speech, and reflected beat structure for popular music and self-similarity across timescales for classical music. In summary, hierarchical temporal structures reflect the behavioural and social processes underlying complex vocalizations and musical performances.