Cross-cultural data shows musical scales evolved to maximise imperfect fifths

Abstract

Musical scales are used in cultures throughout the world, but the question as to how they evolved remains open. Some suggest that scales based on the harmonic series are inherently pleasant, while others propose that scales are chosen that are easy to sing, hear and reproduce accurately. However, testing these theories has been hindered by the sparseness of empirical evidence. Here, to enable such examination, we assimilate data from diverse ethnomusicological sources into a cross-cultural database of scales. We generate populations of scales based on proposed and alternative theories and assess their similarity to empirical distributions from the database. Most scales can be explained as tending to include intervals roughly corresponding to perfect fifths ("imperfect fifths"), and packing arguments explain the salient features of the distributions. Scales are also preferred if their intervals are compressible, which could facilitate efficient communication and memory of melodies. While no single theory can explain all scales, which appear to evolve according to different selection pressures, the simplest harmonicity-based, imperfect-fifths packing model best fits the empirical data.

Cultural evolution and music

“…Despite its youth, the study of the cultural evolution of music has resulted in some important insights. For example, research on traditional and folk music have revealed that scales around the world have a tendency to converge towards similar patterns (McBride and Tlusty, 2019;Brown and Jordania, 2013;Kuroyanagi et al, 2019), musical variation is correlated with social complexity (Lomax, 1968;Wood et al, 2021) and sometimes population history (Brown et al, 2014; but see Matsumae et al, 2021), and that certain styles of music are reliably associated with particular behavioral contexts across cultures (Mehr et al, 2019) according to their acoustic features (Mehr et al, 2018;Hilton et al, 2021). Studies of classical music have found that melodic intervals are associated with particular historical periods (Rodriguez Zivic et al, 2013;Weiß et al, 2019;Harasim et al, 2021), and that tonal complexity and harmonic richness have increased over time ( Weiß et al, 2019;Serra-Peralta et al 2021).…”

“…This nding was consistent despite striking di erences in the scales used in Japanese and English folk music. McBride and Tlusty (2019; recently compiled 896 scales (some theory-driven based on frequency ratios and some actually measured from audio recordings) from 55 sources spanning 39 countries to analyze cross-cultural variation in them. They discovered a strong cross-cultural tendency for scales to have either 5 or 7 notes and to include perfect fths and octaves, supporting previous theoretical and empirical studies (Brown and Jordania, 2013;Kuroyanagi et al, 2019).…”

Music as a coevolved system for social bonding

“…Coordinating with other individuals musically, by aligning acoustic spectra, can sound pleasing and promote bonding. The specific mechanisms and causal relationships behind this effect remain contested (Bowling & Purves 2015;Bowling et al 2017Bowling et al , 2018Harrison & Pearce 2019;Jacoby et al 2019;Large et al 2016;McBride & Tlusty 2020;McDermott et al 2010McDermott et al , 2016Merker et al 2018;Pfordresher & Brown 2017). Regardless, scales facilitate harmony, where individual voices/instruments combine consonantly -another design feature supporting group coordination but not solo performance.…”

Sequence alignment of folk song melodies reveals cross-cultural regularities of musical evolution

“…For example, using the C major scale for reference, a single semitone change could either be between two notes in the same scale (e.g., B-C, E-F) or could lead to a note in a different scale (e.g., C to D b ). Because most scales contain few or no possible 1-semitone intervals between scale degrees, [55][56][57] 1-semitone substitutions are rarer than 2-semitone substitutions despite being a smaller substitution distance (see STAR Methods for an exploratory analysis quantifying such interactions between substitution distance and tonal relationships).…”