High n-gram occurrence probability in baroque, classical and romantic melodies

Alejandro Hernández-Fuentes (), M. del Castillo-Mussot and Candelario Hernández-Gómez ()
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Alejandro Hernández-Fuentes: Facultad de Ciencias, Universidad Nacional Autónoma de México, México City 04510, México
M. del Castillo-Mussot: #x2020;Instituto de Física,Universidad Nacional Autónoma de México, México City 04510, México
Candelario Hernández-Gómez: #x2020;Instituto de Física,Universidad Nacional Autónoma de México, México City 04510, México

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 02, 1-22

Abstract: An n-gram in music is defined as an ordered sequence of n notes of a melodic sequence m. Pm(n) is calculated as the average of the occurrence probability without self-matches of all n-grams in m. Then, Pm(n) is compared to the averages Shuffm(n) and Equipm(n), calculated from random sequences constructed with the same length and set of symbols in m either by shuffling a given sequence or by distributing the set of symbols equiprobably. For all n, both Pm(n)−Shuffm(n), Pm(n)−Equipm(n)≥0, and this differences increases with n and the number of notes, which proves that notes in musical melodic sequences are chosen and arranged in very repetitive ways, in contrast to random music. For instance, for n≤5 and for all analyzed genres we found that 1.6<−log(Pm(n))<8.6, while 1.6<−log(Shuffm(n))<14.5 and 1.9<−log(Equipm(n))<18.3. Pm(n) of baroque and classical genres are larger than the romantic genre one. Pm(n) vs n is very well fitted to stretched exponentials for all songs. This simple method can be applied to any musical genre and generalized to polyphonic sequences.

Keywords: Music; n-gram; occurrence probability; statistics (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0129183121500236

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