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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Alejandro Hernández-Fuentes & M. del Castillo-Mussot & Candelario Hernández-Gómez, 2021. "High n-gram occurrence probability in baroque, classical and romantic melodies," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-22, February.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:02:n:s0129183121500236
    DOI: 10.1142/S0129183121500236
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