Rank-Size Distribution of Notes in Harmonic Music: Hierarchic Shuffling of Distributions

Manuel Río; Germinal Cocho

Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2

Research Article

Rank-Size Distribution of Notes in Harmonic Music: Hierarchic Shuffling of Distributions

Download

560 downloads

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1007/978-3-642-02469-6_98,
    author={Manuel R\^{\i}o and Germinal Cocho},
    title={Rank-Size Distribution of Notes in Harmonic Music: Hierarchic Shuffling of Distributions},
    proceedings={Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2},
    proceedings_a={COMPLEX PART 2},
    year={2012},
    month={5},
    keywords={Ranking distributions Power law distribution Zipf law in Music},
    doi={10.1007/978-3-642-02469-6_98}
}

Manuel Río
Germinal Cocho
Year: 2012
Rank-Size Distribution of Notes in Harmonic Music: Hierarchic Shuffling of Distributions
COMPLEX PART 2
Springer
DOI: 10.1007/978-3-642-02469-6_98

Manuel Río¹^,*, Germinal Cocho¹^,*

1: Universidad Nacional Autónoma de México

*Contact email: mbeltrandelrio@fisica.unam.mx, cocho@fisica.unam.mx

Abstract

We trace the rank size distribution of notes in harmonic music, which on previous works we suggested was much better represented by the Two-parameter, first class Beta distribution than the customary power law, to the ranked mixing of distributions dictated by the harmonic and instrumental nature of the piece. The same representation is shown to arise in other fields by the same type of ranked shuffling of distributions. We include the codon content of intergenic DNA sequences and the ranked distribution of sizes of trees in a determined area as examples. We show that the fittings proposed increase their accuracy with the number of distributions that are mixed and ranked.

Keywords: Ranking distributions Power law distribution Zipf law in Music

Published: 2012-05-11

: http://dx.doi.org/10.1007/978-3-642-02469-6_98