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

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.