Group actions, power mean orbit size, and musical scales
نویسندگان
چکیده
We provide an application of the theory group actions to study musical scales. For any G, finite G-set S, and real number t, we define t-power diameter diamt(G,S) be size maximal orbit S divided by mean elements S. The symmetric S11 acts on set all tonic scales, where a scale is subset Z12 containing 0. show that for t∈[−1,1], among subgroups G S11, heptatonic scales largest subgroup Γ, its conjugate subgroups, generated {(12),(34),(56),(89),(1011)}. unique Γ-orbit consists 32 thāts Hindustani classical music popularized Bhatkhande. This analysis provides reason why these 462 are mathematical interest. also apply our analysis, lesser degree, hexatonic pentatonic
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ژورنال
عنوان ژورنال: Journal of Mathematics and Music
سال: 2021
ISSN: ['1745-9737', '1745-9745']
DOI: https://doi.org/10.1080/17459737.2020.1836686