2016edo: Difference between revisions
it's very text disruptive to have the template in the middle, either put it at the bottom or at the top of theory. |
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== Theory == | == Theory == | ||
2016 is a significantly composite number, with its divisors being {{EDOs| 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008 }}. Its abundancy index is 2.25. | 2016 is a significantly composite number, with its divisors being {{EDOs| 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008 }}. Its abundancy index is 2.25. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|2016}} | |||
Prime harmonics (below 61) with less than 22% error in 2016edo are: 2, 5, 11, 13, 19, 41, 47. With next error being 26% on the 37th harmonic, it is reasonable to make cutoff here. | Prime harmonics (below 61) with less than 22% error in 2016edo are: 2, 5, 11, 13, 19, 41, 47. With next error being 26% on the 37th harmonic, it is reasonable to make cutoff here. | ||
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In the 11-limit, 2016edo tempers out the {{monzo| 0 0 -22 0 3 11 }} comma, which equates a stack of eleven [[25/13]]'s with three [[11/1]]'s. | In the 11-limit, 2016edo tempers out the {{monzo| 0 0 -22 0 3 11 }} comma, which equates a stack of eleven [[25/13]]'s with three [[11/1]]'s. | ||
2016 has a total of 576 numbers coprime to it, which means this is how many generators can reach any point in the octave by being stacked. | |||
One such temperament is 311 & 2016, produced by stacking 1465\2016, and defined for the 2.5.11.13.19.41 subgroup with the comma basis 16777475/16777216, 1171280/1171001, 615288025/615120896, 1180029296875/1179517976576. | |||
=== Fractional octave temperaments === | === Fractional octave temperaments === | ||