24576/24565: Difference between revisions
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m →2.3.5.7.17 subgroup (prime archagall): style and generator |
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We may observe that in a good tuning of archagall there is an accurate [[5/4]] at +13 fourths ([[85/64]]'s) minus five octaves ([[2/1]]'s). Because 75/25 = 3 and 85/5 = 17 this allows us to collapse it into its corresponding prime subgroup. This temperament is very closely related to [[171edo]] for which 171edo is the tuning tempering {S49, S50, S18/S20} which is natural because this temperament tempers S49*S50 = S35 = [[1225/1224]] and (S18/S20)/S49 = [[5832/5831]] while not tempering any of {S49, S50, S18/S20} individually. Note that 171edo is exceptionally efficient and accurate in the 2.3.5.7.17 subgroup, constituting a microtemperament for it. | We may observe that in a good tuning of archagall there is an accurate [[5/4]] at +13 fourths ([[85/64]]'s) minus five octaves ([[2/1]]'s). Because 75/25 = 3 and 85/5 = 17 this allows us to collapse it into its corresponding prime subgroup. This temperament is very closely related to [[171edo]] for which 171edo is the tuning tempering {S49, S50, S18/S20} which is natural because this temperament tempers S49*S50 = S35 = [[1225/1224]] and (S18/S20)/S49 = [[5832/5831]] while not tempering any of {S49, S50, S18/S20} individually. Note that 171edo is exceptionally efficient and accurate in the 2.3.5.7.17 subgroup, constituting a microtemperament for it. | ||
Subgroup: 2.3.5.7.17 | [[Subgroup]]: 2.3.5.7.17 | ||
Comma list: 24576/24565 = S16/S17, 57375/57344 = S15/S16, 1225/1224 = S35 | Comma list: 24576/24565 = S16/S17, 57375/57344 = S15/S16, 1225/1224 = S35 | ||
{{mapping|legend=1| 1 11 -3 20 9 | 0 -23 13 -42 -12 }} | |||
[[CTE]] generator: 85/64 = 491.222{{cent}} | |||
Some good (relative to their size) EDOs supporting it: 22, 149, 171, 193, 215, 320, 364 | Some good (relative to their size) EDOs supporting it: 22, 149, 171, 193, 215, 320, 364 | ||