25th-octave temperaments: Difference between revisions
→Semimanganese: Hemimanganese as hemi- splits gen in half |
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=== Hemimanganese === | === Hemimanganese === | ||
While manganese is a rather bulky temperament, splitting the generator in half lends itself to a high-limit interpretaton, which can be described as the 525 & 2000 temperament. | While manganese is a rather bulky temperament, splitting the generator in half lends itself to a high-limit interpretaton, which can be described as the 525 & 2000 temperament. Hemimanganese maps [[17/14]] into 7\25. | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 4096/4095, 67392/67375, 28600000/28588707, 66997216/66976875 | |||
{{Mapping|legend=1| 25 2 43 89 15 164 | 0 10 4 -5 19 -19 }} | |||
: mapping generators: ~147/143 = 1\25, ~10000/9009 = 180.598 | |||
[[Optimal tuning]] ([[CTE]]): ~10000/9009 = 180.598 | |||
[[Support]]ing [[ET]]s: {{EDOs|525, 1475, 2000, 2525, 3475}} | |||
==== 17-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 4096/4095, 14400/14399, 67392/67375, 361250/361179, 983178/983125 | |||
{{Mapping|legend=1| 25 2 43 89 15 164 121 | 0 10 4 -5 19 -19 -5 }} | |||
: mapping generators: ~147/143 = 1\25, ~272/245 = 180.599 | |||
[[Optimal tuning]] ([[CTE]]): ~272/245 = 180.599 | |||
[[Support]]ing [[ET]]s: {{EDOs|525, 1475, 2000, 2525, 3475}} | |||
==== 19-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 4096/4095, 6175/6174, 14400/14399, 23409/23408, 67392/67375, 89376/89375 | |||
{{Mapping|legend=1| 25 2 43 89 15 164 121 46 | 0 10 4 -5 19 -19 -5 16 }} | |||
: mapping generators: ~1573/1530 = 1\25, ~3773/3400 = 180.598 | |||
[[Optimal tuning]] ([[CTE]]): ~3773/3400 = 180.598 | |||
[[Support]]ing [[ET]]s: {{EDOs|525, 1475, 2000, 2525, 3475}} | |||
==== 23-limit ==== | ==== 23-limit ==== | ||