32nd-octave temperaments: Difference between revisions
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== Germanium == | == Germanium == | ||
It is named after germanium, the 32nd element, defined as 224 & 1376. It tempers out [[3025/3024]], [[4096/4095]], [[4375/4374]] and [[9801/9800]] in the 13-limit, although it should be noted that if only these commas are taken, they make a rank-3 1/2-octave temperament called [[rym]]. | It is named after germanium, the 32nd element, defined as 224 & 1376. It tempers out [[3025/3024]], [[4096/4095]], [[4375/4374]] and [[9801/9800]] in the 13-limit, although it should be noted that if only these commas are taken, they make a rank-3 1/2-octave temperament called [[rym]]. | ||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 3025/3024, 4375/4374, {{monzo|60 -15 -5 -10 1}} | |||
{{Mapping|legend=1| 32 1 -50 239 235 | 0 2 5 -6 -5 }} | |||
: mapping generators: ~134217728/131274675 = 1\32, ~77175/45056 = 932.260 | |||
[[Optimal tuning]] ([[CTE]]): ~77175/45056 = 932.260 | |||
[[Support]]ing [[ET]]s: {{EDOs|224, 704, 928, 1152, 1376, 1600}} | |||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | [[Subgroup]]: 2.3.5.7.11.13 | ||
Comma list: 3025/3024, 4096/4095, 4375/4374, 5942475/5940688 | [[Comma list]]: 3025/3024, 4096/4095, 4375/4374, 5942475/5940688 | ||
{{Mapping|legend=1| 32 1 -50 239 235 193 | 0 2 5 -6 -5 -3 }} | |||
: mapping generators: ~1352/1323 = 1\32, ~245/143 = 932.263 | |||
[[Optimal tuning]] ([[CTE]]): ~245/143 = 932.263 | |||
{{Optimal ET sequence|legend=1| 224, 1376, 1600 }} | {{Optimal ET sequence|legend=1| 224, 1376, 1600 }} | ||