Fractional-octave temperaments: Difference between revisions
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→56th-octave temperaments: expanded upwards, added information, monzo template |
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Line 237: | Line 237: | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
Comma list: | Comma list: {{monzo|-225 24 -56}} | ||
Mapping: 56 89 131, 0 -1 -4 | Mapping: [{{val|56 89 131}}, {{val|0 -1 -4}}] | ||
Mapping generators: ~81/80, ~3/2 | Mapping generators: ~81/80, ~3/2 | ||
Line 249: | Line 249: | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: | Comma list: {{monzo|-12 29 -11 -3}}, {{monzo|47 -7 -7 -7}} | ||
Mapping: 56 56 -1 321, 0 1 4 5 | Mapping: [{{val|56 56 -1 321}}, {{val|0 1 4 -5}}] | ||
Mapping generators: ~81/80, ~3/2 | Mapping generators: ~81/80, ~3/2 | ||
Line 258: | Line 258: | ||
Vals: 224, 1848, 2072 | Vals: 224, 1848, 2072 | ||
===11-limit=== | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 9801/9800, 1019215872/1019046875, 14765025303/14763950080 | |||
Mapping: [{{val|56 56 -1 321 292}}, {{val|0 1 4 5 -3}}] | |||
Mapping generators: ~81/80, ~3/2 | |||
Optimal tuning (CTE): ~3/2 = 701.943 | |||
== 65th-octave temperaments == | == 65th-octave temperaments == | ||
[[65edo]] is accurate for harmonics 3, 5, and 11, so various 65th-octave temperaments actually make sense. | [[65edo]] is accurate for harmonics 3, 5, and 11, so various 65th-octave temperaments actually make sense. |