Fractional-octave temperaments: Difference between revisions

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Eliora (talk | contribs)
56th-octave temperaments: expanded upwards, added information, monzo template
Line 237: Line 237:
Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: [-225 24 -56]
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: [ -12 29 -11 -3], [  47 -7  -7 -7]
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.