Fractional-octave temperaments: Difference between revisions

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 == 44th-octave temperaments ==
-One step of 44edo is very close to the septimal comma, [[64/63]]. The relationship is preserved even up thousands of EDOs.
+One step of 44edo is very close to the septimal comma, [[64/63]]. The relationship is preserved even up thousands of edos.
 === Ruthenium ===
-Named after the 44th element, and can be expressed as the 1848 & 2684 temperament.
+Ruthenium is named after the 44th element, and can be expressed as the 1848 & 2684 temperament.
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: {{monzo|-8  23 -5  -6}}, {{monzo|51 -13 -1 -10}}
+[[Comma list]]: {{monzo| -8  23 -5 -6 }}, {{monzo| 51 -13 -1 -10 }}
-Mapping generators: ~64/63, ~3/2
+[[Mapping]]: [{{val| 44 0 -386 263 }}, {{val| 0 1 7 -2 }}]
-Mapping: [{{val|44 44 -78 175}}, {{val|0 1 7 -2}}]
+Mapping generators: ~64/63, ~3
-Optimal tuning (CTE): ~3/2 = 701.942
+[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9420
-Vals:{{EDOs|836, 1012, 1672, 1848, 2684, 2860, 3696, 4532, 5368}}, ...
+{{Val list|legend=1| 176, 660, 836, 1848, 2684, 4532, 19976, 24508, 29040, 33572 }}
+[[Badness]]: 0.111
 ==== 11-limit ====
 Subgroup: 2.3.5.7.11
-Comma list: 9801/9800, 4348907/14348180, 226492416/226474325
+Comma list: 9801/9800, 1771561/1771470, 67110351/67108864
-Mapping generators: ~64/63, ~3/2
+Mapping: [{{val| 44 0 -386 263 -57 }}, {{val| 0 1 7 -2 3 }}]
-Mapping: [{{val|44 44 -78 175 75}}, {{val|0 1 7 -2 3}}]
+Optimal tuning (CTE): ~3/2 = 701.9429
-Optimal tuning (CTE): ~3/2 = 701.943
+Optiml GPV sequence: {{val list| 176, 660, 836, 1848, 2684, 4532, 15444, 19976e }}
-Vals: {{EDOs|176, 836, 1012, 1672, 1848, 2684, 2860, 3696, 4532}}...
+Badness: 0.0209
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 9801/9800, 1990656/1990625, 1664000/1663893, 1554464925/1554251776
+Comma list: 9801/9800, 196625/196608, 823680/823543, 1771561/1771470
-Mapping: [{{val|44 44 -78 175 75 832}}, {{val|0 1 7 -2 3 -26}}]
+Mapping: [{{val| 44 0 -386 263 -57 1976 }}, {{val| 0 1 7 -2 3 -26 }}]
 Optimal tuning (CTE): ~3/2 = 701.939
-Vals: {{EDOs|836, 1012f, 1672f, 1848, 2684, 3696f, 4532, 5368, 7216}}...
+Optiml GPV sequence: {{val list| 836, 1848, 2684, 7216, 9900, 12584 }}
+Badness: 0.0396
 == 56th-octave temperaments ==