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. | |||
=== Ruthenium === | |||
Named after the 44th element, and can be expressed as the 1848 & 2684 temperament. | |||
Subgroup: 2.3.5.7 | |||
Comma list: -8 23 -5 -6, 51 -13 -1 -10 | |||
Mapping generators: ~64/63, ~3/2 | |||
Mapping: 44 44 -78 175, 0 1 7 -2 | |||
Optimal tuning (CTE): ~3/2 = 701.942 | |||
Vals: 1848, 2684, ... | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 9801/9800, 4348907/14348180, 226492416/226474325 | |||
Mapping generators: ~64/63, ~3/2 | |||
Mapping: 44 44 -78 175 75, 0 1 7 -2 3 | |||
Optimal tuning (CTE): ~3/2 = 701.943 | |||
Vals: 1848, 2684, ... | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 9801/9800, 1990656/1990625, 1664000/1663893, 1554464925/1554251776 | |||
Mapping: 44 44 -78 175 75 832, 0 1 7 -2 3 -26 | |||
Optimal tuning (CTE): ~3/2 = 701.939 | |||
Vals: 1848, 2684, ... | |||
== 56th-octave temperaments == | == 56th-octave temperaments == | ||