Fractional-octave temperaments: Difference between revisions
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== 56th-octave temperaments == | |||
One step of 56edo is close to a syntonic comma. | |||
=== Barium === | |||
Named after the 56th element, and tempers out the [-225 224 -56] comma, which sets 56 syntonic commas equal to the octave. Best expressed as 224 & 2072 temperament. | |||
Subgroup: 2.3.5 | |||
Comma list: [-225 24 -56] | |||
Mapping: 56 89 131, 0 -1 -4 | |||
Mapping generators: ~81/80, ~3/2 | |||
Optimal tuning (CTE): ~3/2 = 701.938 | |||
Vals: {{EDOs|56, 224, 2072, 1848, 2296, 1624, 448, 3920, 4144, 3696, 2520}} | |||
=== 7-limit=== | |||
Subgroup: 2.3.5.7 | |||
Comma list: [ -12 29 -11 -3], [ 47 -7 -7 -7] | |||
Mapping: 56 56 -1 321, 0 1 4 5 | |||
Mapping generators: ~81/80, ~3/2 | |||
Optimal tuning (CTE): ~3/2 = 701.943 | |||
Vals: 224, 1848, 2072 | |||
== 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. | ||