Hemimean family: Difference between revisions
→Hemimean: +2.3.5.7.17 subgroup; rework description as appropriate for an extension of hemimean |
→Hemimean: +semiorion |
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Sval mapping: [{{val| 1 0 0 -3 -5 }}, {{val| 0 1 0 0 5 }}, {{val| 0 0 2 5 1 }}] | Sval mapping: [{{val| 1 0 0 -3 -5 }}, {{val| 0 1 0 0 5 }}, {{val| 0 0 2 5 1 }}] | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702. | Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.1960, ~28/25 = 193.6548 | ||
Optimal GPV sequence: {{Val list| 12, 19g, 31g, …, 87, 99, 217, 229, 316, 328h, 446, 545c, 873cg }} | Optimal GPV sequence: {{Val list| 12, 19g, 31g, …, 87, 99, 217, 229, 316, 328h, 446, 545c, 873cg }} | ||
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Badness: 0.456 | Badness: 0.456 | ||
=== Semiorion === | |||
Semiorion is an alternative subgroup extension of lower complexity, which splits the octave into two. | |||
Subgroup: 2.3.5.7.17 | |||
Comma list: 289/288, 3136/3125 | |||
Sval mapping: [{{val| 2 0 0 -6 5 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 2 5 0 }}] | |||
Sval mapping generators: ~17/12, ~3, ~56/25 | |||
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 702.3471, ~28/25 = 193.6499 | |||
Optimal GPV sequence: {{Val list| 12, 30d, 38d, 50, 62, 68, 106d, 118, 248g, 316g }} | |||
Badness: 1.095 | |||
==== 2.3.5.7.17.19 subgroup ==== | |||
Subgroup: 2.3.5.7.17.19 | |||
Comma list: 289/288, 361/360, 476/475 | |||
Mapping: [{{val| 2 0 0 -6 5 3 }}, {{val| 0 1 0 0 1 1 }}, {{val| 0 0 2 5 0 1 }}] | |||
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 702.509, ~28/25 = 193.669 | |||
Optimal GPV sequence: {{Val list| 12, …, 50, 68, 106d, 118, 248g, 316g }} | |||
Badness: 0.569 | |||
== Belobog == | == Belobog == | ||