Hemimage temperaments: Difference between revisions
Undo. Fractional subgroup temps have their own page already Tag: Undo |
→Degrees: add pretty obvious 17- and 19-limit extensions. the badness here is inconsistent/potentially wrong w.r.t fumica's default badness so i chose to add dirichlet badness. also 20cde is important as an archetype |
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[[Optimal tuning]] ([[POTE]]): ~28/27 = 1\20, ~3/2 = 703.015 | [[Optimal tuning]] ([[POTE]]): ~28/27 = 1\20, ~3/2 = 703.015 | ||
{{Optimal ET sequence|legend=1| 60, 80, 140, 640b, 780b | {{Optimal ET sequence|legend=1| 20cd, 60, 80, 140, 640b, 780b }} | ||
[[Badness]]: 0.106471 | [[Badness]]: 0.106471 | ||
Badness (Dirichlet): 2.694 | |||
=== 11-limit === | === 11-limit === | ||
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Optimal tuning (POTE): ~28/27 = 1\20, ~3/2 = 703.231 | Optimal tuning (POTE): ~28/27 = 1\20, ~3/2 = 703.231 | ||
{{Optimal ET sequence|legend=1| 60e, 80, 140, 360 | {{Optimal ET sequence|legend=1| 20cd, 60e, 80, 140, 360 }} | ||
Badness: 0.046770 | Badness: 0.046770 | ||
Badness (Dirichlet): 1.546 | |||
=== 13-limit === | === 13-limit === | ||
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Optimal tuning (POTE): ~28/27 = 1\20, ~3/2 = 703.080 | Optimal tuning (POTE): ~28/27 = 1\20, ~3/2 = 703.080 | ||
{{Optimal ET sequence|legend=1| 60e, 80, 140 | {{Optimal ET sequence|legend=1| 20cde, 60e, 80, 140 }} | ||
Badness: 0.032718 | Badness: 0.032718 | ||
Badness (Dirichlet): 1.352 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 325/324, 352/351, 1001/1000, 1331/1323, 289/288 | |||
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 | 0 1 2 3 3 0 1 }} | |||
Optimal tuning (CTE): ~28/27 = 1\20, ~3/2 = 703.107 | |||
{{Optimal ET sequence|legend=1| 20cde, 60e, 80, 140 }} | |||
Badness (Dirichlet): 1.171 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 325/324, 352/351, 1001/1000, 1331/1323, 289/288, 400/399 | |||
Mapping: {{mapping| 20 0 -17 -39 -26 74 50 85 | 0 1 2 3 3 0 1 0 }} | |||
Optimal tuning (CTE): ~28/27 = 1\20, ~3/2 = 703.107 | |||
{{Optimal ET sequence|legend=1| 20cde, 60e, 80, 140 }} | |||
Badness (Dirichlet): 1.273 | |||
== Squarschmidt == | == Squarschmidt == | ||