Aberschismic temperaments: Difference between revisions
m Status update |
→Ketchup: replace 19- and 23-limit with no-19 23-limit, which is more natural |
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== Ketchup == | == Ketchup == | ||
Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its ploidacot is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament. | Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its [[ploidacot]] is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: 289/288, 325/324, 352/351, 385/384, | Comma list: 289/288, 325/324, 352/351, 385/384, 442/441 | ||
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }} | Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }} | ||
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Badness (Sintel): 0.845 | Badness (Sintel): 0.845 | ||
=== | === 2.3.5.7.11.13.17.23 subgroup === | ||
Subgroup: 2.3.5.7.11.13.17. | Subgroup: 2.3.5.7.11.13.17.23 | ||
Comma list: | Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390 | ||
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 | Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~17/12 = 600. | * WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}} | ||
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25. | * CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}} | ||
{{Optimal ET sequence|legend=0| 46, 94, | {{Optimal ET sequence|legend=0| 46, 94, 140 }} | ||
Badness (Sintel): | Badness (Sintel): 0.772 | ||
== Undecental == | == Undecental == | ||