Breedsmic temperaments: Difference between revisions
m →Amicable: correction |
→Hemififths: +quadrafifths |
||
| Line 44: | Line 44: | ||
[[Algebraic generator]]: (2 + sqrt(2))/2 | [[Algebraic generator]]: (2 + sqrt(2))/2 | ||
{{Val list|legend=1| 41, 58, 99, 239, 338 | {{Val list|legend=1| 41, 58, 99, 239, 338 }} | ||
[[Badness]]: 0.022243 | [[Badness]]: 0.022243 | ||
| Line 70: | Line 70: | ||
POTE generator: ~11/9 = 351.573 | POTE generator: ~11/9 = 351.573 | ||
Vals: {{Val list| 17c, 41, 58, 99ef }} | Vals: {{Val list| 17c, 41, 58, 99ef, 157eff }} | ||
Badness: 0.019090 | Badness: 0.019090 | ||
| Line 77: | Line 77: | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 2401/2400, 3388/3375, | Comma list: 2401/2400, 3388/3375, 5120/5103 | ||
Mapping: [{{val| 2 0 -35 -15 -47 }}, {{val| 0 2 25 13 34 }}] | Mapping: [{{val| 2 0 -35 -15 -47 }}, {{val| 0 2 25 13 34 }}] | ||
| Line 83: | Line 83: | ||
POTE generator: ~49/40 = 351.505 | POTE generator: ~49/40 = 351.505 | ||
Vals: {{Val list| 58, 140, 198 | Vals: {{Val list| 58, 140, 198 }} | ||
Badness: 0.042487 | Badness: 0.042487 | ||
| Line 96: | Line 96: | ||
POTE generator: ~49/40 = 351.502 | POTE generator: ~49/40 = 351.502 | ||
Vals: {{Val list| 58, 140, 198, 536f | Vals: {{Val list| 58, 140, 198, 536f }} | ||
Badness: 0.021188 | Badness: 0.021188 | ||
=== Quadrafifths === | |||
This has been logged as ''semihemififths'' in Graham Breed's temperament finder, but ''quadrafifths'' arguably makes more sense. | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 2401/2400, 3025/3024, 5120/5103 | |||
Mapping: [{{val| 1 1 -5 -1 8 }}, {{val| 0 4 50 26 -31 }}] | |||
POTE generator: ~243/220 = 175.7378 | |||
Vals: {{Val list| 41, 157, 198, 239, 676b, 915be }} | |||
Badness: 0.0401 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 847/845, 2401/2400, 3025/3024 | |||
Mapping: [{{val| 1 1 -5 -1 8 10 }}, {{val| 0 4 50 26 -31 -43 }}] | |||
POTE generator: ~72/65 = 175.7470 | |||
Vals: {{Val list| 41, 157, 198, 437f, 635bcff }} | |||
Badness: 0.0311 | |||
== Tertiaseptal == | == Tertiaseptal == | ||