Catalog of rank-4 temperaments: Difference between revisions
m Cleanup (2/2) |
+ancient from keenanismic family, +comma list for each temp |
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== Werckismic (441/440) == | == Werckismic (441/440) == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 441/440 | |||
[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}] | [[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}] | ||
| Line 10: | Line 12: | ||
=== Commas 364/363, 441/440 === | === Commas 364/363, 441/440 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 364/363, 441/440 | |||
[[Mapping]]: [{{val| 1 0 0 0 -3 -8 }}, {{val| 0 1 0 0 2 5 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 2 3 }}] | [[Mapping]]: [{{val| 1 0 0 0 -3 -8 }}, {{val| 0 1 0 0 2 5 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 2 3 }}] | ||
| Line 32: | Line 36: | ||
=== Commas 351/350, 441/440 === | === Commas 351/350, 441/440 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 351/350, 441/440 | |||
[[Mapping]]: [{{val| 1 0 0 0 -3 1 }}, {{val| 0 1 0 0 2 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 2 1 }}] | [[Mapping]]: [{{val| 1 0 0 0 -3 1 }}, {{val| 0 1 0 0 2 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 2 1 }}] | ||
| Line 41: | Line 47: | ||
=== Commas 196/195, 352/351 === | === Commas 196/195, 352/351 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 196/195, 352/351 | |||
[[Mapping]]: [{{val| 1 0 0 0 -3 2 }}, {{val| 0 1 0 0 2 -1 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 2 2 }}] | [[Mapping]]: [{{val| 1 0 0 0 -3 2 }}, {{val| 0 1 0 0 2 -1 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 2 2 }}] | ||
| Line 50: | Line 58: | ||
=== Commas 441/440, 847/845 === | === Commas 441/440, 847/845 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 441/440, 847/845 | |||
[[Mapping]]: [{{val| 1 0 0 0 -3 -3 }}, {{val| 0 1 0 0 2 2 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 4 5 }}] | [[Mapping]]: [{{val| 1 0 0 0 -3 -3 }}, {{val| 0 1 0 0 2 2 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 4 5 }}] | ||
| Line 61: | Line 71: | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 385/384 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 -1 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 -1 }}] | ||
Generators: ~2, ~3, ~5, ~7 | Generators: ~2, ~3, ~5, ~7 | ||
[[Transpose]]: [2 3 5 7 385/35] | |||
[[Minimax tuning]]: | |||
* [[11-odd-limit]] | |||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}] | |||
: Eigenmonzos: 2, 3, 7/5, 11/5 | |||
{{Val list|legend=1| 15, 22, 31, 41, 46, 53, 72, 87, 94, 118 }} | {{Val list|legend=1| 15, 22, 31, 41, 46, 53, 72, 87, 94, 118 }} | ||
=== | [[Badness]]: 15.159 × 10<sup>-9</sup> | ||
=== Martwin === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 325/324, 385/384 | |||
Mapping: [{{val| 1 0 0 0 7 2 }}, {{val| 0 1 0 0 1 4 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 0 }}] | Mapping: [{{val| 1 0 0 0 7 2 }}, {{val| 0 1 0 0 1 4 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 0 }}] | ||
Generators: ~2, ~3, ~5, ~7 | Generators: ~2, ~3, ~5, ~7 | ||
[[Transpose]]: [2 3 5 7 385/35 324/25] | |||
Lattice basis: | Lattice basis: | ||
: 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247 | : 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Keenanismic family --> | ||
* [[13-odd-limit|13-]] and [[15-odd-limit]] | * [[13-odd-limit|13-]] and [[15-odd-limit]] | ||
: [{{val| 1 0 0 0 0 0 }}, {{val| 0 1 0 0 0 0 }}, {{val| 2/3 4/3 1/3 0 0 -1/3 }}, {{val| 19/6 -1/6 -1/6 1/2 -1/2 1/6 }}, {{val| 19/6 -1/6 -1/6 -1/2 1/2 1/6 }}, {{val| 2/3 4/3 -2/3 0 0 2/3 }}] | : [{{val| 1 0 0 0 0 0 }}, {{val| 0 1 0 0 0 0 }}, {{val| 2/3 4/3 1/3 0 0 -1/3 }}, {{val| 19/6 -1/6 -1/6 1/2 -1/2 1/6 }}, {{val| 19/6 -1/6 -1/6 -1/2 1/2 1/6 }}, {{val| 2/3 4/3 -2/3 0 0 2/3 }}] | ||
| Line 84: | Line 109: | ||
{{Val list|legend=1| 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253 }} | {{Val list|legend=1| 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253 }} | ||
[[Badness]]: 2.206 × 10<sup>-6</sup> | |||
=== Ancient === | |||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 385/384, 625/624 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 -4 }}, {{val| 0 1 0 0 1 -1 }}, {{val| 0 0 1 0 -1 4 }}, {{val| 0 0 0 1 -1 0 }}] | |||
[[Transpose]]: [2 3 5 7 385/35 625/48] | |||
{{Val list|legend=1| 6, 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190 }} | |||
[[Badness]]: 2.573 × 10<sup>-6</sup> | |||
=== Commas 351/350, 385/384 === | === Commas 351/350, 385/384 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 351/350, 385/384 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 1 }}, {{val| 0 1 0 0 1 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 -1 1 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 1 }}, {{val| 0 1 0 0 1 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 -1 1 }}] | ||
| Line 96: | Line 138: | ||
=== Commas 352/351, 385/384 === | === Commas 352/351, 385/384 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 352/351, 385/384 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 1 -2 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 -1 -1 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 1 -2 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 -1 -1 }}] | ||
| Line 105: | Line 149: | ||
=== Commas 364/363, 385/384 === | === Commas 364/363, 385/384 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 364/363, 385/384 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 1 3 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 -3 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 1 3 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 -3 }}] | ||
| Line 114: | Line 160: | ||
=== Commas 385/384, 847/845 === | === Commas 385/384, 847/845 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 385/384, 847/845 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 7 }}, {{val| 0 1 0 0 1 1 }}, {{val| 0 0 1 1 -2 -2 }}, {{val| 0 0 0 2 -2 -1 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 7 }}, {{val| 0 1 0 0 1 1 }}, {{val| 0 0 1 1 -2 -2 }}, {{val| 0 0 0 2 -2 -1 }}] | ||
| Line 123: | Line 171: | ||
== Swetismic (540/539) == | == Swetismic (540/539) == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 540/539 | |||
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 -2 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 -2 }}] | ||
| Line 132: | Line 182: | ||
=== Commas 540/539, 847/845 === | === Commas 540/539, 847/845 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 540/539, 847/845 | |||
[[Mapping]]: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 0 0 3 3 }}, {{val| 0 0 1 1 -1 -1 }}, {{val| 0 0 0 2 -4 -3 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 0 0 3 3 }}, {{val| 0 0 1 1 -1 -1 }}, {{val| 0 0 0 2 -4 -3 }}] | ||
| Line 141: | Line 193: | ||
=== Commas 540/539, 625/624 === | === Commas 540/539, 625/624 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 540/539, 625/624 | |||
[[Mapping]]: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 0 0 3 -1 }}, {{val| 0 0 1 0 1 4 }}, {{val| 0 0 0 1 -2 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 0 0 3 -1 }}, {{val| 0 0 1 0 1 4 }}, {{val| 0 0 0 1 -2 0 }}] | ||
| Line 150: | Line 204: | ||
=== Commas 540/539, 676/675 === | === Commas 540/539, 676/675 === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 540/539, 676/675 | |||
[[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}] | ||
| Line 159: | Line 215: | ||
== Lehmerismic (3025/3024) == | == Lehmerismic (3025/3024) == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024 | |||
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}] | ||
| Line 168: | Line 226: | ||
== Kalismic (9801/9800) == | == Kalismic (9801/9800) == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 9801/9800 | |||
[[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}] | [[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}] | ||
| Line 177: | Line 237: | ||
=== Commas 1716/1715, 2080/2079 === | === Commas 1716/1715, 2080/2079 === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 1716/1715, 2080/2079 | |||
[[Mapping]]: [{{val| 2 0 0 0 3 -7 }}, {{val| 0 1 0 0 -2 1 }}, {{val| 0 0 1 0 1 0 }}, {{val| 0 0 0 1 1 2 }}] | [[Mapping]]: [{{val| 2 0 0 0 3 -7 }}, {{val| 0 1 0 0 -2 1 }}, {{val| 0 0 1 0 1 0 }}, {{val| 0 0 0 1 1 2 }}] | ||