Dimcomp family: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
||
| Line 8: | Line 8: | ||
[[Mapping]]: [{{val| 4 0 0 -1 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 2 }}] | [[Mapping]]: [{{val| 4 0 0 -1 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 2 }}] | ||
{{ | {{Optimal ET sequence|legend=1| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }} | ||
[[Badness]]: 0.783 × 10<sup>-3</sup> | [[Badness]]: 0.783 × 10<sup>-3</sup> | ||
| Line 19: | Line 19: | ||
[[Mapping]]: [{{val| 4 0 0 -1 5 }}, {{val| 0 1 0 -1 -3 }}, {{val| 0 0 1 2 3 }}] | [[Mapping]]: [{{val| 4 0 0 -1 5 }}, {{val| 0 1 0 -1 -3 }}, {{val| 0 0 1 2 3 }}] | ||
{{ | {{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }} | ||
[[Badness]]: 0.624 × 10<sup>-3</sup> | [[Badness]]: 0.624 × 10<sup>-3</sup> | ||
| Line 30: | Line 30: | ||
Mapping: [{{val| 4 0 0 -1 5 -16 }}, {{val| 0 1 0 -1 -3 -1 }}, {{val| 0 0 1 2 3 4 }}] | Mapping: [{{val| 4 0 0 -1 5 -16 }}, {{val| 0 1 0 -1 -3 -1 }}, {{val| 0 0 1 2 3 4 }}] | ||
{{Optimal ET sequence|legend=1| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }} | |||
Badness: 0.820 × 10<sup>-3</sup> | Badness: 0.820 × 10<sup>-3</sup> | ||
| Line 41: | Line 41: | ||
Mapping: [{{val| 8 1 3 3 16 0 }}, {{val| 0 3 4 5 3 0 }}, {{val| 0 0 0 0 0 1 }}] | Mapping: [{{val| 8 1 3 3 16 0 }}, {{val| 0 3 4 5 3 0 }}, {{val| 0 0 0 0 0 1 }}] | ||
{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }} | |||
Badness: 1.244 × 10<sup>-3</sup> | Badness: 1.244 × 10<sup>-3</sup> | ||
Revision as of 18:08, 7 May 2023
The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, 390625/388962.
Dimcomp
Subgroup: 2.3.5.7
Mapping: [⟨4 0 0 -1], ⟨0 1 0 -1], ⟨0 0 1 2]]
Optimal ET sequence: 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952
Badness: 0.783 × 10-3
Undecimal dimcomp
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 6250/6237
Mapping: [⟨4 0 0 -1 5], ⟨0 1 0 -1 -3], ⟨0 0 1 2 3]]
Optimal ET sequence: 68, 72, 140, 152, 224, 364, 436, 588
Badness: 0.624 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1375/1372, 2080/2079
Mapping: [⟨4 0 0 -1 5 -16], ⟨0 1 0 -1 -3 -1], ⟨0 0 1 2 3 4]]
Optimal ET sequence: 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c
Badness: 0.820 × 10-3
Octopod
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 1375/1372, 4000/3993
Mapping: [⟨8 1 3 3 16 0], ⟨0 3 4 5 3 0], ⟨0 0 0 0 0 1]]
Optimal ET sequence: 72, 144, 152f, 224, 824d
Badness: 1.244 × 10-3