Dimcomp family: Difference between revisions
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The '''dimcomp family''' of rank-3 | {{Technical data page}} | ||
The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962. | |||
== Dimcomp | == Dimcomp == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: [[390625/388962]] | [[Comma list]]: [[390625/388962]] | ||
{{Mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }} | |||
: mapping generators: ~25/21, ~3, ~5 | |||
{{Optimal ET sequence|legend=1| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }} | {{Optimal ET sequence|legend=1| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }} | ||
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[[Badness]]: 0.783 × 10<sup>-3</sup> | [[Badness]]: 0.783 × 10<sup>-3</sup> | ||
== Undecimal dimcomp | == Undecimal dimcomp == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 1375/1372, 6250/6237 | [[Comma list]]: 1375/1372, 6250/6237 | ||
{{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }} | |||
{{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }} | {{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }} | ||
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[[Badness]]: 0.624 × 10<sup>-3</sup> | [[Badness]]: 0.624 × 10<sup>-3</sup> | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 625/624, 1375/1372, 2080/2079 | Comma list: 625/624, 1375/1372, 2080/2079 | ||
Mapping: | Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }} | ||
{{Optimal ET sequence|legend=1| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }} | {{Optimal ET sequence|legend=1| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }} | ||
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Badness: 0.820 × 10<sup>-3</sup> | Badness: 0.820 × 10<sup>-3</sup> | ||
== Octopod | == Octopod == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 540/539, 1375/1372, 4000/3993 | Comma list: 540/539, 1375/1372, 4000/3993 | ||
Mapping: | Mapping: {{mapping| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }} | ||
{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }} | {{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Dimcomp]] | [[Category:Pages with mostly numerical content]] | ||
[[Category:Dimcomp family| ]] <!-- main article --> | |||
[[Category:Dimcomp| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 00:31, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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]]
- mapping generators: ~25/21, ~3, ~5
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