Rastmic rank three clan: Difference between revisions
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== Parahemif == | == Parahemif == | ||
=== 7-limit === | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 1605632/1594323 | |||
[[Mapping]]: [{{val| 1 1 0 -1 }}, {{val| 0 2 0 13 }}, {{val| 0 0 1 0 }}] | |||
{{Val list|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }} | |||
[[Badness]]: 0.607 × 10<sup>-3</sup> | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Mapping]]: [{{val| 1 1 0 -1 2 }}, {{val| 0 2 0 13 5 }}, {{val| 0 0 1 0 0 }}] | [[Mapping]]: [{{val| 1 1 0 -1 2 }}, {{val| 0 2 0 13 5 }}, {{val| 0 0 1 0 0 }}] | ||
{{Val list|legend=1| | {{Val list|legend=1| 17c, 24, 34d, 41, 58, 99e }} * | ||
<nowiki>*</nowiki> [[optimal patent val]]: [[123edo|123]] | |||
[[Badness]]: 1.34547 × 10<sup>-3</sup> | [[Badness]]: 1.34547 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 1 1 0 -1 2 4 }}, {{val| 0 2 0 13 5 -1 }}, {{val| 0 0 1 0 0 0 }}] | Mapping: [{{val| 1 1 0 -1 2 4 }}, {{val| 0 2 0 13 5 -1 }}, {{val| 0 0 1 0 0 0 }}] | ||
Vals: {{Val list| | Vals: {{Val list| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }} | ||
Badness: 1.19366 × 10<sup>-3</sup> | Badness: 1.19366 × 10<sup>-3</sup> | ||
Revision as of 08:21, 27 August 2021
This is a miscellaneous collection of rank-3 rastmic temperaments, tempering out the rastma, 243/242. These temperaments divide the fifth in half and use it as an 11/9 neutral third.
Temperaments not listed include:
- Urania, {81/80, 121/120} → Didymus rank three family #Urania
- Mandos, {176/175, 243/242} → Valinorismic temperaments #Mandos
- Spectacle, {225/224, 243/242} → Marvel family #Spectacle
- Mirage, {225/224, 243/242, 385/384} → Marvel family #Mirage
- Jove, {243/242, 441/440} → Breed family #Jove
- Hagrid, {243/242, 9801/9800} → Cataharry family #Hagrid
Mirwomo
The mirwomo temperament tunes ~36/35 to exactly half of an apotome ~2187/2048, and tunes ~128/105 to exactly half of a perfect fifth ~3/2.
7-limit
Subgroup: 2.3.5.7
Comma list: 33075/32768
Mapping: [⟨1 1 0 6], ⟨0 2 0 -3], ⟨0 0 1 -1]]
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384
Mapping: [⟨1 1 0 6 2], ⟨0 2 0 -3 5], ⟨0 0 1 -1 0]]
Parahemif
7-limit
Subgroup: 2.3.5.7
Comma list: 1605632/1594323
Mapping: [⟨1 1 0 -1], ⟨0 2 0 13], ⟨0 0 1 0]]
Badness: 0.607 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 896/891
Mapping: [⟨1 1 0 -1 2], ⟨0 2 0 13 5], ⟨0 0 1 0 0]]
Badness: 1.34547 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 243/242, 364/363
Mapping: [⟨1 1 0 -1 2 4], ⟨0 2 0 13 5 -1], ⟨0 0 1 0 0 0]]
Vals: Template:Val list
Badness: 1.19366 × 10-3