Rastmic rank three clan: 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 |
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[[POTE generator]]s: ~128/105 = 350.1375, ~5/4 = 383.8665 | [[POTE generator]]s: ~128/105 = 350.1375, ~5/4 = 383.8665 | ||
{{ | {{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d }} | ||
[[Badness]]: 0.770 × 10<sup>-3</sup> | [[Badness]]: 0.770 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~11/9 = 349.9554, ~5/4 = 384.1048 | [[POTE generator]]s: ~11/9 = 349.9554, ~5/4 = 384.1048 | ||
{{ | {{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }} | ||
[[Badness]]: 0.641 × 10<sup>-3</sup> | [[Badness]]: 0.641 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~896/729 = 351.4846, ~5/4 = 386.9396 | [[POTE generator]]s: ~896/729 = 351.4846, ~5/4 = 386.9396 | ||
{{ | {{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }} | ||
[[Badness]]: 0.607 × 10<sup>-3</sup> | [[Badness]]: 0.607 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~11/9 = 351.5347, ~5/4 = 388.0217 | [[POTE generator]]s: ~11/9 = 351.5347, ~5/4 = 388.0217 | ||
{{ | {{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} * | ||
<nowiki>*</nowiki> [[optimal patent val]]: [[123edo|123]] | <nowiki>*</nowiki> [[optimal patent val]]: [[123edo|123]] | ||
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POTE generators: ~11/9 = 351.6908, ~5/4 = 389.1892 | POTE generators: ~11/9 = 351.6908, ~5/4 = 389.1892 | ||
{{Optimal ET sequence|legend=1| 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 18:26, 7 May 2023
The rastmic rank-3 clan of temperaments tempers out the rastma, 243/242. Both no-5 rastmic and no-7 rastmic can be the head of this clan. 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-3 family
- Mandos, {176/175, 243/242} → Valinorsmic temperaments
- Spectacle, {225/224, 243/242} → Marvel family
- Mirage, {225/224, 243/242, 385/384} → Marvel family
- Jove, {243/242, 441/440} → Breed family
- Hagrid, {243/242, 9801/9800} → Cataharry family
- Betarabian, {243/242, 131769/131072} → Alpharabian rank-3 clan
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]]
Mapping generators: ~2, ~128/105, ~5
POTE generators: ~128/105 = 350.1375, ~5/4 = 383.8665
Optimal ET sequence: 17, 21, 24, 31, 41, 72, 281d
Badness: 0.770 × 10-3
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]]
POTE generators: ~11/9 = 349.9554, ~5/4 = 384.1048
Optimal ET sequence: 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde
Badness: 0.641 × 10-3
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]]
Mapping generators: ~2, ~896/729, ~5
POTE generators: ~896/729 = 351.4846, ~5/4 = 386.9396
Optimal ET sequence: 17c, 24, 34d, 41, 58, 99, 239, 338
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]]
POTE generators: ~11/9 = 351.5347, ~5/4 = 388.0217
Optimal ET sequence: 17c, 24, 34d, 41, 58, 99e *
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]]
POTE generators: ~11/9 = 351.6908, ~5/4 = 389.1892
Optimal ET sequence: 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff
Badness: 1.19366 × 10-3