Rastmic rank-3 clan: Difference between revisions
→Parahemif: +7-limit and review edo lists |
+link to betarabian, +tuning data for mirwomo and parahemif |
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* [[Jove]], {243/242, 441/440} → [[Breed family #Jove]] | * [[Jove]], {243/242, 441/440} → [[Breed family #Jove]] | ||
* ''[[Hagrid]]'', {243/242, 9801/9800} → [[Cataharry family #Hagrid]] | * ''[[Hagrid]]'', {243/242, 9801/9800} → [[Cataharry family #Hagrid]] | ||
* ''[[Betarabian]]'', {243/242, 131769/131072} → [[Alpharabian temperaments #Betarabian]] | |||
== Mirwomo == | == Mirwomo == | ||
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[[Mapping]]: [{{val| 1 1 0 6 }}, {{val| 0 2 0 -3 }}, {{val| 0 0 1 -1 }}] | [[Mapping]]: [{{val| 1 1 0 6 }}, {{val| 0 2 0 -3 }}, {{val| 0 0 1 -1 }}] | ||
Mapping generators: ~2, ~128/105, ~5 | |||
[[POTE generator]]s: ~128/105 = 350.1375, ~5/4 = 383.8665 | |||
{{Val list|legend=1| 17, 21, 24, 31, 41, 72, 281d }} | {{Val list|legend=1| 17, 21, 24, 31, 41, 72, 281d }} | ||
[[Badness]]: 0.770 × 10<sup>-3</sup> | |||
=== 11-limit === | === 11-limit === | ||
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[[Mapping]]: [{{val| 1 1 0 6 2 }}, {{val| 0 2 0 -3 5 }}, {{val| 0 0 1 -1 0 }}] | [[Mapping]]: [{{val| 1 1 0 6 2 }}, {{val| 0 2 0 -3 5 }}, {{val| 0 0 1 -1 0 }}] | ||
[[POTE generator]]s: ~11/9 = 349.9554, ~5/4 = 384.1048 | |||
{{Val list|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }} | {{Val list|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }} | ||
[[Badness]]: 0.641 × 10<sup>-3</sup> | |||
== Parahemif == | == Parahemif == | ||
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[[Mapping]]: [{{val| 1 1 0 -1 }}, {{val| 0 2 0 13 }}, {{val| 0 0 1 0 }}] | [[Mapping]]: [{{val| 1 1 0 -1 }}, {{val| 0 2 0 13 }}, {{val| 0 0 1 0 }}] | ||
Mapping generators: ~2, ~896/729, ~5 | |||
[[POTE generator]]s: ~896/729 = 351.4846, ~5/4 = 386.9396 | |||
{{Val list|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }} | {{Val list|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }} | ||
| Line 48: | Line 63: | ||
[[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 }}] | ||
[[POTE generator]]s: ~11/9 = 351.5347, ~5/4 = 388.0217 | |||
{{Val list|legend=1| 17c, 24, 34d, 41, 58, 99e }} * | {{Val list|legend=1| 17c, 24, 34d, 41, 58, 99e }} * | ||
| Line 61: | Line 78: | ||
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 }}] | ||
POTE generators: ~11/9 = 351.6908, ~5/4 = 389.1892 | |||
Vals: {{Val list| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }} | Vals: {{Val list| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }} | ||
Revision as of 12:30, 8 October 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
- Betarabian, {243/242, 131769/131072} → Alpharabian temperaments #Betarabian
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
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
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
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
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
Vals: Template:Val list
Badness: 1.19366 × 10-3