Alphaxenic rank three clan: Difference between revisions
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[[Mapping]]: [{{val| 2 1 0 0 8 }}, {{val| 0 2 0 0 -1 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}] | [[Mapping]]: [{{val| 2 1 0 0 8 }}, {{val| 0 2 0 0 -1 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}] | ||
[[POTE generator]]s: ~11 | Mapping generators: ~363/256, ~16/11, ~5, ~7 | ||
[[POTE generator]]s: ~16/11 = 650.6684, ~5/4 = 385.5751, ~7/4 = 967.9328 | |||
{{Val list|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }} | {{Val list|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }} | ||
Revision as of 12:21, 8 October 2021
This is a collection of rank-3 temperaments that temper out the Alpharabian comma, [-17 2 0 0 4⟩ = 131769/131072, but we can begin with the rank-4 temperament.
Alpharabian
- Not to be confused with Alpharabian tuning.
Subgroup: 2.3.5.7.11
Comma list: 131769/131072
Mapping: [⟨2 1 0 0 8], ⟨0 2 0 0 -1], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
Mapping generators: ~363/256, ~16/11, ~5, ~7
POTE generators: ~16/11 = 650.6684, ~5/4 = 385.5751, ~7/4 = 967.9328
Badness: 1.26 × 10-6
Betarabian
Whenever the rastma is added to the list of commas tempered out among Alpharabian temperaments, you end up with Betarabian, which splits the octave into 24 equal parts. This temperament is named as such because tempering out both the Alpharabian comma and the rastma automatically tempers out the Betarabian comma, and although there are technically other Betarabian temperaments, they have different names.
Subgroup: 2.3.5.7.11
Comma list: 243/242, 131769/131072
Mapping: [⟨24 38 0 0 83], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
Mapping generators: ~33/32, ~5, ~7
Wedgie: ⟨⟨⟨ 0 0 0 24 0 0 38 0 0 83 ]]]
POTE generators: ~5/4 = 385.0647, ~7/4 = 967.3158
Badness: 6.07 × 10-3