Alphaxenic rank three clan: Difference between revisions
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These are rank-3 temperaments that temper out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} = 131769/131072, but we can begin with the rank-4 temperament. | These are rank-3 temperaments that temper out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} = 131769/131072, but we can begin with the rank-4 temperament. | ||
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= Betarabian = | == 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. | 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. | ||
Revision as of 19:21, 3 June 2021
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Todo: expand Wedgie and Badness information missing |
These are 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.
Comma: 131769/131072
POTE generators: ~11/8 = 549.3316 or ~33/32 = 50.6784, ~5/4 = 385.5751, ~7/4 = 967.9328
Map: [<2 1 0 0 8|, <0 2 0 0 -1|, <0 0 1 0 0|, <0 0 0 1 0|]
Wedgie:
EDOs: 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de
Badness:
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.
Commas: 243/242, 131769/131072
POTE generators: ~5/4 = 385.0647, ~7/4 = 967.3158
Map: [<24 38 0 0 83|, <0 0 1 0 0|, <0 0 0 1 0|]
Wedgie:
Badness: