Alphaxenic rank-3 clan: Difference between revisions
m FloraC moved page Alpharabian temperaments to Alpharabian rank three clan: By definition |
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The '''alpharabian rank-3 clan''' of temperaments tempers out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} = 131769/131072. Both no-5 alpharabian and no-7 alpharabian can be the head of this clan, but we can begin with the rank-4 temperament. | |||
Temperaments discussed elsewhere include: | |||
* [[Uniwiz]], {385/384, 9801/9800} → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]] | |||
== Alpharabian == | == Alpharabian == | ||
Revision as of 09:42, 1 March 2022
The alpharabian rank-3 clan of temperaments tempers out the Alpharabian comma, [-17 2 0 0 4⟩ = 131769/131072. Both no-5 alpharabian and no-7 alpharabian can be the head of this clan, but we can begin with the rank-4 temperament.
Temperaments discussed elsewhere include:
- Uniwiz, {385/384, 9801/9800} → Keenanismic temperaments
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 = 650.6784, ~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