Alphaxenic rank three clan: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
m FloraC moved page Alpharabian rank three clan to Alphaxenic rank three clan: We agreed the corresponding temperament of the Alpharabian comma shouldn't be "alpharabian" |
(No difference)
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Revision as of 06:40, 17 June 2023
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
Optimal ET sequence: 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee
Badness: 1.26 × 10-6
Rabic
Whenever the rastma is added to the list of commas tempered out among Alpharabian temperaments, you end up with Rabic, 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.
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
Optimal ET sequence: 24, 48, 72, 264, 336b, 408b, 480bcde
Badness: 6.07 × 10-3