Alphaxenic rank three clan: Difference between revisions
m {{Technical data page}} |
m Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content" |
||
| (One intermediate revision by one other user not shown) | |||
| Line 30: | Line 30: | ||
: mapping generators: ~33/32, ~5, ~7 | : mapping generators: ~33/32, ~5, ~7 | ||
[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158 | [[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158 | ||
| Line 40: | Line 38: | ||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article --> | [[Category:Alphaxenic rank-3 clan| ]] <!-- main article --> | ||
[[Category:Alphaxenic| ]] <!-- key article --> | [[Category:Alphaxenic| ]] <!-- key article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 00:31, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The alphaxenic rank-3 clan of temperaments tempers out the Alpharabian comma, [-17 2 0 0 4⟩ = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.
Temperaments discussed elsewhere include:
- Uniwiz (+385/384) → Keenanismic temperaments
Alphaxenic
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
Optimal tuning (POTE): ~363/256 = 1\2, ~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 alphaxenic 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
Optimal tuning (POTE): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158
Optimal ET sequence: 24, 48, 72, 264, 336b, 408b, 480bcde
Badness: 6.07 × 10-3