Alphaxenic rank three clan: Difference between revisions
m Correction +1 |
m Moving from Category:Temperament collection to Category:Temperament collections using Cat-a-lot |
||
| Line 38: | Line 38: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament | [[Category:Temperament collections]] | ||
[[Category:Alpharabian temperaments| ]] <!-- main article --> | [[Category:Alpharabian temperaments| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 17:08, 28 February 2022
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 = 650.6784, ~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