Alphaxenic rank three clan: Difference between revisions
No edit summary |
m Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content" |
||
| (23 intermediate revisions by 7 users not shown) | |||
| Line 1: | Line 1: | ||
The ''' | {{Technical data page}} | ||
The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out|tempers out]] the [[Alpharabian comma]], {{monzo| -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 #Uniwiz|Keenanismic temperaments]] | |||
== Alphaxenic == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
Comma: 131769/131072 | [[Comma list]]: 131769/131072 | ||
{{Mapping|legend=1| 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|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }} | |||
Badness: | [[Badness]]: 1.26 × 10<sup>-6</sup> | ||
== | == 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: 131769/131072 | [[Comma list]]: 243/242, 131769/131072 | ||
{{Mapping|legend=1| 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|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }} | |||
Badness: | [[Badness]]: 6.07 × 10<sup>-3</sup> | ||
[[Category: | [[Category:Temperament clans]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article --> | |||
[[Category:Alphaxenic| ]] <!-- key article --> | |||
[[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