Alphaxenic rank-3 clan: Difference between revisions

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{{Technical data page}}
The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out|tempers out]] the [[Alpharabian comma]] ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072). Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan.


These are rank-3 temperaments that temper out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} = 131769/131072, but we can begin with the rank-4 temperament.
Temperaments discussed elsewhere include:
* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
* ''[[Rabic]]'' (+243/242) → [[Rastmic rank-3 clan #Rabic|Rastmic rank-3 clan]]


Comma: 131769/131072
[[Category:Temperament clans]]
 
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
POTE generators: ~11/8 = 549.3316 or ~33/32 = 50.6784, ~5/4 = 385.5751, ~7/4 = 967.9328
 
Map: [<2 1 0 0 8|, <0 2 0 0 -1|, <0 0 1 0 0|, <0 0 0 1 0|]
 
Wedgie:
 
EDOs: {{EDOs| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }}
 
Badness:
 
= 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.
 
Commas: 243/242, 131769/131072
 
POTE generators: ~5/4 = 385.0647, ~7/4 = 967.3158
 
Map: [<24 38 0 0 83|, <0 0 1 0 0|, <0 0 0 1 0|]
 
Wedgie:
 
EDOs: {{EDOs| 24, 48, 72, 264 }}
 
Badness:
 
[[Category:Theory]]
[[Category:Temperament]]
[[Category:Alpharabian]]
[[Category:Rank 3]]
[[Category:Rank 3]]

Latest revision as of 11:12, 15 May 2026

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 (monzo: [-17 2 0 0 4⟩, ratio: 131769/131072). Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan.

Temperaments discussed elsewhere include:

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