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.  This temperament is named as such because tempering out both the Alpharabian comma and the rastma automatically tempers out the [[Betarabian comma]].
 
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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