Alphaxenic rank-3 clan: Difference between revisions

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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.  
{{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.  


Temperaments discussed elsewhere include:  
Temperaments discussed elsewhere include:  
* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
 
* ''[[Rabic]]'' (+243/242) → [[Rastmic rank-3 clan #Rabic|Rastmic rank-3 clan]]
== Alphaxenic ==
[[Subgroup]]: 2.3.5.7.11
 
[[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]]: 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 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
 
{{Multival|legend=1|rank=3| 0 0 0 24 0 0 38 0 0 83 }}
 
[[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]]: 6.07 × 10<sup>-3</sup>


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
[[Category:Alphaxenic| ]] <!-- key article -->
[[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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