Alphaxenic rank-3 clan: Difference between revisions

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:

Uniwiz (+385/384) → Keenanismic temperaments
Rabic (+243/242) → Rastmic rank-3 clan

@@ Line 1: / Line 1: @@
-The '''alpharabian rank-3 clan''' of temperaments tempers out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} = 131769/131072. Both no-5 alpharabian and no-7 alpharabian 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:
-* [[Uniwiz]], {385/384, 9801/9800} → [[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]]
-== Alpharabian ==
-: ''Not to be confused with [[Alpharabian tuning]].''
-Subgroup: 2.3.5.7.11
-[[Comma list]]: 131769/131072
-[[Mapping]]: [{{val| 2 1 0 0 8 }}, {{val| 0 2 0 0 -1 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}]
-Mapping generators: ~363/256, ~16/11, ~5, ~7
-[[POTE generator]]s: ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328
-{{Val list|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>
-== 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]]: [{{val| 24 38 0 0 83 }}, {{val| 0 0 1 0 0 }}, {{val| 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 }}
-[[POTE generator]]s: ~5/4 = 385.0647, ~7/4 = 967.3158
-{{Val list|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }}
-[[Badness]]: 6.07 × 10<sup>-3</sup>
-[[Category:Regular temperament theory]]
 [[Category:Temperament clans]]
-[[Category:Alpharabian rank-3 clan| ]] <!-- main article -->
+[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
 [[Category:Rank 3]]

Alphaxenic rank-3 clan: Difference between revisions

Latest revision as of 11:12, 15 May 2026

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