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: @@
-This is a collection of 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.
+{{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.
-== Alpharabian ==
+Temperaments discussed elsewhere include:
-: ''Not to be confused with [[Alpharabian tuning]].''
+* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
+* ''[[Rabic]]'' (+243/242) → [[Rastmic rank-3 clan #Rabic|Rastmic rank-3 clan]]
-Subgroup: 2.3.5.7.11
+[[Category:Temperament clans]]
+[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
-[[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 collection]]
-[[Category:Alpharabian temperaments| ]] <!-- 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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