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| 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.
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| | 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. |
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| == 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]] |
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| Subgroup: 2.3.5.7.11
| | [[Category:Temperament clans]] |
| | | [[Category:Alphaxenic rank-3 clan| ]] <!-- main article --> |
| [[Comma list]]: 131769/131072 | |
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| [[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 }}]
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| Mapping generators: ~363/256, ~16/11, ~5, ~7
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| [[POTE generator]]s: ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328 | |
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| {{Val list|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}
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| [[Badness]]: 1.26 × 10<sup>-6</sup>
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| == Betarabian ==
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| 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.
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| Subgroup: 2.3.5.7.11
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| [[Comma list]]: 243/242, 131769/131072
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| [[Mapping]]: [{{val| 24 38 0 0 83 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}]
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| Mapping generators: ~33/32, ~5, ~7
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| {{Multival|legend=1|rank=3| 0 0 0 24 0 0 38 0 0 83 }}
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| [[POTE generator]]s: ~5/4 = 385.0647, ~7/4 = 967.3158
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| {{Val list|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }}
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| [[Badness]]: 6.07 × 10<sup>-3</sup>
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| [[Category:Regular temperament theory]]
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| [[Category:Temperament collections]]
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| [[Category:Alpharabian temperaments| ]] <!-- main article -->
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| [[Category:Rank 3]] | | [[Category:Rank 3]] |