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~~.

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) → [[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~~

~~[[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:Pages with mostly numerical content]]~~

[[Category:Alphaxenic rank-3 clan| ]]

~~[[Category:Alphaxenic| ]] ~~

[[Category:Rank 3]]

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 {{Technical data page}}
-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.
+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) → [[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
-[[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:Pages with mostly numerical content]]
 [[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
-[[Category:Alphaxenic| ]] <!-- key article -->
 [[Category:Rank 3]]