Alphaxenic rank three clan: Difference between revisions

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The '''~~Alpharabian family~~''' ~~is built up from temperaments that temper~~ out the [[Alpharabian comma]]. ~~Among~~ the ~~members~~ of this ~~family are Quasiquarter and Betarabian~~.

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.

~~== Alpharabian ==~~

Temperaments discussed elsewhere include:

* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]

~~The~~ 11~~-limit parent comma for the quartismic family is the the Alpharabian comma.~~

== Alphaxenic ==

[[Subgroup]]: 2.3.5.7.11

Comma: 131769/131072

[[Comma list]]: 131769/131072

~~POTE:~~

{{Mapping|legend=1| 2 1 0 0 8 | 0 2 0 0 -1 | 0 0 1 0 0 | 0 0 0 1 0 }}

~~Map~~:

: mapping generators: ~363/256, ~16/11, ~5, ~7

~~Wedgie~~:

[[Optimal tuning]] ([[POTE]]): ~363/256 = 1\2, ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328

~~EDOs:~~

{{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}

Badness:

[[Badness]]: 1.26 × 10<sup>-6</sup>

== ~~Betarabian~~ ==

== 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]].

~~Whenever the~~ [[~~243/242|rastma~~]] ~~is added to the list of commas tempered out among Alphrabian temperaments, you end up with a variant of this temperament subfamily~~.

[[Subgroup]]: 2.3.5.7.11

Comma: 131769/131072~~, 243/242~~

[[Comma list]]: 243/242, 131769/131072

~~POTE:~~

~~Map~~:

: mapping generators: ~33/32, ~5, ~7

~~Wedgie~~:

[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158

~~EDOs:~~

{{Optimal ET sequence|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }}

Badness:

[[Badness]]: 6.07 × 10<sup>-3</sup>

[[Category:~~Alpharabian~~]]

[[Category:Temperament clans]]

[[Category:Pages with mostly numerical content]]

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

[[Category:Alphaxenic| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-The '''Alpharabian family''' is built up from temperaments that temper out the [[Alpharabian comma]]. Among the members of this family are Quasiquarter and Betarabian.
+{{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.
-== Alpharabian ==
+Temperaments discussed elsewhere include:
+* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
-The 11-limit parent comma for the quartismic family is the the Alpharabian comma.
+== Alphaxenic ==
+[[Subgroup]]: 2.3.5.7.11
-Comma: 131769/131072
+[[Comma list]]: 131769/131072
-POTE:
+{{Mapping|legend=1| 2 1 0 0 8 | 0 2 0 0 -1 | 0 0 1 0 0 | 0 0 0 1 0 }}
-Map:
+: mapping generators: ~363/256, ~16/11, ~5, ~7
-Wedgie:
+[[Optimal tuning]] ([[POTE]]): ~363/256 = 1\2, ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328
-EDOs:
+{{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}
-Badness:
+[[Badness]]: 1.26 × 10<sup>-6</sup>
-== Betarabian ==
+== 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]].
-Whenever the [[243/242|rastma]] is added to the list of commas tempered out among Alphrabian temperaments, you end up with a variant of this temperament subfamily.
+[[Subgroup]]: 2.3.5.7.11
-Comma: 131769/131072, 243/242
+[[Comma list]]: 243/242, 131769/131072
-POTE:
+{{Mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }}
-Map:
+: mapping generators: ~33/32, ~5, ~7
-Wedgie:
+[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158
-EDOs:
+{{Optimal ET sequence|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }}
-Badness:
+[[Badness]]: 6.07 × 10<sup>-3</sup>
-[[Category:Alpharabian]]
+[[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
+[[Category:Alphaxenic| ]] <!-- key article -->
+[[Category:Rank 3]]