Alphaxenic rank three clan: Difference between revisions

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{{~~todo~~| ~~expand | comment= ''Wedgie'' and ''Badness'' information missing | inline=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.

~~These are 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~~.

== Alpharabian ==

: ''Not to be confused with [[Alpharabian tuning]].''

~~Comma~~: ~~131769/131072~~

Subgroup: 2.3.5.7.11

~~POTE generators~~: ~~~11~~/~~8 = 549.3316 or ~33/32 = 50.6784, ~5/4 = 385.5751, ~7/4 = 967.9328~~

[[Comma list]]: 131769/131072

~~Map~~: [<2 1 0 0 8|~~, <~~0 2 0 0 -1|~~, <~~0 0 1 0 0|~~, <~~0 0 0 1 0|]

[[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 }}]

~~Wedgie~~:

[[POTE generator]]s: ~11/8 = 549.3316, ~5/4 = 385.5751, ~7/4 = 967.9328

~~EDOs:~~ {{~~EDOs~~| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }}

{{Val list|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 ==

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.

~~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

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

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

~~POTE generators~~: ~~~5/4 = 385.0647~~, ~~~7/4 = 967.3158~~

[[Mapping]]: [{{val| 24 38 0 0 83 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}]

~~Map~~: ~~[<24 38 0 0 83|~~, ~~<0 0 1 0 0|~~, ~~<0 0 0 1 0|]~~

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

~~Wedgie:~~

~~EDOs~~: ~~{{EDOs| 24~~, ~~48, 72, 264 }}~~

[[POTE generator]]s: ~5/4 = 385.0647, ~7/4 = 967.3158

~~Badness:~~

[[Category:~~Theory~~]]

[[Badness]]: 6.07 × 10<sup>-3</sup>

[[Category:Temperament]]

[[Category:Alpharabian]]

[[Category:Regular temperament theory]]

[[Category:Temperament collection]]

[[Category:Alpharabian temperaments| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-{{todo| expand | comment= ''Wedgie'' and ''Badness'' information missing | inline=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.
-These are 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.
+== Alpharabian ==
+: ''Not to be confused with [[Alpharabian tuning]].''
-Comma: 131769/131072
+Subgroup: 2.3.5.7.11
-POTE generators: ~11/8 = 549.3316 or ~33/32 = 50.6784, ~5/4 = 385.5751, ~7/4 = 967.9328
+[[Comma list]]: 131769/131072
-Map: [<2 1 0 0 8|, <0 2 0 0 -1|, <0 0 1 0 0|, <0 0 0 1 0|]
+[[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 }}]
-Wedgie:
+[[POTE generator]]s: ~11/8 = 549.3316, ~5/4 = 385.5751, ~7/4 = 967.9328
-EDOs: {{EDOs| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }}
+{{Val list|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 ==
+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.
-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
-Commas: 243/242, 131769/131072
+[[Comma list]]: 243/242, 131769/131072
-POTE generators: ~5/4 = 385.0647, ~7/4 = 967.3158
+[[Mapping]]: [{{val| 24 38 0 0 83 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}]
-Map: [<24 38 0 0 83|, <0 0 1 0 0|, <0 0 0 1 0|]
+Mapping generators: ~33/32, ~5, ~7
-Wedgie:
+{{Multival|legend=1|rank=3| 0 0 0 24 0 0 38 0 0 83 }}
-EDOs: {{EDOs| 24, 48, 72, 264 }}
+[[POTE generator]]s: ~5/4 = 385.0647, ~7/4 = 967.3158
-Badness:
+{{Val list|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }}
-[[Category:Theory]]
+[[Badness]]: 6.07 × 10<sup>-3</sup>
-[[Category:Temperament]]
-[[Category:Alpharabian]]
+[[Category:Regular temperament theory]]
+[[Category:Temperament collection]]
+[[Category:Alpharabian temperaments| ]] <!-- main article -->
 [[Category:Rank 3]]