Alphaxenic rank three clan: Difference between revisions

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m FloraC moved page Alpharabian family to Alpharabian temperaments without leaving a redirect: In accordance to other temperament pages
Rewriting; categories; temperament info (will add wedgies and badnesses later)
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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 Betarabian and Quasiquarter.  There are technically others, however, these others have yet to be named.
{{todo| expand | inline=1 }}


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


Comma: 131769/131072
Comma: 131769/131072


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


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


Wedgie:  
Wedgie:  


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


Badness:
Badness:


== Betarabian ==
= Betarabian =


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.
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.


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


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


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


Wedgie:  
Wedgie:  


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


Badness:
Badness:


[[Category:Theory]]
[[Category:Temperament]]
[[Category:Alpharabian]]
[[Category:Alpharabian]]
[[Category:Rank 3]]

Revision as of 08:30, 2 December 2020

Todo: expand

These are rank-3 temperaments that temper out the Alpharabian comma, [-17 2 0 0 4⟩ = 131769/131072, but we can begin with the rank-4 temperament.

Comma: 131769/131072

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

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

Wedgie:

EDOs: 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de

Badness:

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.

Commas: 243/242, 131769/131072

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

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

Wedgie:

EDOs: 24, 48, 72, 264

Badness:

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