Xenharmonic Wiki

Alphaxenic rank three clan: Difference between revisions

← Older edit
VisualWikitext
Fredg999 category edits (talk | contribs)
autopatrolled, Bots
4,330 edits
 
(7 intermediate revisions by 5 users not shown)
Line 1: Line 1:
The '''alpharabian rank-3 clan''' of temperaments tempers out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} = 131769/131072. Both no-5 alpharabian and no-7 alpharabian can be the head of this clan, but we can begin with the rank-4 temperament.  
{{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.  


Temperaments discussed elsewhere include:  
Temperaments discussed elsewhere include:  
* [[Uniwiz]], {385/384, 9801/9800} → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]


== Alpharabian ==
== Alphaxenic ==
: ''Not to be confused with [[Alpharabian tuning]].''
[[Subgroup]]: 2.3.5.7.11
 
Subgroup: 2.3.5.7.11


[[Comma list]]: 131769/131072
[[Comma list]]: 131769/131072


[[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 }}]
{{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
: mapping generators: ~363/256, ~16/11, ~5, ~7


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


{{Val list|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}
{{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>
[[Badness]]: 1.26 × 10<sup>-6</sup>


== Betarabian ==
== Rabic ==
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 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
[[Subgroup]]: 2.3.5.7.11


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


[[Mapping]]: [{{val| 24 38 0 0 83 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0 }}]
{{Mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }}
 
Mapping generators: ~33/32, ~5, ~7


{{Multival|legend=1|rank=3| 0 0 0 24 0 0 38 0 0 83 }}
: mapping generators: ~33/32, ~5, ~7


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


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


[[Badness]]: 6.07 × 10<sup>-3</sup>
[[Badness]]: 6.07 × 10<sup>-3</sup>


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Alpharabian rank-3 clan| ]] <!-- main article -->
[[Category:Pages with mostly numerical content]]
[[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
[[Category:Alphaxenic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Alphaxenic_rank_three_clan"