Alphaxenic rank-3 clan: Difference between revisions

Line 1:

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:

Line 11:

{{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 tuning]]s:

* [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}}, ~5/4 = 385.6773{{c}}, ~7/4 = 968.1894{{c}}

: [[error map]]: {{val| +0.318 -0.094 -0.000 -0.000 -0.897 }}

* [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}}, ~5/4 = 385.7900{{c}}, ~7/4 = 968.1927{{c}}

: error map: {{val| 0.000 -0.491 -0.524 -0.633 -2.050 }}

{{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]] (Sintel): 23.0

== Rabic ==

Line 28:

Line 31:

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

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

[[Optimal tuning]]s:

* [[WE]]: ~33/32 = 50.0220{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}

: [[error map]]: {{val| +0.538 -1.104 -0.002 -0.002 +0.541 }}

* [[CWE]]: ~33/32 = 50.0000{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}

: error map: {{val| 0.000 -1.955 -0.937 -1.133 -1.318 }}

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

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

[[Badness]]: 6.~~07 × 10<sup>-3</sup>~~

[[Badness]] (Sintel): 7.30

[[Category:Temperament clans]]

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

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

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
 {{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:
@@ Line 11: / Line 11: @@
 {{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 tuning]]s:
+* [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}}, ~5/4 = 385.6773{{c}}, ~7/4 = 968.1894{{c}}
+: [[error map]]: {{val| +0.318 -0.094 -0.000 -0.000 -0.897 }}
+* [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}}, ~5/4 = 385.7900{{c}}, ~7/4 = 968.1927{{c}}
+: error map: {{val| 0.000 -0.491 -0.524 -0.633 -2.050 }}
 {{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]] (Sintel): 23.0
 == Rabic ==
@@ Line 28: / Line 31: @@
 {{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 tuning]]s:
+* [[WE]]: ~33/32 = 50.0220{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}
+: [[error map]]: {{val| +0.538 -1.104 -0.002 -0.002 +0.541 }}
+* [[CWE]]: ~33/32 = 50.0000{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}
+: error map: {{val| 0.000 -1.955 -0.937 -1.133 -1.318 }}
-{{Optimal ET sequence|legend=1| 24, 48, 72, 264, 336b, 408b, 480bcde }}
+{{Optimal ET sequence|legend=1| 24, 48(d), 72, 264, 336b, 408b, 480bcde }}
-[[Badness]]: 6.07 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 7.30
 [[Category:Temperament clans]]
 [[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
-[[Category:Alphaxenic| ]] <!-- key article -->
 [[Category:Rank 3]]