Keenanismic temperaments: Difference between revisions

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This is a collection of [[rank-3 ~~temperament|rank-3]] [[~~temperament]]s [[tempering out]] the keenanisma, [[385/384]]. For the [[rank-4]] keenanismic temperament, see [[Keenanismic family]].

This is a collection of [[rank-3 temperament]]s [[tempering out]] the keenanisma, [[385/384]]. For the [[rank-4]] keenanismic temperament, see [[Keenanismic family]].

Temperaments discussed elsewhere include:

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* [[Zeus]] (+121/120 or 176/175) → [[Porwell family #Zeus|Porwell family]] and [[Biyatismic clan #Zeus|Biyatismic clan]]

* [[Starling]] (+126/125) → [[Starling family #Undecimal starling|Starling family]]

* [[Marvel]] (+225/224) → [[Marvel family #Undecimal marvel ~~(unimarv)~~|Marvel family]]

* [[Marvel]] (+225/224) → [[Marvel family #Undecimal marvel|Marvel family]]

* ''[[Mirwomo]]'' (+243/242) → [[Rastmic rank-3 clan #Mirwomo|Rastmic rank-3 clan]]

* [[Sensamagic]] (+245/243) → [[Sensamagic family #Undecimal sensamagic|Sensamagic family]]

* [[Portent]] (+441/440) → [[Gamelismic family #Portent|Gamelismic family]]

* ''[[Diaschismic rank-3 family#Augustus|Augustus]]'' (+1232/1215) → [[Diaschismic rank-3 family #Augustus|Diaschismic rank-3 family]]

* ''[[Diaschismic rank-3 family #Augustus|Augustus]]'' (+1232/1215) → [[Diaschismic rank-3 family #Augustus|Diaschismic rank-3 family]]

* ''[[Agni]]'' (+1375/1372) → [[Breed family #Agni|Breed family]]

* ''[[Akea]]'' (+2200/2187) → [[Hemifamity family #Akea|Hemifamity family]]

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* ''[[Enlil]]'' (+6250/6237) → [[Kleismic rank-3 family #Enlil|Kleismic rank-3 family]]

Considered below are ''uniwiz'' and ''tritiwiz''.

Considered below are uniwiz and tritiwiz.

== Uniwiz ==

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: mapping generators: ~99/70, ~16/11, ~5

[[Optimal tuning]] ([[~~CTE~~]]): ~99/70 = 600.0000{{c}}, ~16/11 = ~~651~~.~~1082~~{{c}}, ~5/4 = 385.~~5778~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 600.2029{{c}}, ~16/11 = 650.9604{{c}}, ~5/4 = 385.1616{{c}}

: [[error map]]: {{val| +0.406 +0.169 -0.341 -0.498 -0.655 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~16/11 = 650.8311{{c}}, ~5/4 = 385.1658{{c}}

: error map: {{val| 0.000 -0.293 -1.148 -1.499 -2.149 }}

{{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }}

[[Badness]] (~~Smith~~): 0.~~529 × 10-3~~

[[Badness]] (Sintel): 0.636

=== 2.3.5.7.11.17 subgroup ===

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Gencom mapping: {{mapping| 2 1 0 7 8 0 6 | 0 2 0 3 -1 0 2 | 0 0 1 -1 0 0 0 }}

Optimal ~~tuning (CTE)~~: ~17/12 = 600.0000{{c}}, ~16/11 = ~~651~~.~~2344~~{{c}}, ~5/4 = 385.~~7289~~{{c}}

Optimal tunings:

* WE: ~99/70 = 600.2365{{c}}, ~16/11 = 651.0126{{c}}, ~5/4 = 385.1864{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 650.8664{{c}}, ~5/4 = 385.1951{{c}}

{{Optimal ET sequence|legend=0| 22, 46, 68, 72, 118, 190g, 212g, 284g, 330eg, 402degg }}

Badness (~~Smith~~): 0.~~340 × 10-3~~

Badness (Sintel): 0.351

== Tritiwiz ==

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: mapping generators: ~2, ~11/10, ~5

[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~11/10 = ~~165~~.~~8258~~{{c}}, ~5/4 = 384.~~6711~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0000{{c}}, ~11/10 = 166.1752{{c}}, ~5/4 = 384.3796{{c}}

: [[error map]]: {{val| +0.400 +0.320 -1.133 -0.684 +0.438 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 166.0419{{c}}, ~5/4 = 384.3625{{c}}

: error map: {{val| 0.000 -0.081 -1.951 -1.718 -0.914 }}

{{Optimal ET sequence|legend=1| 15, 22, 37, 50, 65, 72, 159, 231, 253, 325c, 412cd, 484cd }}

[[Badness]] (~~Smith~~): 0.~~732 × 10-3~~

[[Badness]] (Sintel): 0.879

[[Category:Temperament collections]]

[[Category:Keenanismic temperaments| ]]

~~[[Category:Keenanismic| ]] ~~

[[Category:Rank 3]]

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 {{Technical data page}}
-This is a collection of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out]] the keenanisma, [[385/384]]. For the [[rank-4]] keenanismic temperament, see [[Keenanismic family]].
+This is a collection of [[rank-3 temperament]]s [[tempering out]] the keenanisma, [[385/384]]. For the [[rank-4]] keenanismic temperament, see [[Keenanismic family]].
 Temperaments discussed elsewhere include:
@@ Line 9: / Line 9: @@
 * [[Zeus]] (+121/120 or 176/175) → [[Porwell family #Zeus|Porwell family]] and [[Biyatismic clan #Zeus|Biyatismic clan]]
 * [[Starling]] (+126/125) → [[Starling family #Undecimal starling|Starling family]]
-* [[Marvel]] (+225/224) → [[Marvel family #Undecimal marvel (unimarv)|Marvel family]]
+* [[Marvel]] (+225/224) → [[Marvel family #Undecimal marvel|Marvel family]]
 * ''[[Mirwomo]]'' (+243/242) → [[Rastmic rank-3 clan #Mirwomo|Rastmic rank-3 clan]]
 * [[Sensamagic]] (+245/243) → [[Sensamagic family #Undecimal sensamagic|Sensamagic family]]
 * [[Portent]] (+441/440) → [[Gamelismic family #Portent|Gamelismic family]]
-* ''[[Diaschismic rank-3 family#Augustus|Augustus]]'' (+1232/1215) → [[Diaschismic rank-3 family #Augustus|Diaschismic rank-3 family]]
+* ''[[Diaschismic rank-3 family #Augustus|Augustus]]'' (+1232/1215) → [[Diaschismic rank-3 family #Augustus|Diaschismic rank-3 family]]
 * ''[[Agni]]'' (+1375/1372) → [[Breed family #Agni|Breed family]]
 * ''[[Akea]]'' (+2200/2187) → [[Hemifamity family #Akea|Hemifamity family]]
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 * ''[[Enlil]]'' (+6250/6237) → [[Kleismic rank-3 family #Enlil|Kleismic rank-3 family]]
-Considered below are ''uniwiz'' and ''tritiwiz''.
+Considered below are uniwiz and tritiwiz.
 == Uniwiz ==
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 : mapping generators: ~99/70, ~16/11, ~5
-[[Optimal tuning]] ([[CTE]]): ~99/70 = 600.0000{{c}}, ~16/11 = 651.1082{{c}}, ~5/4 = 385.5778{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 600.2029{{c}}, ~16/11 = 650.9604{{c}}, ~5/4 = 385.1616{{c}}
+: [[error map]]: {{val| +0.406 +0.169 -0.341 -0.498 -0.655 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~16/11 = 650.8311{{c}}, ~5/4 = 385.1658{{c}}
+: error map: {{val| 0.000 -0.293 -1.148 -1.499 -2.149 }}
 {{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de }}
-[[Badness]] (Smith): 0.529 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.636
 === 2.3.5.7.11.17 subgroup ===
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 Gencom mapping: {{mapping| 2 1 0 7 8 0 6 | 0 2 0 3 -1 0 2 | 0 0 1 -1 0 0 0 }}
-Optimal tuning (CTE): ~17/12 = 600.0000{{c}}, ~16/11 = 651.2344{{c}}, ~5/4 = 385.7289{{c}}
+Optimal tunings:
+* WE: ~99/70 = 600.2365{{c}}, ~16/11 = 651.0126{{c}}, ~5/4 = 385.1864{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~16/11 = 650.8664{{c}}, ~5/4 = 385.1951{{c}}
 {{Optimal ET sequence|legend=0| 22, 46, 68, 72, 118, 190g, 212g, 284g, 330eg, 402degg }}
-Badness (Smith): 0.340 × 10<sup>-3</sup>
+Badness (Sintel): 0.351
 == Tritiwiz ==
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 : mapping generators: ~2, ~11/10, ~5
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~11/10 = 165.8258{{c}}, ~5/4 = 384.6711{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0000{{c}}, ~11/10 = 166.1752{{c}}, ~5/4 = 384.3796{{c}}
+: [[error map]]: {{val| +0.400 +0.320 -1.133 -0.684 +0.438 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 166.0419{{c}}, ~5/4 = 384.3625{{c}}
+: error map: {{val| 0.000 -0.081 -1.951 -1.718 -0.914 }}
 {{Optimal ET sequence|legend=1| 15, 22, 37, 50, 65, 72, 159, 231, 253, 325c, 412cd, 484cd }}
-[[Badness]] (Smith): 0.732 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.879
 [[Category:Temperament collections]]
 [[Category:Keenanismic temperaments| ]] <!-- main article -->
-[[Category:Keenanismic| ]] <!-- key article -->
 [[Category:Rank 3]]