Mirwomo temperaments: Difference between revisions

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This is a collection of [[~~Rank~~-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[mirwomo comma]], ~~33075/32768 =~~ {{monzo| -15 3 2 2 }}. For the rank-3 temperament, see [[Mirwomo ~~family~~]].

This is a collection of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] the [[mirwomo comma]], ({{monzo|legend=1| -15 3 2 2 }}, [[ratio]]: 33075/32768). For the rank-3 temperament, see [[Rastmic rank-3 clan #Mirwomo]].

~~Considered below is caleb.~~ Temperaments dicussed elsewhere are:

Temperaments dicussed elsewhere are:

* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]

* [[Mohajira]] (+6144/6125) → [[Meantone family #Mohajira|Meantone family]]

* ''[[Salsa]]'' (+245/243) → [[Schismatic family #Salsa|Schismatic family]]

* ''[[Anguirus]]'' (+49/48) → [[Diaschismic family #Anguirus|Diaschismic family]]

* [[Monkey]] (+875/864) → [[Tetracot family #Monkey|Tetracot family]]

* ''[[Sentinel]]'' (+1728/1715) → [[Orwellismic temperaments #Sentinel|Orwellismic temperaments]]

* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]

* ''[[Zarvo]]'' (+4375/4374) → [[Gravity family #Zarvo|Gravity family]]

* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt|Würschmidt family]]

* ''[[Miracle]]'' (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]

* ''[[Salsa]]'' (+245/243) → [[Schismatic family #Salsa|Schismatic family]]

* ''[[Monkey]]'' (+875/864) → [[Tetracot family #Monkey|Tetracot family]]

* ''[[Aurora]]'' (+1029/1000) → [[Keegic temperaments #Aurora|Keegic temperaments]]

* ''[[~~Sentinel~~]]'' (+~~1728~~/~~1715~~) → [[~~Orwellismic temperaments #Sentinel|Orwellismic temperaments]]~~

* [[Whitewood]] (+36/35) → [[Whitewood family #Septimal whitewood|Whitewood family]]

* ''[[Zarvo]]'' (+4375/4374) → [[Gravity family #Zarvo|Gravity family]]

* ''[[Mohajira]]'' (+6144/6125) → [[Meantone family #~~Mohajira~~|~~Meantone~~ family]]

* ''[[Hours]]'' (+19683/19600) → [[Compton family #Hours|Compton family]]

Considered below is caleb.

== Caleb ==

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[[Comma list]]: 33075/32768, 250047/250000

: ~~Mapping~~ generators: ~63/50, ~~~126~~/~~125~~

: mapping generators: ~63/50, ~5/4

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~63/50 = 400.~~000¢~~, ~5/4 = 383.~~425¢~~

* [[WE]]: ~63/50 = 400.2698{{c}}, ~5/4 = 383.6637{{c}}

* [[CWE]]: ~63/50 = 400.~~000¢~~, ~5/4 = 383.~~409¢~~

: [[error map]]: {{val| +0.809 -0.242 -1.031 -0.607 }}

* [[CWE]]: ~63/50 = 400.0000{{c}}, ~5/4 = 383.4090{{c}}

: error map: {{val| 0.000 -1.501 -2.905 -2.916 }}

{{Optimal ET sequence|legend=1| 3, 69, 72, 363cdd, 435ccdd, …, 651bcccddd }}

[[Badness]] (Sintel): 4.~~028~~

[[Badness]] (Sintel): 4.03

=== 11-limit ===

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Comma list: 441/440, 4125/4096, 4375/4356

Mapping: {{mapping| 3 ~~5 7 8 10~~ | 0 -6 -1 10 9 }}

Mapping: {{mapping| 3 -1 6 18 19 | 0 6 1 -10 -9 }}

Optimal tunings:

* ~~CTE~~: ~44/35 = 400.~~000¢~~, ~5/4 = 383.~~377¢~~

* WE: ~44/35 = 400.2557{{c}}, ~5/4 = 383.6664{{c}}

* CWE: ~44/35 = 400.~~000¢~~, ~5/4 = 383.~~414¢~~

* CWE: ~44/35 = 400.0000{{c}}, ~5/4 = 383.4138{{c}}

{{Optimal ET sequence|legend=0| 3, 69, 72, 291cde, 363cdde, ~~435ccdde~~, ~~507bccdde~~ }}

{{Optimal ET sequence|legend=0| 3, 69, 72, 291cde, 363cdde, …, 579bccddee }}

Badness (Sintel): 1.~~750~~

Badness (Sintel): 1.75

=== 13-limit ===

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Comma list: 169/168, 364/363, 441/440, 625/624

Mapping: {{mapping| 3 ~~5 7 8 10 11~~ | 0 -6 -1 10 9 2 }}

Mapping: {{mapping| 3 -1 6 18 19 13 | 0 6 1 -10 -9 -2 }}

Optimal tunings:

* ~~CTE~~: ~44/35 = 400.~~000¢~~, ~5/4 = 383.~~346¢~~

* WE: ~44/35 = 400.3228{{c}}, ~5/4 = 383.7260{{c}}

* CWE: ~44/35 = 400.~~000¢~~, ~5/4 = 383.~~406¢~~

* CWE: ~44/35 = 400.0000{{c}}, ~5/4 = 383.4063{{c}}

Badness (Sintel): 1.~~602~~

Badness (Sintel): 1.60

[[Category:Temperament collections]]

[[Category:Mirwomo temperaments| ]]

~~[[Category:Mirwomo| ]] ~~

[[Category:Rank 2]]

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 {{Technical data page}}
-This is a collection of [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[mirwomo comma]], 33075/32768 = {{monzo| -15 3 2 2 }}. For the rank-3 temperament, see [[Mirwomo family]].
+This is a collection of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] the [[mirwomo comma]], ({{monzo|legend=1| -15 3 2 2 }}, [[ratio]]: 33075/32768). For the rank-3 temperament, see [[Rastmic rank-3 clan #Mirwomo]].
-Considered below is caleb. Temperaments dicussed elsewhere are:
+Temperaments dicussed elsewhere are:
 * ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
+* [[Mohajira]] (+6144/6125) → [[Meantone family #Mohajira|Meantone family]]
+* ''[[Salsa]]'' (+245/243) → [[Schismatic family #Salsa|Schismatic family]]
 * ''[[Anguirus]]'' (+49/48) → [[Diaschismic family #Anguirus|Diaschismic family]]
+* [[Monkey]] (+875/864) → [[Tetracot family #Monkey|Tetracot family]]
+* ''[[Sentinel]]'' (+1728/1715) → [[Orwellismic temperaments #Sentinel|Orwellismic temperaments]]
+* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
+* ''[[Zarvo]]'' (+4375/4374) → [[Gravity family #Zarvo|Gravity family]]
 * ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt|Würschmidt family]]
-* ''[[Miracle]]'' (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* ''[[Salsa]]'' (+245/243) → [[Schismatic family #Salsa|Schismatic family]]
-* ''[[Monkey]]'' (+875/864) → [[Tetracot family #Monkey|Tetracot family]]
 * ''[[Aurora]]'' (+1029/1000) → [[Keegic temperaments #Aurora|Keegic temperaments]]
-* ''[[Sentinel]]'' (+1728/1715) → [[Orwellismic temperaments #Sentinel|Orwellismic temperaments]]
+* [[Whitewood]] (+36/35) → [[Whitewood family #Septimal whitewood|Whitewood family]]
-* ''[[Zarvo]]'' (+4375/4374) → [[Gravity family #Zarvo|Gravity family]]
-* ''[[Mohajira]]'' (+6144/6125) → [[Meantone family #Mohajira|Meantone family]]
 * ''[[Hours]]'' (+19683/19600) → [[Compton family #Hours|Compton family]]
+Considered below is caleb.
 == Caleb ==
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 [[Comma list]]: 33075/32768, 250047/250000
-{{Mapping|legend=1| 3 5 7 8 | 0 -6 -1 10 }}
+{{Mapping|legend=1| 3 -1 6 18 | 0 6 1 -10 }}
-: Mapping generators: ~63/50, ~126/125
+: mapping generators: ~63/50, ~5/4
 [[Optimal tuning]]s:
-* [[CTE]]: ~63/50 = 400.000¢, ~5/4 = 383.425¢
+* [[WE]]: ~63/50 = 400.2698{{c}}, ~5/4 = 383.6637{{c}}
-* [[CWE]]: ~63/50 = 400.000¢, ~5/4 = 383.409¢
+: [[error map]]: {{val| +0.809 -0.242 -1.031 -0.607 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~5/4 = 383.4090{{c}}
+: error map: {{val| 0.000 -1.501 -2.905 -2.916 }}
-{{Optimal ET sequence|legend=1| 3, 69, 72 }}
+{{Optimal ET sequence|legend=1| 3, 69, 72, 363cdd, 435ccdd, …, 651bcccddd }}
-[[Badness]] (Sintel): 4.028
+[[Badness]] (Sintel): 4.03
 === 11-limit ===
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 Comma list: 441/440, 4125/4096, 4375/4356
-Mapping: {{mapping| 3 5 7 8 10 | 0 -6 -1 10 9 }}
+Mapping: {{mapping| 3 -1 6 18 19 | 0 6 1 -10 -9 }}
 Optimal tunings:
-* CTE: ~44/35 = 400.000¢, ~5/4 = 383.377¢
+* WE: ~44/35 = 400.2557{{c}}, ~5/4 = 383.6664{{c}}
-* CWE: ~44/35 = 400.000¢, ~5/4 = 383.414¢
+* CWE: ~44/35 = 400.0000{{c}}, ~5/4 = 383.4138{{c}}
-{{Optimal ET sequence|legend=0| 3, 69, 72, 291cde, 363cdde, 435ccdde, 507bccdde }}
+{{Optimal ET sequence|legend=0| 3, 69, 72, 291cde, 363cdde, …, 579bccddee }}
-Badness (Sintel): 1.750
+Badness (Sintel): 1.75
 === 13-limit ===
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 Comma list: 169/168, 364/363, 441/440, 625/624
-Mapping: {{mapping| 3 5 7 8 10 11 | 0 -6 -1 10 9 2 }}
+Mapping: {{mapping| 3 -1 6 18 19 13 | 0 6 1 -10 -9 -2 }}
 Optimal tunings:
-* CTE: ~44/35 = 400.000¢, ~5/4 = 383.346¢
+* WE: ~44/35 = 400.3228{{c}}, ~5/4 = 383.7260{{c}}
-* CWE: ~44/35 = 400.000¢, ~5/4 = 383.406¢
+* CWE: ~44/35 = 400.0000{{c}}, ~5/4 = 383.4063{{c}}
 {{Optimal ET sequence|legend=0| 3, 69, 72 }}
-Badness (Sintel): 1.602
+Badness (Sintel): 1.60
 [[Category:Temperament collections]]
 [[Category:Mirwomo temperaments| ]] <!-- main article -->
-[[Category:Mirwomo| ]] <!-- key article -->
 [[Category:Rank 2]]