Mirwomo temperaments: Difference between revisions

(10 intermediate revisions by 4 users not shown)

Line 1:

~~These are~~ rank-2 temperaments ~~that temper~~ 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]].

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]]

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

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

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

Considered below is caleb.

== Caleb ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

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

~~[[Mapping]]: [~~{{~~val~~| 3 ~~5 7 8 }}, {{val~~| 0 -6 -1 10 }}]

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

[[~~POTE generator~~]]: ~5/4 = 383.~~405~~

[[Optimal tuning]]s:

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

: [[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]]: 0.~~159160~~

[[Badness]] (Sintel): 4.03

=== 11-limit ===

Line 21:

Line 41:

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

Mapping: [{{~~val~~| 3 5 ~~7 8 10~~ }}, {{~~val~~| 0 -6 -1 10 9 }}]

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

Optimal tunings:

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

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

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

Badness (Sintel): 1.75

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

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

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

~~POTE generator~~: ~5/4 = 383.~~421~~

Optimal tunings:

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

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

{{Optimal ET sequence|legend=1| 3, 69, 72~~, 291cde, 363cdde, 435ccdde, 507bccdde~~ }}

Badness: 0.~~052938~~

Badness (Sintel): 1.60

[[Category:Temperament collections]]

[[Category:Mirwomo]]

[[Category:Mirwomo temperaments| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-These are rank-2 temperaments that temper out the [[mirwomo comma]], 33075/32768 = {{monzo| -15 3 2 2 }}. For the rank-3 temperament, see [[Mirwomo family]].
+{{Technical data page}}
+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]].
-Temperaments dicussed elsewhere include [[Diaschismic family|anguirus]], [[Keegic temperaments|aurora]], [[Dicot family|dichotic]], [[Compton family|hours]], [[Gamelismic clan|miracle]], [[Meantone family|mohajira]], [[Tetracot family|monkey]], [[Sensamagic clan|salsa]], [[Orwellismic temperaments|sentinel]], [[Würschmidt family|worschmidt]], and [[Gravity family|zarvo]].
+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]]
+* ''[[Aurora]]'' (+1029/1000) → [[Keegic temperaments #Aurora|Keegic temperaments]]
+* [[Whitewood]] (+36/35) → [[Whitewood family #Septimal whitewood|Whitewood family]]
+* ''[[Hours]]'' (+19683/19600) → [[Compton family #Hours|Compton family]]
+Considered below is caleb.
 == Caleb ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 33075/32768, 250047/250000
-[[Mapping]]: [{{val| 3 5 7 8 }}, {{val| 0 -6 -1 10 }}]
+{{Mapping|legend=1| 3 -1 6 18 | 0 6 1 -10 }}
+: mapping generators: ~63/50, ~5/4
-[[POTE generator]]: ~5/4 = 383.405
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.2698{{c}}, ~5/4 = 383.6637{{c}}
+: [[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]]: 0.159160
+[[Badness]] (Sintel): 4.03
 === 11-limit ===
@@ Line 21: / Line 41: @@
 Comma list: 441/440, 4125/4096, 4375/4356
-Mapping: [{{val| 3 5 7 8 10 }}, {{val| 0 -6 -1 10 9 }}]
+Mapping: {{mapping| 3 -1 6 18 19 | 0 6 1 -10 -9 }}
+Optimal tunings:
+* WE: ~44/35 = 400.2557{{c}}, ~5/4 = 383.6664{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~5/4 = 383.4138{{c}}
+{{Optimal ET sequence|legend=0| 3, 69, 72, 291cde, 363cdde, …, 579bccddee }}
+Badness (Sintel): 1.75
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 169/168, 364/363, 441/440, 625/624
+Mapping: {{mapping| 3 -1 6 18 19 13 | 0 6 1 -10 -9 -2 }}
-POTE generator: ~5/4 = 383.421
+Optimal tunings:
+* WE: ~44/35 = 400.3228{{c}}, ~5/4 = 383.7260{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~5/4 = 383.4063{{c}}
-{{Optimal ET sequence|legend=1| 3, 69, 72, 291cde, 363cdde, 435ccdde, 507bccdde }}
+{{Optimal ET sequence|legend=0| 3, 69, 72 }}
-Badness: 0.052938
+Badness (Sintel): 1.60
 [[Category:Temperament collections]]
-[[Category:Mirwomo]]
+[[Category:Mirwomo temperaments| ]] <!-- main article -->
 [[Category:Rank 2]]