Mirwomo temperaments: Difference between revisions

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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 not dicussed here include [[Diaschismic family|anguirus]], [[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]]


= Caleb =
Considered below is caleb.
Subgroup: 2.3.5.7
 
== Caleb ==
[[Subgroup]]: 2.3.5.7


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


{{Val list|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 ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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


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


Badness: 0.052938
Badness (Sintel): 1.60


[[Category:Temperament]]
[[Category:Temperament collections]]
[[Category:Mirwomo]]
[[Category:Mirwomo temperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 06:00, 1 May 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 temperaments tempering out the mirwomo comma, (monzo: [-15 3 2 2⟩, ratio: 33075/32768). For the rank-3 temperament, see Rastmic rank-3 clan #Mirwomo.

Temperaments dicussed elsewhere are:

Considered below is caleb.

Caleb

Subgroup: 2.3.5.7

Comma list: 33075/32768, 250047/250000

Mapping: [⟨3 -1 6 18], ⟨0 6 1 -10]]

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

Optimal tunings:

  • WE: ~63/50 = 400.2698 ¢, ~5/4 = 383.6637 ¢
error map: ⟨+0.809 -0.242 -1.031 -0.607]
  • CWE: ~63/50 = 400.0000 ¢, ~5/4 = 383.4090 ¢
error map: ⟨0.000 -1.501 -2.905 -2.916]

Optimal ET sequence: 3, 69, 72, 363cdd, 435ccdd, …, 651bcccddd

Badness (Sintel): 4.03

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨3 -1 6 18 19], ⟨0 6 1 -10 -9]]

Optimal tunings:

  • WE: ~44/35 = 400.2557 ¢, ~5/4 = 383.6664 ¢
  • CWE: ~44/35 = 400.0000 ¢, ~5/4 = 383.4138 ¢

Optimal ET sequence: 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: [⟨3 -1 6 18 19 13], ⟨0 6 1 -10 -9 -2]]

Optimal tunings:

  • WE: ~44/35 = 400.3228 ¢, ~5/4 = 383.7260 ¢
  • CWE: ~44/35 = 400.0000 ¢, ~5/4 = 383.4063 ¢

Optimal ET sequence: 3, 69, 72

Badness (Sintel): 1.60

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