Breed family: Difference between revisions

Freyr: notation
Implement the proposed changes (see talk)
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: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5


{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
{{Optimal ET sequence|legend=1| 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}


[[Badness]] (Sintel): 0.593
[[Badness]] (Sintel): 0.593


=== 13-limit ===
=== Pavaka ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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Badness (Sintel): 0.863
Badness (Sintel): 0.863
=== Svaha ===
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384, 1375/1372
Mapping: {{mapping| 1 1 1 2 5 4 | 0 2 1 1 0 6 | 0 0 2 1 -3 -4 }}
Optimal tunings:
* WE: ~2 = 1200.3582{{c}}, ~49/40 = 351.0784{{c}}, ~10/7 = 617.0054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0491{{c}}, ~10/7 = 616.8317{{c}}
{{Optimal ET sequence|legend=0| 41, 68, 72, 140, 212, 393ce, 465cef, 677cdeeff }}
Badness (Sintel): 0.997


== Zisa ==
== Zisa ==
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=== 13-limit ===
=== 13-limit ===
Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.
Tridecimal freya maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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=== Eir ===
=== Eir ===
[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.
Eir maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament. {{U|VIxen}} named this extension after a healer goddess or valkyrie from the Norse mythology, as it extends freya via the [[ibnsinma]], which evokes associations with medicine.  


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0880{{c}}, ~84/55 = 733.2482{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0880{{c}}, ~84/55 = 733.2482{{c}}


{{Optimal ET sequence|legend=0| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
{{Optimal ET sequence|legend=0| 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}


Badness (Sintel): 0.543
Badness (Sintel): 0.543


==== 17-limit ====
==== 2.3.5.7.11.13.19 subgroup ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.19
 
Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
 
Mapping: {{mapping| 1 1 -1 1 5 5 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 -5 12 }}
 
Optimal tunings:
* WE: ~2 = 1200.0038{{c}}, ~49/40 = 351.0756{{c}}, ~84/55 = 733.2270{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0755{{c}}, ~84/55 = 733.2246{{c}}
 
{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}


Badness (Sintel): 0.665
Comma list: 1540/1539, 2080/2079, 2401/2400, 3025/3024


==== 19-limit ====
Subgroup-val mapping: {{mapping| 1 1 -1 1 5 5 3 | 0 2 3 2 1 6 -2 | 0 0 4 2 -3 -5 3 }}
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
 
Mapping: {{mapping| 1 1 -1 1 5 5 -5 3 | 0 2 3 2 1 6 6 -2 | 0 0 4 2 -3 -5 12 3 }}


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.0015{{c}}, ~49/40 = 351.0770{{c}}, ~84/55 = 733.2252{{c}}
* WE: ~2 = 1199.9951{{c}}, ~49/40 = 351.0906{{c}}, ~84/55 = 733.2475{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0768{{c}}, ~84/55 = 733.2243{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.0913{{c}}, ~84/55 = 733.2473{{c}}


{{Optimal ET sequence|legend=0| 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815 }}
{{Optimal ET sequence|legend=0| 41, 72, 113, 157, 198, 270, 581, 851, 2085, 2355f }}


Badness (Sintel): 0.712
Badness (Sintel): 0.500


=== Heimlaug ===
=== Heimlaug ===
VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.
Heimlaug maps [[351/350]] and [[625/624]] to the half-kleisma and has [[benediction]] as a subtemperament. VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders, as it extends freya via the [[1001/1000|fairytale comma]], adding to the mystical theme.  


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Badness (Sintel): 0.562
Badness (Sintel): 0.562
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 936/935, 1001/1000, 1225/1224
Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}
Optimal tunings:
* WE: ~2 = 1200.0446{{c}}, ~49/40 = 350.9662{{c}}, ~26/17 = 733.3826{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9724{{c}}, ~26/17 = 733.3515{{c}}
{{Optimal ET sequence|legend=0| 31, 64be, 72, 103, 167, 198g, 239, 270 }}
Badness (Sintel): 0.789


== Vili ==
== Vili ==