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Breed family: Difference between revisions

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Badness (Sintel): 2.29
Badness (Sintel): 2.29


=== Jofur ===
=== Jovis ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 144/143, 196/195, 243/242
Comma list: 243/242, 351/350, 441/440


Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}
Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1198.9534{{c}}, ~11/9 = 351.1412{{c}}, ~10/7 = 618.3494{{c}}
* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.2536{{c}}, ~10/7 = 618.5932{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}


{{Optimal ET sequence|legend=0| 27e, 31, 41, 58, 99ef, 157eff }}
{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}


Badness (Sintel): 0.701
Badness (Sintel): 0.507


=== Jovis ===
=== Jofur ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 243/242, 351/350, 441/440
Comma list: 144/143, 196/195, 243/242


Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.1435{{c}}, ~11/9 = 350.4354{{c}}, ~10/7 = 618.1775{{c}}
* WE: ~2 = 1198.9534{{c}}, ~11/9 = 351.1412{{c}}, ~10/7 = 618.3494{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4402{{c}}, ~10/7 = 618.1759{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.2536{{c}}, ~10/7 = 618.5932{{c}}


{{Optimal ET sequence|legend=0| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
{{Optimal ET sequence|legend=0| 27e, 31, 41, 58, 99ef, 157eff }}


Badness (Sintel): 0.507
Badness (Sintel): 0.701


== Agni ==
== Agni ==
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== Lif ==
== Lif ==
Lif tempers out the [[olympia]] and readily extends to the [[13-limit]] and the no-17 [[19-limit]] such that the undevicesimal schisma of [[513/512]] is equated with [[441/440]][[~]][[540/539]].  
Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the undevicesimal schisma of [[513/512]] is also equated with the schisma.  


This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma [[lifthrasirsma]], after the human survivors of Ragnarök.  
This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.  


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
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== Freya ==
== Freya ==
Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


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[[Badness]] (Sintel): 0.204
[[Badness]] (Sintel): 0.204


[[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3
[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3


=== 13-limit ===
=== 13-limit ===
Freya's canonical 13-limit extension 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.  
[[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.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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=== 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.  
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.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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==== 17-limit ====
==== 17-limit ====
Equave 10/7 and 16-note scales with that period are of interest.
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


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* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}


{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *
<nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]
 
<nowiki/>* optimal patent val: [[1241edo|1241]]


Badness (Sintel): 0.873
Badness (Sintel): 0.873
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: error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}
: error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}


{{Optimal ET sequence|legend=1| 72, …, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
{{Optimal ET sequence|legend=1| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}


[[Badness]] (Sintel): 0.330
[[Badness]] (Sintel): 0.330
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* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}
* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}


{{Optimal ET sequence|legend=0| 72, …, 171, 198, 270, 639, 711, 981, 1692e }}
{{Optimal ET sequence|legend=0| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}


Badness (Sintel): 0.706
Badness (Sintel): 0.706
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