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Breed family: Difference between revisions

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{{Technical data page}}
The '''breed family''' of [[temperament]]s are [[Rank-3 temperament|rank-3]] [[microtemperament]]s which [[Tempering out|temper out]] [[2401/2400]]. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick.  
The '''breed family''' of [[temperament]]s are [[Rank-3 temperament|rank-3]] [[microtemperament]]s which [[Tempering out|temper out]] [[2401/2400]]. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick.  


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[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.5
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5
 
[[Optimal tuning]] (POTE): ~2 = 1\1, ~49/40 = 350.9664, ~10/7 = 617.6720


{{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}
{{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}
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Scales: [[breed11]]
Scales: [[breed11]]
; Music
* ''Bodacious Breed'' (archived 2010) by [[Gene Ward Smith]] – [http://www.archive.org/details/BodaciousBreed details] | [http://www.archive.org/download/BodaciousBreed/Genewardsmith-BodaciousBreed.mp3 play] – breed in 441edo tuning


== Jove ==
== Jove ==
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[[Minimax tuning]]:
[[Minimax tuning]]:
* [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11
* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11
 
[[Optimal tuning]] (POTE): ~2 = 1\1, ~11/9 = 350.5034, ~10/7 = 617.8275


{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
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Minimax tuning:
Minimax tuning:
* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.13/9
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/5.13/9
* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13
 
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.7179, ~10/7 = 617.8286


{{Optimal ET sequence|legend=1| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
Optimal ET sequence: {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}


Badness: 0.624 × 10<sup>-3</sup>
Badness: 0.624 × 10<sup>-3</sup>
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Minimax tuning:
Minimax tuning:
* 17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9
* 17-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.17/9


{{Optimal ET sequence|legend=1| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.6947, ~10/7 = 617.5315
 
Optimal ET sequence: {{Optimal ET sequence| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}


Badness: 0.741 × 10<sup>-3</sup>
Badness: 0.741 × 10<sup>-3</sup>
==== Heartlandia ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 1452/1445
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}
: mapping generators: ~2, ~119/108, ~27/17
Optimal tuning (POTE): ~2 = 1\1, ~119/108 = 175.4177, ~27/17 = 793.9762
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 243/242, 324/323, 364/363, 441/440
Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}
Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.3862, ~19/12 = 793.9558
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}


=== Jofur ===
=== Jofur ===
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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 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}


{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 99ef, 157eff }}
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.4477, ~10/7 = 618.8891
 
Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 41, 58, 99ef, 157eff }}


Badness: 0.749 × 10<sup>-3</sup>
Badness: 0.749 × 10<sup>-3</sup>
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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 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}


{{Optimal ET sequence|legend=1| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.3935, ~10/7 = 618.1036
 
Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}


Badness: 0.542 × 10<sup>-3</sup>
Badness: 0.542 × 10<sup>-3</sup>
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* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}]
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.11/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
 
[[Optimal tuning]] (POTE): ~2 = 1\1, ~49/40 = 350.7145, ~10/7 = 617.0044


{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
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Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}
Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}


{{Optimal ET sequence|legend=1| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 350.6803, ~10/7 = 617.1448
 
Optimal ET sequence: {{Optimal ET sequence| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}


Badness: 0.923 × 10<sup>-3</sup>
Badness: 0.923 × 10<sup>-3</sup>
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Badness: 0.830 × 10<sup>-3</sup>
Badness: 0.830 × 10<sup>-3</sup>
== Lif ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 2401/2400, 131072/130977
{{Mapping|legend=1| 1 1 1 2 8 | 0 2 1 1 -12 | 0 0 2 1 -2 }}
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~49/40 = 351.0959, ~10/7 = 617.6652
{{Optimal ET sequence|legend=1| 41, 89, 130, 229, 270, 581, 670, 711, 981, 1251, 2232e }}
[[Badness]]: 0.793 × 10<sup>-3</sup>
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095
Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}
Optimal tuning (CTE): ~2 = 1\1, ~49/40 = 351.0960, ~10/7 = 617.6533
{{Optimal ET sequence|legend=1| 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562 }}
Badness: 0.579 × 10<sup>-3</sup>
=== 2.3.5.7.11.13.19 subgroup ===
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400
Sval mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}
Optimal tuning (CTE): ~2 = 1\1, ~49/40 = 351.1007, ~10/7 = 617.6501
{{Optimal ET sequence|legend=1| 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413 }}
Badness: 0.499 × 10<sup>-3</sup>


== Baldur ==
== Baldur ==
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* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.11/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7


{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}
{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}
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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.
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.
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Breed family| ]] <!-- main article -->
[[Category:Breed family| ]] <!-- main article -->
[[Category:Breed| ]] <!-- key article -->
[[Category:Breed| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Breed_family"