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Breed family: Difference between revisions

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The '''breed family''' of temperaments are rank-3 microtemperaments which 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.  
{{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.  


== Breed ==
== Breed ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2401/2400
[[Comma list]]: 2401/2400


[[Mapping]]: [{{val| 1 1 1 2 }}, {{val| 0 2 1 1 }}, {{val| 0 0 2 1 }}]
{{Mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}


Mapping generators: ~2, ~49/40, ~10/7
: mapping generators: ~2, ~49/40, ~10/7


[[Mapping to lattice]]: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]
[[Mapping to lattice]]: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]
Line 17: Line 18:


[[Minimax tuning]]:
[[Minimax tuning]]:
* 7- and [[9-odd-limit]] eigenmonzos (unchanged-intervals): 2, 6/5, 5/4
* [[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 }}
Line 26: Line 29:


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 ==
{{main| Jove }}
{{Main| Jove }}


Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.
Jove (formerly known as wonder) tempers out 243/242 and 441/440. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.


Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 243/242, 441/440
[[Comma list]]: 243/242, 441/440


[[Mapping]]: [{{val| 1 1 1 2 2 }}, {{val| 0 2 1 1 5 }}, {{val| 0 0 2 1 0 }}]
{{Mapping|legend=1| 1 1 1 2 2 | 0 2 1 1 5 | 0 0 2 1 0 }}


Mapping generators: ~2, ~11/9, ~10/7
[[Minimax tuning]]:
* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11


[[Minimax tuning]]:
[[Optimal tuning]] (POTE): ~2 = 1\1, ~11/9 = 350.5034, ~10/7 = 617.8275
* [[11-odd-limit]] eigenmonzos (unchanged-intervals): 2, 7/5, 11/8


{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
Line 53: Line 59:


Comma list: 243/242, 364/363, 441/440
Comma list: 243/242, 364/363, 441/440
Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}


Minimax tuning:
Minimax tuning:
* 13-odd-limit eigenmonzos (unchanged-intervals): 2, 10/9, 13/10
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/5.13/9
* 15-odd-limit eigenmonzos (unchanged-intervals): 2, 15/13, 7/5
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13


Mapping: [{{val| 1 1 1 2 2 1 }}, {{val| 0 2 1 1 5 11 }}, {{val| 0 0 2 1 0 -1 }}]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.7179, ~10/7 = 617.8286


Mapping generators: ~2, ~11/9, ~10/7
Optimal ET sequence: {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
 
{{Optimal ET sequence|legend=1| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}


Badness: 0.624 × 10<sup>-3</sup>
Badness: 0.624 × 10<sup>-3</sup>
Line 71: Line 77:
Comma list: 243/242, 364/363, 441/440, 595/594
Comma list: 243/242, 364/363, 441/440, 595/594


Mapping: [{{val| 1 1 1 2 2 1 3 }}, {{val| 0 2 1 1 5 11 9 }}, {{val| 0 0 2 1 0 -1 -3 }}]
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}


Mapping generators: ~2, ~11/9, ~10/7
Minimax tuning:
* 17-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.17/9


Minimax tuning:
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.6947, ~10/7 = 617.5315
* 17-odd-limit eigenmonzos (unchanged-intervals): 2, 18/17, 6/5


{{Optimal ET sequence|legend=1| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
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 ===
Line 87: Line 117:
Comma list: 144/143, 196/195, 243/242
Comma list: 144/143, 196/195, 243/242


Mapping: [{{val| 1 1 1 2 2 4 }}, {{val| 0 2 1 1 5 -1 }}, {{val| 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 }}


Mapping generators: ~2, ~11/9, ~10/7
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.4477, ~10/7 = 618.8891


{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 99ef, 157eff }}
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>
Line 100: Line 130:
Comma list: 243/242, 351/350, 441/440
Comma list: 243/242, 351/350, 441/440


Mapping: [{{val| 1 1 1 2 2 2 }}, {{val| 0 2 1 1 5 -3 }}, {{val| 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 }}


Mapping generators: ~2, ~11/9, ~10/7
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.3935, ~10/7 = 618.1036


{{Optimal ET sequence|legend=1| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
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>


== Agni ==
== Agni ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 385/384, 1375/1372
[[Comma list]]: 385/384, 1375/1372


[[Mapping]]: [{{val| 1 1 1 2 5 }}, {{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
{{Mapping|legend=1| 1 1 1 2 5 | 0 2 1 1 0 | 0 0 2 1 -3 }}
 
Mapping generators: ~2, ~49/40, ~10/7


Mapping to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
Mapping to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
Line 126: Line 154:
* [[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]]s (unchanged-intervals): 2, 4/3, 11/10
: [[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 }}
Line 137: Line 167:
Comma list: 385/384, 625/624, 1375/1372
Comma list: 385/384, 625/624, 1375/1372


Mapping: [{{val| 1 1 1 2 5 -1 }}, {{val| 0 2 1 1 0 2 }}, {{val| 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 tuning (POTE): ~2 = 1\1, ~49/40 = 350.6803, ~10/7 = 617.1448


{{Optimal ET sequence|legend=1| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
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>


== Zisa ==
== Zisa ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 2401/2400, 5632/5625
[[Comma list]]: 2401/2400, 5632/5625


[[Mapping]]: [{{val| 1 1 1 2 -3 }}, {{val| 0 2 1 1 8 }}, {{val| 0 0 2 1 8 }}]
{{Mapping|legend=1| 1 1 1 2 -3 | 0 2 1 1 8 | 0 0 2 1 8 }}


{{Optimal ET sequence|legend=1| 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c }}
{{Optimal ET sequence|legend=1| 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c }}
Line 159: Line 191:
Comma list: 1001/1000, 1716/1715, 4096/4095
Comma list: 1001/1000, 1716/1715, 4096/4095


Mapping: [{{val| 1 1 1 2 -3 7 }}, {{val| 0 2 1 1 8 -6 }}, {{val| 0 0 2 1 8 -3 }}]
Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}


{{Optimal ET sequence|legend=1| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}
{{Optimal ET sequence|legend=1| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}


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 ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 2401/2400, 9801/9800
[[Comma list]]: 2401/2400, 9801/9800


[[Mapping]]: [{{val| 2 0 1 3 7 }}, {{val| 0 2 1 1 -2 }}, {{val| 0 0 2 1 3 }}]
{{Mapping|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }}


[[Mapping generator]]s: ~99/70, ~343/198, ~10/7
: mapping generators: ~99/70, ~343/198, ~10/7


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[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]]s (unchanged-intervals): 5/4, 14/11
: [[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 }}
Line 190: Line 261:
Comma list: 676/675, 1001/1000, 1716/1715
Comma list: 676/675, 1001/1000, 1716/1715


Mapping: [{{val| 2 0 1 3 7 -1 }}, {{val| 0 2 1 1 -2 4 }}, {{val| 0 0 2 1 3 2 }}]
Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}


{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}
{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}
Line 201: Line 272:


== Freya ==
== Freya ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 2401/2400, 3025/3024
[[Comma list]]: 2401/2400, 3025/3024


[[Mapping]]: [{{val| 1 1 3 3 2 }}, {{val| 0 2 3 2 1 }}, {{val| 0 0 -4 -2 3 }}]
{{Mapping|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }}


Mapping generators: ~2, ~49/40, ~55/42
: mapping generators: ~2, ~49/40, ~55/42


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 223: Line 294:
Comma list: 2401/2400, 3025/3024, 4096/4095
Comma list: 2401/2400, 3025/3024, 4096/4095


Mapping: [{{val| 1 1 3 3 2 4 }}, {{val| 0 2 3 2 1 -9 }}, {{val| 0 0 -4 -2 3 6 }}]
Mapping: {{mapping| 1 1 3 3 2 4 | 0 2 3 2 1 -9 | 0 0 -4 -2 3 6 }}
 
Mapping generators: ~2, ~49/40, ~55/42


{{Optimal ET sequence|legend=1| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}
{{Optimal ET sequence|legend=1| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}
Line 234: Line 303:


=== 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


Comma list: 2080/2079, 2401/2400, 3025/3024
Comma list: 2080/2079, 2401/2400, 3025/3024


Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 2 3 2 1 6 }}, {{val| 0 0 -4 -2 3 5 }}]
Mapping: {{mapping| 1 1 3 3 2 0 | 0 2 3 2 1 6 | 0 0 -4 -2 3 5 }}
 
Mapping generators: ~2, ~49/40, ~55/42


{{Optimal ET sequence|legend=1| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
{{Optimal ET sequence|legend=1| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
Line 251: Line 320:
Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400


Mapping: [{{val| 1 1 3 3 2 0 7 }}, {{val| 0 2 3 2 1 6 6 }}, {{val| 0 0 -4 -2 3 5 -12 }}]
Mapping: {{mapping| 1 1 3 3 2 0 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 5 -12 }}
 
Mapping generators: ~2, ~49/40, ~55/42


{{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}
{{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}
Line 264: Line 331:
Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199


Mapping: [{{val| 1 1 3 3 2 0 7 6 }}, {{val| 0 2 3 2 1 6 6 -2 }}, {{val| 0 0 -4 -2 3 5 -12 -3 }}]
Mapping: {{mapping| 1 1 3 3 2 0 7 6 | 0 2 3 2 1 6 6 -2 | 0 0 -4 -2 3 5 -12 -3 }}


Mapping generators: ~2, ~49/40, ~55/42
Mapping generators: ~2, ~49/40, ~55/42
Line 273: Line 340:


=== 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


Comma list: 1001/1000, 1716/1715, 3025/3024
Comma list: 1001/1000, 1716/1715, 3025/3024


Mapping: [{{val| 1 1 3 3 2 7 }}, {{val| 0 2 3 2 1 6 }}, {{val| 0 0 -4 -2 3 -13 }}]
Mapping: {{mapping| 1 1 3 3 2 7 | 0 2 3 2 1 6 | 0 0 -4 -2 3 -13 }}
 
Mapping generators: ~2, ~49/40, ~55/42


{{Optimal ET sequence|legend=1| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
{{Optimal ET sequence|legend=1| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
Line 292: Line 359:
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715


Mapping: [{{val| 1 1 3 3 2 7 7 }}, {{val| 0 2 3 2 1 6 6 }}, {{val| 0 0 -4 -2 3 -13 -12 }}]
Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 -13 -12 }}


Mapping generators: ~2, ~49/40, ~17/13
: mapping generators: ~2, ~49/40, ~17/13


{{Optimal ET sequence|legend=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
{{Optimal ET sequence|legend=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
Line 301: Line 368:


== Vili ==
== Vili ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 2401/2400, 391314/390625
[[Comma list]]: 2401/2400, 391314/390625


[[Mapping]]: [{{val| 1 1 5 4 10 }}, {{val| 0 2 3 2 6 }}, {{val| 0 0 -6 -3 -14 }}]
{{Mapping|legend=1| 1 1 5 4 10 | 0 2 3 2 6 | 0 0 -6 -3 -14 }}


{{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}
{{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}
Line 316: Line 383:
Comma list: 1001/1000, 1716/1715, 4225/4224
Comma list: 1001/1000, 1716/1715, 4225/4224


Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 3 2 6 1 }}, {{val| 0 0 -6 -3 -14 -1 }}]
Mapping: {{mapping| 1 1 5 4 10 4 | 0 2 3 2 6 1 | 0 0 -6 -3 -14 -1 }}


{{Optimal ET sequence|legend=1| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
{{Optimal ET sequence|legend=1| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
Line 323: Line 390:


== Frigg ==
== Frigg ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 2401/2400, 644204/643125
[[Comma list]]: 2401/2400, 644204/643125


[[Mapping]]: [{{val| 1 1 3 3 4 }}, {{val| 0 2 3 2 4 }}, {{val| 0 0 -10 -5 -11 }}]
{{Mapping|legend=1| 1 1 3 3 4 | 0 2 3 2 4 | 0 0 -10 -5 -11 }}


{{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}
{{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}
Line 338: Line 405:
Comma list: 1001/1000, 1716/1715, 10648/10647
Comma list: 1001/1000, 1716/1715, 10648/10647


Mapping: [{{val| 1 1 3 3 4 5 }}, {{val| 0 2 3 2 4 3 }}, {{val| 0 0 -10 -5 -11 -14 }}]
Mapping: {{mapping| 1 1 3 3 4 5 | 0 2 3 2 4 3 | 0 0 -10 -5 -11 -14 }}


{{Optimal ET sequence|legend=1| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
Line 347: Line 414:


== Ennealimmic ==
== Ennealimmic ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 2401/2400, 4375/4374
[[Comma list]]: 2401/2400, 4375/4374


[[Mapping]]: [{{val| 9 1 1 12 0 }}, {{val| 0 2 3 2 0 }}, {{val| 0 0 0 0 1 }}]
{{Mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}


Mapping generators: 27/25, 5/3, 11
: mapping generators: ~27/25, ~5/3, ~11


{{Optimal ET sequence|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}
{{Optimal ET sequence|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}
Line 364: Line 431:
Comma list: 2080/2079, 2401/2400, 4375/4374
Comma list: 2080/2079, 2401/2400, 4375/4374


Mapping: [{{val| 9 1 1 12 0 -31 }}, {{val| 0 2 3 2 0 5 }}, {{val| 0 0 0 0 1 1 }}]
Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}


{{Optimal ET sequence|legend=1| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}
{{Optimal ET sequence|legend=1| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}
Line 371: Line 438:


[[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:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Breed_family"