Breed family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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The '''breed family''' of | 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|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }} | |||
: 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 }}] | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and [[9-odd-limit]] | * [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.5 | ||
{{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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== Jove == | == Jove == | ||
{{ | {{Main| Jove }} | ||
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|legend=1| 1 1 1 2 2 | 0 2 1 1 5 | 0 0 2 1 0 }} | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11 | ||
{{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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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 | * 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.13/9 | ||
* 15-odd-limit | * 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13 | ||
{{Optimal ET sequence|legend=1| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }} | {{Optimal ET sequence|legend=1| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }} | ||
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Comma list: 243/242, 364/363, 441/440, 595/594 | Comma list: 243/242, 364/363, 441/440, 595/594 | ||
Mapping: | Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }} | ||
Minimax tuning: | Minimax tuning: | ||
* 17-odd-limit | * 17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9 | ||
{{Optimal ET sequence|legend=1| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }} | {{Optimal ET sequence|legend=1| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }} | ||
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Comma list: 144/143, 196/195, 243/242 | Comma list: 144/143, 196/195, 243/242 | ||
Mapping: | 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 ET sequence|legend=1| 27e, 31, 41, 58, 99ef, 157eff }} | ||
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Comma list: 243/242, 351/350, 441/440 | Comma list: 243/242, 351/350, 441/440 | ||
Mapping: | 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 ET sequence|legend=1| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }} | ||
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== 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|legend=1| 1 1 1 2 5 | 0 2 1 1 0 | 0 0 2 1 -3 }} | |||
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 }}] | ||
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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 | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) 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| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }} | ||
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Comma list: 385/384, 625/624, 1375/1372 | Comma list: 385/384, 625/624, 1375/1372 | ||
Mapping: | 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 ET sequence|legend=1| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }} | ||
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== 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|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 }} | ||
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Comma list: 1001/1000, 1716/1715, 4096/4095 | Comma list: 1001/1000, 1716/1715, 4096/4095 | ||
Mapping: | 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 }} | ||
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== 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|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }} | |||
: 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 | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) 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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Comma list: 676/675, 1001/1000, 1716/1715 | Comma list: 676/675, 1001/1000, 1716/1715 | ||
Mapping: | 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 }} | ||
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== 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|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }} | |||
: mapping generators: ~2, ~49/40, ~55/42 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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Comma list: 2401/2400, 3025/3024, 4096/4095 | Comma list: 2401/2400, 3025/3024, 4096/4095 | ||
Mapping: | Mapping: {{mapping| 1 1 3 3 2 4 | 0 2 3 2 1 -9 | 0 0 -4 -2 3 6 }} | ||
{{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 }} | ||
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Comma list: 2080/2079, 2401/2400, 3025/3024 | Comma list: 2080/2079, 2401/2400, 3025/3024 | ||
Mapping: | Mapping: {{mapping| 1 1 3 3 2 0 | 0 2 3 2 1 6 | 0 0 -4 -2 3 5 }} | ||
{{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 }} | ||
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Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400 | Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400 | ||
Mapping: | Mapping: {{mapping| 1 1 3 3 2 0 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 5 -12 }} | ||
{{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 }} | ||
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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: | 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 | ||
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Comma list: 1001/1000, 1716/1715, 3025/3024 | Comma list: 1001/1000, 1716/1715, 3025/3024 | ||
Mapping: | Mapping: {{mapping| 1 1 3 3 2 7 | 0 2 3 2 1 6 | 0 0 -4 -2 3 -13 }} | ||
{{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 }} | ||
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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: | 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 | |||
{{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 }} | ||
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== 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|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 }} | ||
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Comma list: 1001/1000, 1716/1715, 4225/4224 | Comma list: 1001/1000, 1716/1715, 4225/4224 | ||
Mapping: | 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 }} | ||
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== 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|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 }} | ||
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Comma list: 1001/1000, 1716/1715, 10648/10647 | Comma list: 1001/1000, 1716/1715, 10648/10647 | ||
Mapping: | 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> | ||
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== 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|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }} | |||
: 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 }} | ||
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Comma list: 2080/2079, 2401/2400, 4375/4374 | Comma list: 2080/2079, 2401/2400, 4375/4374 | ||
Mapping: | 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 }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Breed family| ]] <!-- main article --> | [[Category:Breed family| ]] <!-- main article --> | ||
[[Category:Breed| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] |