Breed family: Difference between revisions
m fix heading structure |
m Cleanup |
||
| Line 2: | Line 2: | ||
== Breed == | == Breed == | ||
Subgroup: 2.3.5.7 | |||
[[ | [[Comma list]]: 2401/2400 | ||
[[Mapping]]: [{{val| 1 1 1 2 }}, {{val| 0 2 1 1 }}, {{val| 0 0 2 1 }}] | |||
Mapping generators: ~2, ~49/40, ~10/7 | |||
Map to lattice: [{{val|0 2 -1 0}}, {{val|0 0 -2 -1}}] | Map to lattice: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}] | ||
Lattice basis: | |||
: 49/40 length = 0.7858, 8/7 length = 1.1241 | |||
: Angle (49/40, 8/7) = 107.367° | |||
[[Minimax tuning]]: | |||
* 7- and [[9-odd-limit]] eigenmonzos: 2, 6/5, 5/4 | |||
{{Val list|legend=1| 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d }} | {{Val list|legend=1| 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.0153 × 10<sup>-3</sup> | ||
[[Projection pair]]: 3 = ~2401/800 to 2.5.7 | [[Projection pair]]: 3 = ~2401/800 to 2.5.7 | ||
| Line 25: | Line 27: | ||
Scales: [[breed11]] | Scales: [[breed11]] | ||
== Jove | == 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. 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. | ||
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 generators: ~2, ~11/9, ~10/7 | |||
[[Minimax tuning]]: | |||
* [[11-odd-limit]] eigenmonzos: 2, 7/5, 11/8 | |||
{{Val list|legend=1| 31, 41, 58, 72, 130, 161, 171, 202 }} | {{Val list|legend=1| 31, 41, 58, 72, 130, 161, 171, 202 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.241 × 10<sup>-3</sup> | ||
Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9 | Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9 | ||
; Music | |||
* [http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3 By Jove!] in [[jove41]] by Chris Vaisvil | * [http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3 By Jove!] in [[jove41]] by Chris Vaisvil | ||
=== Jovial | === Jovial === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 243/242, 364/363, 441/440 | Comma list: 243/242, 364/363, 441/440 | ||
| Line 52: | Line 59: | ||
* 15-odd-limit eigenmonzos: 2, 15/13, 7/5 | * 15-odd-limit eigenmonzos: 2, 15/13, 7/5 | ||
Mapping: [{{val|1 1 1 2 2 1}}, {{val|0 2 1 1 5 11}}, {{val|0 0 2 1 0 -1}}] | Mapping: [{{val| 1 1 1 2 2 1 }}, {{val| 0 2 1 1 5 11 }}, {{val| 0 0 2 1 0 -1 }}] | ||
Mapping generators: 2, ~11/9, ~10/7 | Mapping generators: ~2, ~11/9, ~10/7 | ||
Vals: {{Val list| 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e }} | Vals: {{Val list| 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e }} | ||
Badness: 0. | Badness: 0.624 × 10<sup>-3</sup> | ||
==== 17-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
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 generators: ~2, ~11/9, ~10/7 | |||
Minimax tuning: | Minimax tuning: | ||
* 17-odd-limit eigenmonzos: 2, 18/17, 6/5 | * 17-odd-limit eigenmonzos: 2, 18/17, 6/5 | ||
Vals: {{Val list| 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg }} | |||
Badness: 0.741 × 10<sup>-3</sup> | |||
=== Jofur === | |||
Subgroup: 2.3.5.7.11.13 | |||
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 generators: 2, ~11/9, ~10/7 | Mapping generators: ~2, ~11/9, ~10/7 | ||
Vals: {{Val list| 31, 41, 58, 89f, 99ef, 157ef }} | Vals: {{Val list| 31, 41, 58, 89f, 99ef, 157ef }} | ||
Badness: 0. | Badness: 0.749 × 10<sup>-3</sup> | ||
=== Jovis === | |||
Subgroup: 2.3.5.7.11.13 | |||
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 generators: 2, ~11/9, ~10/7 | Mapping generators: ~2, ~11/9, ~10/7 | ||
Vals: {{Val list| 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef }} | Vals: {{Val list| 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef }} | ||
Badness: 0. | Badness: 0.542 × 10<sup>-3</sup> | ||
== Freya == | |||
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 generators: ~2, ~49/40, ~55/42 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 11-odd-limit eigenmonzos: 2, 14/11, 4/3 | * 11-odd-limit eigenmonzos: 2, 14/11, 4/3 | ||
{{Val list|legend=1| 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde }} | |||
[[Badness]]: 0.170 × 10<sup>-3</sup> | |||
[[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
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: [{{val| 1 1 3 3 2 4 }}, {{val| 0 2 3 2 1 -9 }}, {{val| 0 0 -4 -2 3 6 }}] | ||
Mapping generators: 2, ~49/40, ~55/42 | Mapping generators: ~2, ~49/40, ~55/42 | ||
Vals: {{Val list| 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }} | Vals: {{Val list| 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }} | ||
Badness: 0. | Badness: 0.855 × 10<sup>-3</sup> | ||
Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3 | Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3 | ||
== Baldur | == Baldur == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 2401/2400, 9801/9800 | |||
[|1 | [[Mapping]]: [{{val| 2 0 1 3 7 }}, {{val| 0 2 1 1 -2 }}, {{val| 0 0 2 1 3 }}] | ||
|0 0 1 | |||
[[ | [[Mapping generator]]s: ~99/70, ~343/198, ~10/7 | ||
[[Minimax tuning]]: | |||
* [[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 }}] | |||
: [[Eigenmonzo]]s: 5/4, 14/11 | |||
{{Val list|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }} | |||
[[Badness]]: 0.166 × 10<sup>-3</sup> | |||
[[Projection pair]]s: 2 9801/4900 3 117649/39204 7 9801/1400 11 913517247483640899/83082326424002500 to 5.7/2.99/4 | |||
=== Greenland === | |||
Subgroup: 2.3.5.7.11.13 | |||
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 }}] | |||
Vals: {{Val list| 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf }} | |||
Badness: 0. | Badness: 0.433 × 10<sup>-3</sup> | ||
Complexity spectrum: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9 | |||
Projection pairs: 2 19600/9801 3 676/225 5 10400/2079 7 20384000/2910897 11 19208000000000000/1750211597736459 13 5026736/385875 to 10/7.200/99.26/15 | Projection pairs: 2 19600/9801 3 676/225 5 10400/2079 7 20384000/2910897 11 19208000000000000/1750211597736459 13 5026736/385875 to 10/7.200/99.26/15 | ||
== Agni | == Agni == | ||
[[Comma]] | Subgroup: 2.3.5.7.11 | ||
[[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 generators: ~2, ~49/40, ~10/7 | |||
Map to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}] | |||
Lattice basis: | |||
: 49/40 length = 0.756, 10/7 length = 0.819 | |||
: Angle (49/40, 10/7) = 106.460 degrees | |||
[[Minimax tuning]]: | |||
* [[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 }}] | |||
: [[Eigenmonzo]]s: 2, 4/3, 11/10 | |||
{{Val list|legend=1| 27, 31, 41, 68, 72, 140, 171e, 181, 212, 284, 496ce, 527ce }} | |||
[[Badness]]: 0.494 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
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 }}] | |||
Vals: {{Val list| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef }} | |||
Badness: 0.923 × 10<sup>-3</sup> | |||
== Vili == | |||
Subgroup: 2.3.5.7.11 | |||
[[ | [[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 }}] | ||
{{Val list|legend=1| 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583 }} | |||
[[Badness]]: 1.26 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1001/1000, 2401/2400, 10985/10976 | |||
Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 3 2 6 1 }}, {{val| 0 0 -6 -3 -14 -1 }}] | |||
Vals: {{Val list| 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef }} | |||
Badness: 0.738 × 10<sup>-3</sup> | |||
== Zisa == | |||
Subgroup: 2.3.5.7.11 | |||
[[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 }}] | |||
{{Val list|legend=1| 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c }} | |||
[[Badness]]: 0.640 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2401/2400, 4096/4095, 5632/5625 | |||
Mapping: [{{val| 1 1 1 2 -3 7 }}, {{val| 0 2 1 1 8 -6 }}, {{val| 0 0 2 1 8 -3 }}] | |||
Vals: {{Val list| 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }} | |||
Badness: 0. | Badness: 0.830 × 10<sup>-3</sup> | ||
== | == Frigg == | ||
Subgroup: 2.3.5.7.11 | |||
[[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 }}] | |||
{{Val list|legend=1| 51, 58, 103, 161, 212, 270, 643, 913 }} | |||
[[Badness]]: 1.79 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1001/1000, 2401/2400, 10648/10647 | |||
Mapping: [{{val| 1 1 3 3 4 5 }}, {{val| 0 2 3 2 4 3 }}, {{val| 0 0 -10 -5 -11 -14 }}] | |||
Vals: {{Val list| 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef }} | |||
Badness: 0.934 × 10<sup>-3</sup> | |||
== Ennealimmic == | |||
Subgroup: 2.3.5.7.11 | |||
[[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 generators: 27/25, 5/3, 11 | |||
{{Val list|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d }} | |||
[[Badness]]: 0.275 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
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 }}] | |||
Vals: {{Val list| 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e }} | |||
Badness: 0. | Badness: 0.755 × 10<sup>-3</sup> | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Breed]] | [[Category:Breed]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||