Breed family

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.

Breed

Comma: 2401/2400

Minimax tuning:

• 7- and 9-odd-limit minimax eigenmonzos: 2, 6/5, 5/4

Lattice basis: 49/40 length = 0.7858, 8/7 length = 1.1241

Angle(49/40, 8/7) = 107.367°

Map to lattice: [⟨0 2 -1 0], ⟨0 0 -2 -1]]

Mapping: [⟨1 1 1 2], ⟨0 2 1 1], ⟨0 0 2 1]]

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

Badness: 0.0000153

Projection pair: 3 = ~2401/800 to 2.5.7

Scales: breed11

Jove, aka Wonder

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.

Comma list: 243/242, 441/440

Minimax tuning:

• 11-odd-limit eigenmonzos: 2, 7/5, 11/8

Mapping: [⟨1 1 1 2 2], ⟨0 2 1 1 5], ⟨0 0 2 1 0]]

Mapping generators: 2, ~11/9, ~10/7

Badness: 0.000241

Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9

• By Jove! in jove41 by Chris Vaisvil

Jovial

Comma list: 243/242, 364/363, 441/440

Minimax tuning:

• 13-odd-limit eigenmonzos: 2, 10/9, 13/10
• 15-odd-limit eigenmonzos: 2, 15/13, 7/5

Mapping: [⟨1 1 1 2 2 1], ⟨0 2 1 1 5 11], ⟨0 0 2 1 0 -1]]

Mapping generators: 2, ~11/9, ~10/7

Vals: Template:Val list

Badness: 0.000624

17-limit

Comma list: 243/242, 364/363, 441/440, 595/594

Minimax tuning:

• 17-odd-limit eigenmonzos: 2, 18/17, 6/5

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

Vals: Template:Val list

Badness: 0.000741

Jofur

Comma list: 144/143, 196/195, 243/242

Map: [⟨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

Vals: Template:Val list

Badness: 0.000749

Jovis

Comma list: 243/242, 351/350, 441/440

Map: [⟨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

Vals: Template:Val list

Badness: 0.000542

Freya

Comma list: 2401/2400, 3025/3024

Minimax tuning:

• 11-odd-limit eigenmonzos: 2, 14/11, 4/3

Mapping: [⟨1 1 3 3 2], ⟨0 2 3 2 1], ⟨0 0 -4 -2 3]]

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

Badness: 0.000170

Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3

13-limit

Comma list: 2401/2400, 3025/3024, 4096/4095

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

Vals: Template:Val list

Badness: 0.000855

Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3

Baldur

Commas: 2401/2400, 9801/9800

11-limit minimax

[|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, |0 0 1 0 0>, |23/16 0 5/8 1/8 -1/8>, |23/16 0 5/8 -7/8 7/8>]

Eigenmonzos: 5/4, 14/11

Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|]

Generators: 99/70, 343/198, 10/7

EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de

Badness: 0.000166

Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11 913517247483640899/83082326424002500 to 5.7/2.99/4

Greenland

Commas: 676/675, 1001/1000, 1716/1715

Map: [<2 0 1 3 7 -1|, <0 2 1 1 -2 4|, <0 0 2 1 3 2|]

Edos: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf

Badness: 0.000433

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

Agni

Commas: 385/384, 1375/1372

11-limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |23/10 3/10 2/5 0 -2/5>, |12/5 2/5 1/5 0 -1/5>, |23/10 3/10 -3/5 0 3/5>]

Eigenmonzos: 2, 4/3, 11/10

Lattice basis: 49/40 length 0.756, 10/7 length 0.819

Angle(49/40, 10/7) = 106.460 degrees

Map to lattice: [<0 2 1 1 0|, <0 0 2 1 -3|]

Map: [<1 1 1 2 5|, <0 2 1 1 0|, <0 0 2 1 -3|]

Generators: 2, 49/40, 10/7

Edos: 27, 31, 41, 68, 72, 140, 171e, 181, 212, 284, 496ce, 527ce

Badness: 0.000494

13-limit

Commas: 385/384, 1375/1372, 625/624

Map: [<1 1 1 2 5 -1|, <0 2 1 1 0 2|, <0 0 2 1 -3 8|]

EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef

Badness: 0.000923

Vili

Commas: 2401/2400, 391314/390625

Map: [<1 1 5 4 10|, <0 2 3 2 6|, <0 0 -6 -3 -14|]

EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583

Badness: 0.00126

13-limit

Commas: 2401/2400, 10985/10976, 1001/1000

Map: [<1 1 5 4 10 4|, <0 2 3 2 6 1|, <0 0 -6 -3 -14 -1|]

EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef

Badness: 0.000738

Zisa

Commas: 2401/2400, 5632/5625

Map: [<1 1 1 2 -3|, <0 2 1 1 8|, <0 0 2 1 8|]

EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c

Badness: 0.000640

13-limit

Commas: 2401/2400, 5632/5625, 4096/4095

Map: [<1 1 1 2 -3 7|, <0 2 1 1 8 -6|, <0 0 2 1 8 -3|]

EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241

Badness: 0.000830

Frigg

Commas: 2401/2400, 644204/643125

Map: [<1 1 3 3 4|, <0 2 3 2 4|, <0 0 -10 -5 -11|]

EDOs: 51, 58, 103, 161, 212, 270, 643, 913

Badness: 0.00179

13-limit

Commas: 1001/1000, 2401/2400, 10648/10647

Map: [<1 1 3 3 4 5|, <0 2 3 2 4 3|, <0 0 -10 -5 -11 -14|]

EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef

Badness: 0.000934

Ennealimmic

Commas: 2401/2400, 4375/4374

Map: [<9 1 1 12 0|, <0 2 3 2 0|, <0 0 0 0 1|]

Generators: 27/25, 5/3, 11

EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d

Badness: 0.000275

13-limit

Commas: 2080/2079, 2401/2400, 4375/4374

Map: [<9 1 1 12 0 -31|, <0 2 3 2 0 5|, <0 0 0 0 1 1|]

EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e

Badness: 0.000755