Breed family

Breed is a 7-limit microtemperament which tempers 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.

Vital statistics

Comma c = 2401/2400

7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat

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 degrees

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

Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]

Generators: 2, 49/40, 10/7

EDOs: 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d

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.

11-limit

Commas: 243/242, 441/440

Minimax tuning

[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>, |0 0 0 0 1>]

Eigenmonzos: 2, 7/5, 11/8

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

EDOs: 31, 41, 58, 72, 130, 161, 171, 202

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

Commas: 243/242, 441/440, 364/363

13-limit minimax

[|1 0 0 0 0 0>, |17/11 -12/11 2/11 0 0 4/11>, |34/11 -46/11 15/11 0 0 8/11>, |35/11 -26/11 8/11 0 0 5/11>, |37/11 -30/11 5/11 0 0 10/11>, |34/11 -46/11 4/11 0 0 19/11>]

Eigenmonzos: 2, 10/9, 13/9

15-limit minimax

[|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>, |7/2 -1/8 9/4 -19/8 0 1/8>, |7/2 -1/8 5/4 -11/8 0 1/8>, |9/2 -5/8 5/4 -15/8 0 5/8>, |11/2 -11/8 7/4 -25/8 0 11/8>]

Eigenmonzos: 2, 15/13, 7/5

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

EDOs: 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e

Badness: 0.000624

17-limit

Commas: 243/242, 441/440, 364/363, 595/594

17-limit minimax

[|1 0 0 0 0 0 0>, |3/7 -2 6/7 0 0 0 4/7>, |3/7 -3 13/7 0 0 0 4/7>, |11/7 -2 8/7 0 0 0 3/7>, |4/7 -5 15/7 0 0 0 10/7>, |-2 -10 4 0 0 0 3>, |6/7 -6 12/7 0 0 0 15/7>]

Eigenmonzos: 2, 18/17, 6/5

Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|]

Generators: 2, 11/9, 10/7

Edos: 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg

Badness: 0.000741

Jofur

Commas: 243/242, 441/440, 144/143

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

EDOs: 31, 41, 58, 89f, 99ef, 157ef

Badness: 0.000749

Jovis

Commas: 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|]

EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef

Badness: 0.000542

Freya

11-limit

Commas: 2401/2400, 3025/3024

11-limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |11/10 11/10 0 4/5 -4/5>, |9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]

Eigenmonzos: 2, 14/11, 4/3

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

EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde

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

Commas: 2401/2400, 3025/3024, 4096/4095

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

Generators: 2, 49/40, 55/42

Edos: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615

Badness: 0.000855

Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 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

{{#rreplace: 25/24 not only in two equal parts (49/48, 50/49) but also four equal parts (99/98, 100/99, 105/104, 91/90)

Commas: 676/675, 1001/1000, 1716/1715|/(\d+)(\D+)?\/(\d+)(\D+)?/|\1/\3\2\4}}

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

Edos: {{#rreplace: 1210f, 1480cf, 1750cf|/(\d+)(\D+)?/|\1\2}}

EDOs: {{#rreplace: 58 68 72 130 140 198 202 212 270 328 338 400 410 468 540 598 608 670 680 738 800 810 878 940 950 1008 1080 1148|/(\d+)(\D+)?/|\1\2}}

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

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