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
- 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
- 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
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
- 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