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
Subgroup: 2.3.5.7
Comma list: 2401/2400
Mapping: [⟨1 1 1 2], ⟨0 2 1 1], ⟨0 0 2 1]]
- mapping generators: ~2, ~49/40, ~10/7
Mapping to lattice: [⟨0 2 -1 0], ⟨0 0 -2 -1]]
Lattice basis:
- 49/40 length = 0.7858, 8/7 length = 1.1241
- Angle (49/40, 8/7) = 107.367°
- 7- and 9-odd-limit eigenmonzo (unchanged-interval) basis: 2.3.5
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 350.9664, ~10/7 = 617.6720
Optimal ET sequence: 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d
Badness: 0.0153 × 10-3
Projection pair: 3 = ~2401/800 to 2.5.7
Scales: breed11
- Music
- Bodacious Breed (archived 2010) by Gene Ward Smith – details | play – breed in 441edo tuning
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
Comma list: 243/242, 441/440
Mapping: [⟨1 1 1 2 2], ⟨0 2 1 1 5], ⟨0 0 2 1 0]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.5034, ~10/7 = 617.8275
Optimal ET sequence: 27e, 31, 41, 58, 72, 130, 202
Badness: 0.241 × 10-3
Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9
Jovial
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440
Mapping: [⟨1 1 1 2 2 1], ⟨0 2 1 1 5 11], ⟨0 0 2 1 0 -1]]
Minimax tuning:
- 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.13/9
- 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.7179, ~10/7 = 617.8286
Optimal ET sequence: 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e
Badness: 0.624 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 595/594
Mapping: [⟨1 1 1 2 2 1 3], ⟨0 2 1 1 5 11 9], ⟨0 0 2 1 0 -1 -3]]
Minimax tuning:
- 17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.6947, ~10/7 = 617.5315
Optimal ET sequence: 27effg, 31fg, 41, 58, 72, 130, 171, 243
Badness: 0.741 × 10-3
Heartlandia
Subgroup: 2.3.5.7.11.13.17
Comma list: 243/242, 364/363, 441/440, 1452/1445
Mapping: [⟨1 1 1 2 2 1 3], ⟨0 4 0 1 10 23 12], ⟨0 0 2 1 0 -1 -1]]
- mapping generators: ~2, ~119/108, ~27/17
Optimal tuning (POTE): ~2 = 1\1, ~119/108 = 175.4177, ~27/17 = 793.9762
Optimal ET sequence: 14cf, 27effg, 41, 89, 130g
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 243/242, 324/323, 364/363, 441/440
Mapping: [⟨1 1 1 2 2 1 3 3], ⟨0 4 0 1 10 23 12 4], ⟨0 0 2 1 0 -1 -1 1]]
Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.3862, ~19/12 = 793.9558
Optimal ET sequence: 14cf, 27effg, 41, 89, 130g
Jofur
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 243/242
Mapping: [⟨1 1 1 2 2 4], ⟨0 2 1 1 5 -1], ⟨0 0 2 1 0 0]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.4477, ~10/7 = 618.8891
Optimal ET sequence: 27e, 31, 41, 58, 99ef, 157eff
Badness: 0.749 × 10-3
Jovis
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 441/440
Mapping: [⟨1 1 1 2 2 2], ⟨0 2 1 1 5 -3], ⟨0 0 2 1 0 5]]
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.3935, ~10/7 = 618.1036
Optimal ET sequence: 27e, 31, 45ef, 58, 72, 103, 130, 233, 363
Badness: 0.542 × 10-3
Agni
Subgroup: 2.3.5.7.11
Comma list: 385/384, 1375/1372
Mapping: [⟨1 1 1 2 5], ⟨0 2 1 1 0], ⟨0 0 2 1 -3]]
Mapping to lattice: [⟨0 2 1 1 0], ⟨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
- [[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⟩]
- eigenmonzo (unchanged-interval) basis: 2.3.11/5
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 350.7145, ~10/7 = 617.0044
Optimal ET sequence: 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee
Badness: 0.494 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624, 1375/1372
Mapping: [⟨1 1 1 2 5 -1], ⟨0 2 1 1 0 2], ⟨0 0 2 1 -3 8]]
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 350.6803, ~10/7 = 617.1448
Optimal ET sequence: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff
Badness: 0.923 × 10-3
Zisa
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 5632/5625
Mapping: [⟨1 1 1 2 -3], ⟨0 2 1 1 8], ⟨0 0 2 1 8]]
Optimal ET sequence: 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c
Badness: 0.640 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 4096/4095
Mapping: [⟨1 1 1 2 -3 7], ⟨0 2 1 1 8 -6], ⟨0 0 2 1 8 -3]]
Optimal ET sequence: 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241
Badness: 0.830 × 10-3
Lif
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 131072/130977
Mapping: [⟨1 1 1 2 8], ⟨0 2 1 1 -12], ⟨0 0 2 1 -2]]
Optimal tuning (CTE): ~2 = 1\1, ~49/40 = 351.0959, ~10/7 = 617.6652
Optimal ET sequence: 41, 89, 130, 229, 270, 581, 670, 711, 981, 1251, 2232e
Badness: 0.793 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095
Mapping: [⟨1 1 1 2 8 7], ⟨0 2 1 1 -12 -6], ⟨0 0 2 1 -2 -3]]
Optimal tuning (CTE): ~2 = 1\1, ~49/40 = 351.0960, ~10/7 = 617.6533
Optimal ET sequence: 41, 89, 99, 130, 270, 581, 711, 981, 1292, 1562
Badness: 0.579 × 10-3
2.3.5.7.11.13.19 subgroup
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400
Sval mapping: [⟨1 1 1 2 8 7 0], ⟨0 2 1 1 -12 -6 11], ⟨0 0 2 1 -2 -3 2]]
Optimal tuning (CTE): ~2 = 1\1, ~49/40 = 351.1007, ~10/7 = 617.6501
Optimal ET sequence: 41, 89, 130, 229, 270, 581, 851, 1562, 1832, 2413
Badness: 0.499 × 10-3
Baldur
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800
Mapping: [⟨2 0 1 3 7], ⟨0 2 1 1 -2], ⟨0 0 2 1 3]]
- mapping generators: ~99/70, ~343/198, ~10/7
- [[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⟩]
- eigenmonzo (unchanged-interval) basis: 2.5.11/7
Optimal ET sequence: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de
Badness: 0.166 × 10-3
Projection pairs: 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: [⟨2 0 1 3 7 -1], ⟨0 2 1 1 -2 4], ⟨0 0 2 1 3 2]]
Optimal ET sequence: 58, 72, 130, 198, 270, 940, 1210f
Badness: 0.433 × 10-3
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
Freya
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 3025/3024
Mapping: [⟨1 1 3 3 2], ⟨0 2 3 2 1], ⟨0 0 -4 -2 3]]
- mapping generators: ~2, ~49/40, ~55/42
- 11-odd-limit eigenmonzos (unchanged-intervals): 2, 14/11, 4/3
Optimal ET sequence: 31, 41, 72, 167, 188, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee
Badness: 0.170 × 10-3
Projection pairs: ~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
Mapping: [⟨1 1 3 3 2 4], ⟨0 2 3 2 1 -9], ⟨0 0 -4 -2 3 6]]
Optimal ET sequence: 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615
Badness: 0.855 × 10-3
Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3
Eir
VIxen named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the ibnsinma that evokes associations with medicine.
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 3025/3024
Mapping: [⟨1 1 3 3 2 0], ⟨0 2 3 2 1 6], ⟨0 0 -4 -2 3 5]]
Optimal ET sequence: 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f
Badness: 0.581 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
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: 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815
Badness: 0.700 × 10-3
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
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
Optimal ET sequence: 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815
Badness: 0.692 × 10-3
Heimlaug
VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the fairytale comma and the ainisma, both adding to the mystical theme. The one of prophecy is bolstered by that this extension has benediction as a subtemperament.
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 3025/3024
Mapping: [⟨1 1 3 3 2 7], ⟨0 2 3 2 1 6], ⟨0 0 -4 -2 3 -13]]
Optimal ET sequence: 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f
Badness: 0.601 × 10-3
17-limit
Equave 10/7 and 16-note scales with that period are of interest.
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
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: 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270
Badness: 0.829 × 10-3
Vili
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 391314/390625
Mapping: [⟨1 1 5 4 10], ⟨0 2 3 2 6], ⟨0 0 -6 -3 -14]]
Optimal ET sequence: 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583
Badness: 1.26 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 4225/4224
Mapping: [⟨1 1 5 4 10 4], ⟨0 2 3 2 6 1], ⟨0 0 -6 -3 -14 -1]]
Optimal ET sequence: 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f
Badness: 0.738 × 10-3
Frigg
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 644204/643125
Mapping: [⟨1 1 3 3 4], ⟨0 2 3 2 4], ⟨0 0 -10 -5 -11]]
Optimal ET sequence: 45e, 58, 103, 161, 212, 270, 643, 913, 1183e
Badness: 1.79 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 1716/1715, 10648/10647
Mapping: [⟨1 1 3 3 4 5], ⟨0 2 3 2 4 3], ⟨0 0 -10 -5 -11 -14]]
Optimal ET sequence: 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef *
Badness: 0.934 × 10-3
Ennealimmic
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 4375/4374
Mapping: [⟨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: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd
Badness: 0.275 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4375/4374
Mapping: [⟨9 1 1 12 0 -31], ⟨0 2 3 2 0 5], ⟨0 0 0 0 1 1]]
Optimal ET sequence: 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e
Badness: 0.755 × 10-3