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== Breed ==
== Breed ==
Breed has the same lattice structure as 2.5.7 JI. In terms of extension from the 5-limit, it splits 25/6 into four equal parts representing 10/7.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Revision as of 23:42, 1 February 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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

Breed has the same lattice structure as 2.5.7 JI. In terms of extension from the 5-limit, it splits 25/6 into four equal parts representing 10/7.

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°

Minimax tuning:

Optimal tunings:

  • WE: ~2 = 1200.021¢, ~49/40 = 350.972¢, ~10/7 = 617.683¢
  • CWE: ~2 = 1200.000¢, ~49/40 = 350.974¢, ~10/7 = 617.681¢

Optimal ET sequence: 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d

Badness (Sintel): 0.067

Projection pair: ~3 = ~2401/800 to 2.5.7

Scales: breed11

Music

Jove

Main article: 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]]

Minimax tuning:

Optimal tunings:

  • WE: ~2 = 1200.098¢, ~11/9 = 350.532¢, ~10/7 = 617.878¢
  • CWE: ~2 = 1200.000¢, ~11/9 = 350.537¢, ~10/7 = 617.871¢

Optimal ET sequence: 27e, 31, 41, 58, 72, 130, 202

Badness (Sintel): 0.290

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 unchanged-interval (eigenmonzo) basis: 2.9/5.13/9
  • 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13

Optimal tunings:

  • WE: ~2 = 1199.977¢, ~11/9 = 350.711¢, ~10/7 = 617.817¢
  • CWE: ~2 = 1200.000¢, ~11/9 = 350.713¢, ~10/7 = 617.818¢

Optimal ET sequence: 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e

Badness (Sintel): 0.583

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 unchanged-interval (eigenmonzo) basis: 2.5/3.17/9

Optimal tunings:

  • WE: ~2 = 1200.088¢, ~11/9 = 350.720¢, ~10/7 = 617.577¢
  • CWE: ~2 = 1200.000¢, ~11/9 = 350.714¢, ~10/7 = 617.561¢

Optimal ET sequence: 27effg, 31fg, 41, 58, 72, 130, 171, 243

Badness (Sintel): 0.704

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 tunings:

  • WE: ~2 = 1199.559¢, ~119/108 = 175.353¢, ~27/17 = 793.685¢
  • CWE: ~2 = 1200.000¢, ~119/108 = 175.371¢, ~27/17 = 793.756¢

Optimal ET sequence: 14cf, 27effg, 41, 89, 130g

Badness (Sintel): 2.843

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 tunings:

  • WE: ~2 = 1199.733¢, ~21/19 = 175.347¢, ~19/12 = 793.779¢
  • CWE: ~2 = 1200.000¢, ~21/19 = 175.358¢, ~19/12 = 793.819¢

Optimal ET sequence: 14cf, 27effg, 41, 89, 130g

Badness (Sintel): 2.294

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 tunings:

  • WE: ~2 = 1198.953¢, ~11/9 = 351.141¢, ~10/7 = 618.349¢
  • CWE: ~2 = 1200.000¢, ~11/9 = 351.254¢, ~10/7 = 618.593¢

Optimal ET sequence: 27e, 31, 41, 58, 99ef, 157eff

Badness (Sintel): 0.701

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 tunings:

  • WE: ~2 = 1200.144¢, ~11/9 = 350.435¢, ~10/7 = 618.177¢
  • CWE: ~2 = 1200.000¢, ~11/9 = 350.440¢, ~10/7 = 618.176¢

Optimal ET sequence: 27e, 31, 45ef, 58, 72, 103, 130, 233, 363

Badness (Sintel): 0.507

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

Minimax tuning:

[[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⟩]
unchanged-interval (eigenmonzo) basis: 2.3.11/5

Optimal tunings:

  • WE: ~2 = 1200.417¢, ~49/40 = 350.836¢, ~10/7 = 617.219¢
  • CWE: ~2 = 1200.000¢, ~49/40 = 350.837¢, ~10/7 = 616.991¢

Optimal ET sequence: 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee

Badness (Sintel): 0.593

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 tunings:

  • WE: ~2 = 1200.441¢, ~49/40 = 350.809¢, ~10/7 = 617.372¢
  • CWE: ~2 = 1200.000¢, ~49/40 = 350.805¢, ~10/7 = 617.157¢

Optimal ET sequence: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff

Badness (Sintel): 0.863

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

Minimax tuning:

[[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⟩]
unchanged-interval (eigenmonzo) basis: 2.5.11/7

Optimal tunings:

  • WE: ~99/70 = 600.015¢, ~343/198 = 950.972¢, ~10/7 = 617.701¢
  • CWE: ~99/70 = 600.000¢, ~343/198 = 950.956¢, ~10/7 = 617.702¢

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

Badness (Sintel): 0.200

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 tunings:

  • WE: ~99/70 = 599.987¢, ~26/15 = 951.054¢, ~10/7 = 617.806¢
  • CWE: ~99/70 = 600.000¢, ~26/15 = 951.069¢, ~10/7 = 617.807¢

Optimal ET sequence: 58, 72, 130, 198, 270, 940, 1210f

Badness (Sintel): 0.415

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

Midnatssol

Subgroup: 2.3.5.7.11.13.17

Comma list: 289/288, 442/441, 561/560, 676/675

Mapping: [⟨2 0 1 3 7 -1 5], ⟨0 2 1 1 -2 4 2], ⟨0 0 2 1 3 2 0]]

Optimal tunings:

  • WE: ~17/12 = 600.112¢, ~26/15 = 951.191¢, ~10/7 = 617.610¢
  • CWE: ~17/12 = 600.000¢, ~26/15 = 951.063¢, ~10/7 = 617.584¢

Optimal ET sequence: 58, 72, 130, 140, 198, 270g

Badness (Sintel): 0.720

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

Minimax tuning:

  • 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 *

* optimal patent val: 1241

Badness: 0.934 × 10-3

Ennealimmic

Not to be confused with Ennealimnic.

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

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