Minortonic family

This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone.

Comma: |-16 35 -17>

POTE generator: ~10/9 = 182.466

Map: [<1 16 32|, <0 -17 -35|]

EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091

Mitonic

As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17>. Flipping that gives the 5-limit wedgie <<17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.

However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in 171edo. The wedgie is now <<17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.

Commas: 4375/4374, 2100875/2097152

POTE generator: ~10/9 = 182.458

Map: [<1 16 32 -15|, <0 -17 -35 21|]

EDOs: 7, 13, 33, 46, 125, 171

Badness: 0.0252

Domain

Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament terrain.

Commas: 250047/250000, 645700815/645657712

POTE generator: ~10/9 = 182.467

Map: [<3 14 26 28|, <0 -17 -35 -36|]

EDOS: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038

Badness: 0.0140