Minortonic family

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Minortonic family tempers out the minortone comma (also known as "minortonma"), [-16 35 -17. The head of this family is five-limit minortone temperament, with generator a minor tone.

Minortone temperament

Subgroup: 2.3.5

Comma: [-16 35 -17

Mapping: [1 -1 -3], 0 17 35]]

POTE generator: ~10/9 = 182.466

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Badness: 0.029765

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 171 EDO. 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.

Subgroup: 2.3.5.7

Comma list: 4375/4374, 2100875/2097152

Mapping: [1 -1 -3 6], 0 17 35 -21]]

POTE generator: ~10/9 = 182.458

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Badness: 0.025184

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.

Subgroup: 2.3.5.7

Comma list: 250047/250000, 645700815/645657712

Mapping: [3 -3 -9 -8], 0 17 35 36]]

POTE generator: ~10/9 = 182.467

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Badness: 0.013979