Minortonic family: Difference between revisions
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[[EDO|EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 | [[EDO|EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 | ||
__FORCETOC__ | __FORCETOC__ | ||
=Mitonic= | = Mitonic = | ||
{{see also|Ragismic microtemperaments #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. | 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. | ||
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[[Map|Map]]: [<1 16 32 -15|, <0 -17 -35 21|] | [[Map|Map]]: [<1 16 32 -15|, <0 -17 -35 21|] | ||
[[EDO| | [[EDO|EDOs]]: {{EDOs|7, 20c, 33c, 46, 125, 171}} | ||
[[Badness|Badness]]: 0.0252 | [[Badness|Badness]]: 0.0252 | ||
Revision as of 12:31, 11 October 2020
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, 20c, 33c, 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