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This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone.
This family tempers out the minortone comma (also known as "minortonma"), {{Monzo|-16 35 -17}}. The head of this family is five-limit minortone temperament, with generator a minor tone.


[[Comma|Comma]]: |-16 35 -17>
== Minortone temperament ==
Subgroup: 2.3.5


[[POTE_tuning|POTE generator]]: ~10/9 = 182.466
[[Comma]]: {{Monzo|-16 35 -17}}


[[Map|Map]]: [<1 16 32|, <0 -17 -35|]
[[Mapping]]: [{{val|1 -1 -3}}, {{val|0 17 35}}]


[[EDO|EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091
[[POTE generator]]: ~10/9 = 182.466
__FORCETOC__
 
== Mitonic ==
{{Val list|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}
 
[[Badness]]: 0.029765
 
== Mitonic ==
{{see also|Ragismic microtemperaments #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, {{Monzo|-16 35 -17}}. Flipping that gives the 5-limit wedgie {{Multival|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|171EDO]]. The wedgie is now {{Multival|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.


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|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.
Subgroup: 2.3.5.7


[[Comma|Comma]]s: 4375/4374, 2100875/2097152
[[Comma list]]: 4375/4374, 2100875/2097152


[[POTE_generator|POTE generator]]: ~10/9 = 182.458
[[Mapping]]: [{{val|1 -1 -3 6}}, {{val|0 17 35 -21}}]


[[Map|Map]]: [<1 16 32 -15|, <0 -17 -35 21|]
[[POTE generator]]: ~10/9 = 182.458


[[EDO|EDOs]]: {{EDOs|7, 20c, 33c, 46, 125, 171}}
{{Val list|legend=1| 46, 125, 171 }}


[[Badness|Badness]]: 0.0252
[[Badness]]: 0.025184


== Domain ==
== 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 [[Chromatic_pairs#Terrain|terrain]].
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 [[Chromatic pairs #Terrain|terrain]].


[[Comma|Comma]]s: 250047/250000, 645700815/645657712
Subgroup: 2.3.5.7


[[POTE_generator|POTE generator]]: ~10/9 = 182.467
[[Comma list]]: 250047/250000, 645700815/645657712


[[Map|Map]]: [<3 14 26 28|, <0 -17 -35 -36|]
[[Mapping]]: [{{val|3 -3 -9 -8}}, {{val|0 17 35 36}}]


[[EDO|EDO]]S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038
[[POTE generator]]: ~10/9 = 182.467


[[Badness|Badness]]: 0.0140
{{Val list|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}
 
[[Badness]]: 0.013979


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Minortonic]]
[[Category:Minortonic]]
[[Category:Todo:intro]]
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