Sensamagic clan: Difference between revisions
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* ''[[clyde]]'', {245/243, 3136/3125} → [[Kleismic family #Clyde]] | * ''[[clyde]]'', {245/243, 3136/3125} → [[Kleismic family #Clyde]] | ||
* ''[[bamity]]'', {245/243, 64827/64000} → [[Amity family #Bamity]] | * ''[[bamity]]'', {245/243, 64827/64000} → [[Amity family #Bamity]] | ||
* ''[[fourfives]]'', {245/243, 235298/234375} → [[Fifive family #Fourfives]] | |||
Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo|283EDO]] is the [[optimal patent val]]. | Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo|283EDO]] is the [[optimal patent val]]. | ||
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[[Bohpier]] is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]]. | [[Bohpier]] is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]]. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with 19e&27 temperament (sensi extension).'' | This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with 19e&27 temperament (sensi extension).'' | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Pycnic == | == Pycnic == | ||
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Magus == | == Magus == | ||
Magus temperament tempers out 50331648/48828125 (salegu) in the 5-limit. This temperament can be described as 46&49 temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). Alternative extension [[Starling temperaments #Amigo|amigo]] (43&46) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out. | Magus temperament tempers out 50331648/48828125 (salegu) in the 5-limit. This temperament can be described as 46&49 temperament, which tempers out the sensamagic and 28672/28125 (sazoquingu). Alternative extension [[Starling temperaments #Amigo|amigo]] (43&46) tempers out the same 5-limit comma as the magus, but with the [[126/125|starling comma]] (126/125) rather than the sensamagic tempered out. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||