Schismatic family: Difference between revisions

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The 5-limit parent comma for the '''schismatic''' (or '''schismic''') '''family''' is the [[schisma]] of 32805/32768, which is the amount by which the [[Pythagorean comma]] exceeds the [[Didymus comma]] (81/80), or alternatively put, the difference between a [[5/4|just major third]] and a [[8192/6561|Pythagorean diminished fourth]]. The generator is a fifth and 5/4 is represented by a diminished fourth.

This defies the tradition of tertian harmony, as the just major triad on C is C~~-Fb-~~G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-vE-G.

This defies the tradition of tertian harmony, as the just major triad on C is {{nowrap|{{dash|C, F♭, G|hair|med}}}}, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as {{nowrap|{{dash|C, vE, G|hair|med}}}}.

== Schismatic aka helmholtz ==

The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''helmholtz''', '''schismic''' or '''schismatic''', which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 ~~cents~~, this falls into the range of microtempering. You could also try 1/9 schisma, with pure minor thirds and a minutely better 5th, or 2/17 schisma, with both thirds flat by 1/17 of a schisma, although the differences would be very hard to distinguish unless using a large gamut.

The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''helmholtz''', '''schismic''' or '''schismatic''', which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244{{cent}}, this falls into the range of microtempering. You could also try 1/9 schisma, with pure minor thirds and a minutely better 5th, or 2/17 schisma, with both thirds flat by 1/17 of a schisma, although the differences would be very hard to distinguish unless using a large gamut.

[[Subgroup]]: 2.3.5

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 The 5-limit parent comma for the '''schismatic''' (or '''schismic''') '''family''' is the [[schisma]] of 32805/32768, which is the amount by which the [[Pythagorean comma]] exceeds the [[Didymus comma]] (81/80), or alternatively put, the difference between a [[5/4|just major third]] and a [[8192/6561|Pythagorean diminished fourth]]. The generator is a fifth and 5/4 is represented by a diminished fourth.
-This defies the tradition of tertian harmony, as the just major triad on C is C-Fb-G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-vE-G.
+This defies the tradition of tertian harmony, as the just major triad on C is {{nowrap|{{dash|C, F&#x266D;, G|hair|med}}}}, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as {{nowrap|{{dash|C, vE, G|hair|med}}}}.
 == Schismatic aka helmholtz ==
-The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''helmholtz''', '''schismic''' or '''schismatic''', which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering. You could also try 1/9 schisma, with pure minor thirds and a minutely better 5th, or 2/17 schisma, with both thirds flat by 1/17 of a schisma, although the differences would be very hard to distinguish unless using a large gamut.
+The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''helmholtz''', '''schismic''' or '''schismatic''', which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244{{cent}}, this falls into the range of microtempering. You could also try 1/9 schisma, with pure minor thirds and a minutely better 5th, or 2/17 schisma, with both thirds flat by 1/17 of a schisma, although the differences would be very hard to distinguish unless using a large gamut.
 [[Subgroup]]: 2.3.5