Schismatic family: Difference between revisions

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== Schismic ==

The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''schismic, helmholtz''', or historically '''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.

{{Main|Schismic and garibaldi}}The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''schismic, helmholtz''', or historically '''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 schismic; [[118edo]] is a more expansive schismic system with a particularly flat tuning. In exact analogy with 1/4 comma meantone there is also 1/8 schismic, 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, or even simply leaving the fifths just and collapsing schismic to a simple relabeling of the 3-limit, although the differences would be very hard to distinguish unless using a large gamut.

[[Subgroup]]: 2.3.5

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== Garibaldi ==

~~{{Main| Garibaldi temperament }}~~

Garibaldi tempers out the [[garischisma]], equating the [[64/63|septimal comma]] with both the [[syntonic comma]] and the [[Pythagorean comma]]. The 7/4 is found at -14 fifths, represented by the double diminished octave (C-Cbb), or down-minor seventh (C-vBb) with the down-arrow representing the comma step. It necessitates a sharper fifth than pure. Its [[S-expression]]-based comma list is {[[5120/5103|S8/S9]], [[225/224|S15]]}.

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 == Schismic ==
-The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''schismic, helmholtz''', or historically '''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.
+{{Main|Schismic and garibaldi}}The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''schismic, helmholtz''', or historically '''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 schismic; [[118edo]] is a more expansive schismic system with a particularly flat tuning. In exact analogy with 1/4 comma meantone there is also 1/8 schismic, 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, or even simply leaving the fifths just and collapsing schismic to a simple relabeling of the 3-limit, although the differences would be very hard to distinguish unless using a large gamut.
 [[Subgroup]]: 2.3.5
@@ Line 55: / Line 55: @@
 == Garibaldi ==
-{{Main| Garibaldi temperament }}
 Garibaldi tempers out the [[garischisma]], equating the [[64/63|septimal comma]] with both the [[syntonic comma]] and the [[Pythagorean comma]]. The 7/4 is found at -14 fifths, represented by the double diminished octave (C-Cbb), or down-minor seventh (C-vBb) with the down-arrow representing the comma step. It necessitates a sharper fifth than pure. Its [[S-expression]]-based comma list is {[[5120/5103|S8/S9]], [[225/224|S15]]}.