Schismatic family: Difference between revisions

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|53EDO]] is a possible tuning for schismatic, but you need [[118edo|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.

Subgroup: 2.3.5

[[POTE generator]]: ~3/2 = 701.736

=== Seven-limit extensions ===

* Garibaldi adds [[garischisma|{{monzo|25 -14 0 -1}}]],  

* Grackle adds {{monzo|-44 26 0 1}},  

* Schism adds [[64/63|{{monzo|6 -2 0 -1}}]],  

* Pontiac adds {{monzo|-59 39 0 -1}}.  

* Bischismic adds {{monzo|-69 40 0 2}} and has a fifth generator with a half-octave period.  

* Guiron adds [[1029/1024|{{monzo|-10 1 0 3}}]], with an 8/7 generator, three of which give the fifth.  

* Term adds {{monzo|-94 54 0 3}} with a 1/3 octave period.  

* Sesquiquartififths adds {{monzo|-35 15 0 4}} and slices the fifth in four.

Temperaments discussed elsewhere include [[Sensamagic clan #Salsa|salsa]], [[Gamelismic clan #Guiron|guiron]] and [[Porwell temperaments #Hemischis|hemischis]]. Remarkable subgroup temperaments include [[No-sevens subgroup temperaments #Nestoria|nestoria]] and [[No-sevens subgroup temperaments #Photia|photia]].

{{main| Garibaldi temperament }}

Subgroup: 2.3.5.7

[[POTE generator]]: ~3/2 = 702.085