Septischisma

The septischisma or garysma is a very small 7-limit comma measuring about 3.80 cents. It can be considered the septimal counterpart of the schisma: whereas the schisma is the difference between the Pythagorean comma and the syntonic comma, the garischisma is the difference between the septimal comma and the Pythagorean comma. Equivalently, it can be described as the amount by which a stack of two apotomes falls short of a septimal whole tone. It is also the difference between the aberschisma and the schisma in the full 7-limit.

Interval information

Ratio	33554432/33480783
Factorization	225 × 3-14 × 7-1
Monzo	[25 -14 0 -1⟩
Size in cents	3.804081¢
Names	septischisma, garysma
Color name	ssr2, sasaru 2nd, ssrM, sasaruma
FJS name	[math]\displaystyle{ \text{d2}_{7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	49.9968
Weil norm (log2 max(n, d))	50
Wilson norm (sopfr(nd))	99
Comma size	small
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It factors into the following 11- and 13-limit commas:

• The symbiotic comma and olympia;
• The wilschisma and the minisma.

Temperaments

Tempering out this comma in the full 7-limit leads to the rank-3 septischismic temperament, or in the 2.3.7 subgroup, the rank-2 gary temperament. See Garischismic family for the family of rank-3 temperaments where it is tempered out. See Garischismic clan for the clan of rank-2 temperaments where it is tempered out.

Etymology

Its name used to be garischisma, which comes from the temperament garibaldi and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. This etymology partly lingers in the subgroup temperament gary. The current name is trivial.