Septischisma

Interval information

Ratio	33554432/33480783
Factorization	225 × 3-14 × 7-1
Monzo	[25 -14 0 -1⟩
Size in cents	3.804081¢
Names	septischisma, gary comma
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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The septischisma, a.k.a. gary comma, 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 septischisma 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 Pythagorean apotomes falls short of a septimal whole tone. It is also the difference between the aberschisma and the schisma in the full 7-limit.

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 Septischismic family for the family of rank-3 temperaments where it is tempered out. See Septischismic clan for the clan of rank-2 temperaments where it is tempered out.

Etymology

The name of this comma used to be garischisma, from the temperament garibaldi and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. This name partly lingers in the subgroup temperament gary and a number of other rank-2 temperaments.

The current name is a trivial contraction of septimal schisma into one word.