Garischisma

Interval information

Ratio	33554432/33480783
Factorization	225 × 3-14 × 7-1
Monzo	[25 -14 0 -1⟩
Size in cents	3.804081¢
Names	garischisma, septimal schisma
Color name	ssr2, sasaru 2nd, Sasaru comma
FJS name	[math]\displaystyle{ \text{d2}_{7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	49.9968
Weil height (log2 max(n, d))	50
Wilson height (sopfr(nd))	99
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.3331 bits
Comma size	small
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The garischisma or septimal schisma is a small 7-limit comma measuring about 3.80 cents. While the schisma is the difference between the Pythagorean comma and the syntonic comma, the garischisma, in contrast, is the difference between the Pythagorean comma and the septimal comma. It can also be described as the difference between the septimal whole tone and a stack of two apotomes.

In the 11-limit, it factors into simpler commas as (19712/19683)(131072/130977).

Temperaments

Tempering out this comma in the full 7-limit leads to the rank-3 garischismic 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.