Garischisma

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Interval information
Ratio 33554432/33480783
Factorization 225 × 3-14 × 7-1
Monzo [25 -14 0 -1
Size in cents 3.8040814¢
Names garischisma,
septimal schisma
Color name ssr2, sasaru 2nd,
Sasaru comma
FJS name [math]\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]\sqrt{n\cdot d}[/math])
~2.46027 bits
Comma size small
open this interval in xen-calc

The garischisma or septimal schisma is a 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.

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 Olympic clan #Cassaschismic for the rank-3 temperament. See Garischismic clan for the clan of rank-2 temperaments where it is tempered out.

See also