Garischisma
Ratio | 33554432/33480783 |
Factorization | 2^{25} × 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 (log_{2} nd) | 49.9968 |
Weil height (log_{2} max(n, d)) | 50 |
Wilson height (sopfr (nd)) | 99 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.3331 bits |
Comma size | small |
open this interval in xen-calc |
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.