Garischisma
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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{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 two apotomes.
Temperaments
Tempering it out in the full 7-limit leads to the rank-3 garischismic temperament.
Garischismic (41 & 53 & 270)
Subgroup: 2.3.5.7
Comma list: 33554432/33480783
Mapping: [⟨1 0 0 25], ⟨0 1 0 -14], ⟨0 0 1 0]]
POTE generators: ~3/2 = 702.2079, ~5/4 = 386.5100
Optimal GPV sequence: 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd
Badness: 1.313 × 10^{-3}
See also
- Garischismic clan, the rank-2 clan where it is tempered out
- Small comma