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
FJS name [math]\text{d2}_{7}[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 n⋅d) 49.9968
Weil height (max(n, d)) 33554432
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 sequence12, 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