Garischisma

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
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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