1029/1024

Interval information

Ratio	1029/1024
Factorization	2-10 × 3 × 73
Monzo	[-10 1 0 3⟩
Size in cents	8.43272 ¢
Names	slendric comma, gamelisma, gamelan residue
Color name	Lz32, latrizo 2nd, Latrizo comma
FJS name	[math]\displaystyle{ \text{m2}^{7,7,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	20.007
Weil norm (log2 max(n, d))	20.0141
Wilson norm (sopfr(nd))	44
Comma size	small
S-expression	S7/S8
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1029/1024, the slendric comma or gamelisma, is a small 7-limit (also 2.3.7-subgroup) comma measuring about 8.43 cents. It is the amount by which a stack of three 8/7's falls short of 3/2, and the ratio between 49/48 (S7) and 64/63 (S8), which gives it the S-expression of S7/S8, making it an ultraparticular comma.

Commatic relations

This comma is the difference between a Pythagorean limma and a stack of three septimal commas, as well as the difference between a Pythagorean countercomma and a stack of three septimal schismas.

In the full 7-limit it factorizes into superparticulars as (225/224)⋅(2401/2400). It also factorizes into the following constituent superparticulars in the higher limits:

• 385/384 and 441/440 (subgroup: 2.3.5.7.11)
• 343/342 and 513/512 (subgroup: 2.3.7.19)
• 273/272 and 833/832 (subgroup: 2.3.7.13.17)
• 217/216 and 3969/3968 (subgroup: 2.3.7.31)

Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7's while doing minimal additional damage to 2.3.7 itself.

Temperaments

Tempering out this comma alone in the 2.3.7 subgroup leads to the rank-2 slendric temperament, or in the full 7-limit, the rank-3 gamelismic temperament. In either case, it enables the slendric pentad, and the perfect fifth is split into three equal parts, one for 8/7 and two for 21/16. In addition, the Pythagorean limma is also split into three, one for 64/63~49/48 and two for 28/27. It therefore provides the little interval known as a quark.

See Gamelismic family for the rank-3 family where it is tempered out. See Gamelismic clan for the rank-2 clan where it is tempered out.

Etymology

This comma was known as the gamelan residue no later than May 2001. It was allegedly named by Adriaan Fokker. The name gamelisma, a contracted form of gamelan residue, appeared somewhat later.

It may also be called the slendrisma or gamelic comma, as systematic derivations of slendric comma and gamelisma, respectively.

Trivia

This comma differs from the orgonisma by a tiny margin, 67110351/67108864 (0.04 ¢).