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]\text{m2}^{7,7,7}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	20.007
Weil height (log2 max(n, d))	20.0141
Wilson height (sopfr(nd))	44
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.83722 bits
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 8.4 cents. It is the amount by which a stack of three 8/7's falls short of 3/2, and the ratio between S7 = 49/48 and S8 = 64/63, which gives it the S-expression of S7/S8, making it an ultraparticular comma.

Commatic relations

This comma factorizes into superparticulars as:

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

Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7s 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 (256/243) 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.