1029/1024
| Interval information |
gamelisma,
gamelan residue
Latrizo comma
reduced harmonic
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
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)
- 225/224 × 2401/2400 (subgroup: 2.3.5.7)
- 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[1]. 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.