1029/1024: Difference between revisions
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'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]]. | '''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. 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 == | == Commatic relations == | ||
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== Temperaments == | == 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 [[256/243|Pythagorean limma (256/243)]] is also split into three, one for | 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 [[256/243|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. | 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. | ||
Revision as of 17:58, 8 February 2025
| Interval information |
gamelisma,
gamelan residue
Latrizo comma
reduced harmonic
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[1].