1029/1024: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = gamelisma, gamelan residue | | Name = slendric comma, gamelisma, gamelan residue | ||
| Color name = Lz<sup>3</sup>2, latrizo 2nd,<br>Latrizo comma | | Color name = Lz<sup>3</sup>2, latrizo 2nd,<br>Latrizo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''1029/1024''', the '''gamelisma''', is a [[7-limit]] (also 2.3.7 subgroup) [[ | '''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 == | ||
* [[Gamelismic family]] | This comma factorizes into [[superparticular]]s as: | ||
* [[217/216]] × [[3969/3968]] (subgroup: [[31-limit|2.3.7.31]]) | |||
* [[225/224]] × [[2401/2400]] (subgroup: [[7-limit|2.3.5.7]]) | |||
* [[273/272]] × [[833/832]] (subgroup: [[17-limit|2.3.7.13.17]]) | |||
* [[343/342]] × [[513/512]] (subgroup: [[19-limit|2.3.7.19]]) | |||
* [[385/384]] × [[441/440]] (subgroup: [[11-limit|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 [[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. | |||
== Etymology == | |||
This comma was known as the ''gamelan residue'' no later than May 2001. It was allegedly named by [[Adriaan Fokker]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_22907.html Yahoo! Tuning Group| ''Re: "Miracle Scale" -- comparing notes on an exciting week'']</ref>. 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. | |||
== Notes == | |||
[[Category:Slendric]] | [[Category:Slendric]] | ||
[[Category:Gamelismic]] | [[Category:Gamelismic]] | ||
[[Category:Commas named after musical traditions]] | |||
Latest revision as of 12:41, 11 June 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)
- 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.