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|2.3.7-subgroup]]) [[comma]] measuring about 8. | '''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma|small]] [[7-limit]] (also [[2.3.7 subgroup|2.3.7-subgroup]]) [[comma]] measuring about 8.43 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between [[49/48]] ({{S|7}}) and [[64/63]] ({{S|8}}), which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma. | ||
== Commatic relations == | == 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 schisma]]s | 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 schisma]]s. | ||
In the full 7-limit it factorizes into [[superparticular]]s as ([[225/224]])⋅([[2401/2400]]). It also factorizes into the following constituent superparticulars in the higher limits: | In the full 7-limit it factorizes into [[superparticular]]s as ([[225/224]])⋅([[2401/2400]]). It also factorizes into the following constituent superparticulars in the higher limits: | ||
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== Etymology == | == 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> | 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. | 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{{C}}). | |||
== References == | |||
[[Category:Slendric]] | [[Category:Slendric]] | ||
[[Category:Gamelismic]] | [[Category:Gamelismic]] | ||
[[Category:Commas named after musical traditions]] | [[Category:Commas named after musical traditions]] | ||
Latest revision as of 21:07, 22 October 2026
| 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 8.43 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.[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.
Trivia
This comma differs from the orgonisma by a tiny margin, 67110351/67108864 (0.04 ¢).