1029/1024: Difference between revisions
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{{Interwiki | |||
| en = 1029/1024 | |||
| de = 1029/1024 | |||
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{{Infobox Interval | {{Infobox Interval | ||
| Name = slendric comma, gamelisma, gamelan residue | | Name = slendric comma, gamelisma, gamelan residue | ||
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| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''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 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between [[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 == | |||
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: | |||
* [[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/ | 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 == | == Temperaments == | ||
Tempering out this comma alone in the | [[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. | 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 == | == 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. | |||
== Notes == | == Notes == | ||