1029/1024: Difference between revisions
mNo edit summary |
Expand & misc. cleanup |
||
| (9 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Interwiki | |||
| en = 1029/1024 | |||
| de = 1029/1024 | |||
}} | |||
{{Infobox Interval | {{Infobox Interval | ||
| Name = slendric comma, gamelisma, gamelan residue | | Name = slendric comma, gamelisma, gamelan residue | ||
| Line 4: | Line 8: | ||
| 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 8/7's while doing minimal additional damage to 2.3.7 itself. | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma alone in the 7 | [[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 == | == 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 == | ||
Latest revision as of 09:10, 6 May 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 8.4 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.