1029/1024: Difference between revisions

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'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[7-limit]] (also 2.3.7 subgroup) [[~~small~~ comma]] measuring about 8.4 ~~cents~~. It is the amount by which a stack of three [[8/7]]s falls short of [[3/2]]. ~~Tempering out this~~ comma ~~for the~~ 2.3.7 subgroup ~~leads to~~ [[~~slendric~~]] ~~temperament. In addition to the perfect fifth being split into three equal parts, the~~ [[~~256~~/~~243~~|~~Pythagorean limma (256~~/~~243)~~]] ~~is also split into three in the same way, one for~~ [[64/63]]~[[49/48]] ~~and two for~~ [[28/27]]~~. It therefore provides the little interval known as a~~ [[~~quark~~]].

'''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 ==

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 7~~-limit~~ leads to the rank-3 [[~~gamelismic~~]] temperament, or in the ~~2.3.~~7 ~~[[subgroup]]~~, the rank-2 [[~~slendric~~]] temperament. In either case, it enables the [[slendric pentad]]. 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.

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>.

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 ==

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-'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[7-limit]] (also 2.3.7 subgroup) [[small comma]] measuring about 8.4 cents. It is the amount by which a stack of three [[8/7]]s falls short of [[3/2]]. Tempering out this comma for the 2.3.7 subgroup leads to [[slendric]] temperament. In addition to the perfect fifth being split into three equal parts, the [[256/243|Pythagorean limma (256/243)]] is also split into three in the same way, one for [[64/63]]~[[49/48]] and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].
+'''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 ==
+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 7-limit leads to the rank-3 [[gamelismic]] temperament, or in the 2.3.7 [[subgroup]], the rank-2 [[slendric]] temperament. In either case, it enables the [[slendric pentad]]. 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.
+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>.
+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 ==