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]].

== 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 ==

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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]].
 == 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 ==