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]]) [[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]].

== Commatic relations ==

This comma factorizes into [[superparticular]]s as:

* [[273/272]] × [[833/832]] (subgroup: 2.3.7.13.17)

* [[385/384]] × [[441/440]] (subgroup: 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 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]].

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.

@@ Line 6: / Line 6: @@
 '''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]].
+== Commatic relations ==
+This comma factorizes into [[superparticular]]s as:
+* [[273/272]] × [[833/832]] (subgroup: 2.3.7.13.17)
+* [[385/384]] × [[441/440]] (subgroup: 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 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]].
+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.