1029/1024: Difference between revisions

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{{Interwiki

| en = 1029/1024

| de = 1029/1024

}}

{{Infobox Interval

~~| JI glyph =~~

| Name = slendric comma, gamelisma, gamelan residue

~~| Ratio = 1029/1024~~

| Color name = Lz32, latrizo 2nd, Latrizo comma

~~| Monzo = -10 1 0 3~~

| Comma = yes

~~| Cents = 8.4327~~

| Name = gamelisma, gamelan residue

~~| Sound =~~

| Color name = z32, ~~trizo~~ 2nd

| ~~FJS name~~ = ~~m27,7,7~~

}}

'''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 ==

[[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]]<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.

~~'''1029/1024''', the '''gamelisma''', is the amount by which three [[8/7]]s fall short of one [[3/2]]. Tempering out this comma leads to [[slendric]] temperament.~~

== Notes ==

[[Category:~~7-limit~~]]

[[Category:Slendric]]

[[Category:~~Interval~~]]

[[Category:Gamelismic]]

[[Category:~~Small comma~~]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
+{{Interwiki
+| en = 1029/1024
+| de = 1029/1024
+}}
 {{Infobox Interval
-| JI glyph =
+| Name = slendric comma, gamelisma, gamelan residue
-| Ratio = 1029/1024
+| Color name = Lz<sup>3</sup>2, latrizo 2nd,<br>Latrizo comma
-| Monzo = -10 1 0 3
+| Comma = yes
-| Cents = 8.4327
-| Name = gamelisma, gamelan residue
-| Sound =
-| Color name = z<sup>3</sup>2, trizo 2nd
-| FJS name = m2<sup>7,7,7</sup>
 }}
+'''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 ==
+[[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]]<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.
-'''1029/1024''', the '''gamelisma''', is the amount by which three [[8/7]]s fall short of one [[3/2]]. Tempering out this comma leads to [[slendric]] temperament.
+== Notes ==
-[[Category:7-limit]]
+[[Category:Slendric]]
-[[Category:Interval]]
+[[Category:Gamelismic]]
-[[Category:Small comma]]
+[[Category:Commas named after musical traditions]]