540/539: Difference between revisions

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{{Infobox Interval

~~| Ratio = 540/539~~

~~| Monzo = 2 3 1 -2 -1~~

~~| Cents = 3.20896~~

| Name = swetisma

| Color name =

| Color name = 1urry-2, lururuyo negative 2nd

| ~~FJS name =~~

| Comma = yes

~~| Sound~~ =

}}

'''540/539''', the '''swetisma''', is a [[comma]] in the [[11-limit]], equal to ([[15/11]])/([[7/6]])<sup>2</sup>, to ([[12/11]])([[15/14]])/([[7/6]]) ~~or to~~ ([[99/98]])/([[121/120]]). ~~Thus, tempering~~ any two of 99/98, 121/120 and 540/539 will result in the third of the three being tempered, resulting in the rank-3 temperament [[~~Big Brother~~]]. More generally, tempering 540/539 leads to [[swetismic temperaments]].

'''540/539''', the '''swetisma''', is an [[unnoticeable comma]] in the [[11-limit]], equal to ([[15/11]])/([[7/6]])<sup>2</sup> or to ([[12/11]])([[15/14]])/([[7/6]]). In terms of commas, it is ([[99/98]])/([[121/120]]), ([[225/224]])/([[385/384]]), and ([[243/242]])/([[441/440]]).

== Temperaments ==

[[Tempering out]] any two of 99/98, 121/120 and 540/539 will result in the third of the three being tempered, resulting in the rank-3 temperament [[big brother]]. More generally, tempering out 540/539 leads to [[swetismic temperaments]] and enables [[swetismic chords]].

See [[Rank-4 temperament #Swetismic (540/539)]] for the rank-4 swetismic temperament. See [[Swetismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

== Etymology ==

The swetisma was named by [[Manuel Op de Coul]] no later than 2004, after the Dutch ethnomusicologist Wouter Swets<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10195.html#10199 Yahoo! Tuning Group | ''Comma names'']</ref>.

== See also ==

* [[Swetismic chords]]

* [[Rank-4 temperament #Swetismic (540/539)]]

* [[Swetismic temperaments]], a collection of rank-3 temperaments where it is tempered out

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

~~[[Category:11-limit]]~~

== Notes ==

~~[[Category:Unnoticeable commas]]~~

~~[[Category:Superparticular]]~~

[[Category:Swetismic]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 540/539
-| Monzo = 2 3 1 -2 -1
-| Cents = 3.20896
 | Name = swetisma
-| Color name =
+| Color name = 1urry-2, lururuyo negative 2nd
-| FJS name =
+| Comma = yes
-| Sound =
 }}
-'''540/539''', the '''swetisma''', is a [[comma]] in the [[11-limit]], equal to ([[15/11]])/([[7/6]])<sup>2</sup>, to ([[12/11]])([[15/14]])/([[7/6]]) or to ([[99/98]])/([[121/120]]). Thus, tempering any two of 99/98, 121/120 and 540/539 will result in the third of the three being tempered, resulting in the rank-3 temperament [[Big Brother]]. More generally, tempering 540/539 leads to [[swetismic temperaments]].
+'''540/539''', the '''swetisma''', is an [[unnoticeable comma]] in the [[11-limit]], equal to ([[15/11]])/([[7/6]])<sup>2</sup> or to ([[12/11]])([[15/14]])/([[7/6]]). In terms of commas, it is ([[99/98]])/([[121/120]]), ([[225/224]])/([[385/384]]), and ([[243/242]])/([[441/440]]).
+== Temperaments ==
+[[Tempering out]] any two of 99/98, 121/120 and 540/539 will result in the third of the three being tempered, resulting in the rank-3 temperament [[big brother]]. More generally, tempering out 540/539 leads to [[swetismic temperaments]] and enables [[swetismic chords]].
+See [[Rank-4 temperament #Swetismic (540/539)]] for the rank-4 swetismic temperament. See [[Swetismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.
+== Etymology ==
+The swetisma was named by [[Manuel Op de Coul]] no later than 2004, after the Dutch ethnomusicologist Wouter Swets<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10195.html#10199 Yahoo! Tuning Group | ''Comma names'']</ref>.
 == See also ==
-* [[Swetismic chords]]
-* [[Rank-4 temperament #Swetismic (540/539)]]
-* [[Swetismic temperaments]], a collection of rank-3 temperaments where it is tempered out
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-[[Category:11-limit]]
+== Notes ==
-[[Category:Unnoticeable commas]]
-[[Category:Superparticular]]
 [[Category:Swetismic]]
+[[Category:Commas named after music theorists]]