540/539: Difference between revisions

Line 3:

| Comma = yes

}}

'''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 a [[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]]).

== Temperaments ==

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]] 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 ==

Line 9:

Line 14:

== 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]]

@@ Line 3: / Line 3: @@
 | Comma = yes
 }}
-'''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 a [[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]]).
+== Temperaments ==
+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]] 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 ==
@@ Line 9: / Line 14: @@
 == 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]]