540/539: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 4:

| Comma = yes

}}

'''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]]).

'''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 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]].

[[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.

Line 15:

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

Line 21:

Line 20:

[[Category:Swetismic]]

[[Category:Commas named after music theorists]]

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
-'''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]]).
+'''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 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]].
+[[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.
@@ Line 15: / Line 15: @@
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
@@ Line 21: / Line 20: @@
 [[Category:Swetismic]]
+[[Category:Commas named after music theorists]]