540/539: Difference between revisions

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'''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.

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== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

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 | 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.
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 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]