540/539: Difference between revisions
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'''540/539''', the '''swetisma''', is | '''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 == | == 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. | 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 == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Revision as of 13:34, 22 June 2024
| Interval information |
reduced
540/539, the swetisma, is an unnoticeable comma in the 11-limit, equal to (15/11)/(7/6)2 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[1].