540/539

Interval information

Ratio	540/539
Factorization	22 × 33 × 5 × 7-2 × 11-1
Monzo	[2 3 1 -2 -1⟩
Size in cents	3.208961¢
Name	swetisma
Color name	1urry-2, lururuyo negative 2nd
FJS name	[math]\text{d}{-2}^{5}_{7,7,11}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	18.151
Weil height (log2 max(n, d))	18.1536
Wilson height (sopfr(nd))	43
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.29549 bits
Comma size	unnoticeable
S-expression	S12 / S14
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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.

See also

• List of superparticular intervals