# 540/539

 Ratio 540/539 Factorization 22 × 33 × 5 × 7-2 × 11-1 Monzo [2 3 1 -2 -1⟩ Size in cents 3.2089612¢ Name swetisma Color name 1urry-2, lururuyo negative 2nd FJS name $\text{d}{-2}^{5}_{7,7,11}$ 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, $\sqrt{nd}$) ~1.29549 bits Comma size unnoticeable S-expression S12 / S14 open this interval in xen-calc

540/539, the swetisma, is a 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).

## 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

The swetisma was named by Manuel Op de Coul no later than 2004, after the Dutch ethnomusicologist Wouter Swets[1].