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 | [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 |
| open this interval in xen-calc | |
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].