540/539
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Ratio | 540/539 |
Factorization | 2^{2} × 3^{3} × 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 (log_{2} nd) | 18.151 |
Weil height (log_{2} max(n, d)) | 18.1536 |
Wilson height (sopfr (nd)) | 43 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.48492 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]}.