540/539

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Interval information
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 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].

See also

Notes