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
FJS name [math]\text{d}{-2}^{5}_{7,7,11}[/math]
Special properties superparticular,
reduced
Tenney height (log2 n⋅d) 18.151
Weil height (max(n, d)) 540
Benedetti height (n⋅d) 291060
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.4434 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, to (12/11)(15/14)/(7/6) or to (99/98)/(121/120). Thus, 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.

See also