50/49

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Interval information
Ratio 50/49
Factorization 2 × 52 × 7-2
Monzo [1 0 2 -2
Size in cents 34.975615¢
Names jubilisma,
small septimal sixth-tone,
(septimal) tritonic diesis
Color name rryy-2, biruyo negative 2nd,
Biruyo comma
FJS name [math]\text{d}{-2}^{5,5}_{7,7}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 11.2586
Weil height (log2 max(n, d)) 11.2877
Wilson height (sopfr (nd)) 26
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.51795 bits
Comma size medium
S-expression S5 / S7
open this interval in xen-calc

50/49, the jubilisma (also small septimal sixth-tone or septimal tritonic diesis) is a 7-limit medium comma. It is the only superparticular comma in the 7-limit aside from 126/125 which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = (10/7)/(7/5). It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, however, it can be equated with other commas; for example (36/35)/(50/49) = 126/125, (45/44)/(50/49) = 441/440, (50/49)/(55/54) = 540/539, (50/49)/(56/55) = 1375/1372, (50/49)/(64/63) = 225/224, (50/49)/(65/64) = 640/637, (50/49)/(66/65) = 1625/1617, (50/49)/(78/77) = 275/273 and (50/49)/(81/80) = 4000/3969.

Temperaments

Tempering out this comma equates the 7/5 with 10/7, its octave complement, leading to temperaments where the square root of two does service for both. See Jubilismic family for the rank-3 family where it is tempered out. See Jubilismic clan for the rank-2 clan where it is tempered out.

Equal temperaments tempering out 50/49 include 12edo, 22edo, 26edo, 38edo, 48edo and 54edo.

See also