50/49
Ratio | 50/49 |
Factorization | 2 × 5^{2} × 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 (log_{2} nd) | 11.2586 |
Weil height (log_{2} 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
- List of superparticular intervals
- 49/48 – the large septimal sixth-tone