50/49

Interval information

Ratio	50/49
Factorization	2 × 52 × 7-2
Monzo	[1 0 2 -2⟩
Size in cents	34.97561¢
Names	small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma
Color name	rryy-2, biruyo negative 2nd, Biruyo comma
FJS name	[math]\displaystyle{ \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
Comma size	medium
S-expression	S5 / S7
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50/49, the small septimal diesis (a.k.a. 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 and 4375/4374 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, (10/7)/(7/5).

English Wikipedia has an article on:

Septimal third tone #Septimal sixth tone

Temperaments

Tempering out this comma equates the two septimal tritones (i.e. 7/5 and 10/7) with each other, leading to temperaments where sqrt(2/1) approximates both. In the 2.5.7 subgroup, this is known as the jubilic temperament, and the comma is thus known as the jubilisma.

It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, but 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
• (50/49)/(81/80) = 4000/3969

See Jubilismic family for the rank-3 family where it is tempered out, and 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