50/49

Interval information

Ratio	50/49
Factorization	2 × 52 × 7-2
Monzo	[1 0 2 -2⟩
Size in cents	34.97561¢
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
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English Wikipedia has an article on:

Septimal third tone#Septimal sixth tone

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 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, 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
• (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