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 norm (log2 nd)	11.2586
Weil norm (log2 max(n, d))	11.2877
Wilson norm (sopfr(nd))	26
Comma size	medium
S-expression	S5/S7
Open this interval in xen-calc

English Wikipedia has an article on:

Septimal third tone #Septimal sixth tone

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).

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. In the full 7-limit, this comma further equates 15/14 and 21/20 and enables all the jubilismic chords.

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
• (49/48)/(50/49) = 2401/2400
• (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.

Approximations

Edo approximations for 50/49 (34.98 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
31	1\31	38.71	+3.73	+9.65
32	1\32	37.50	+2.52	+6.73
33	1\33	36.36	+1.39	+3.82
34	1\34	35.29	+0.32	+0.90
35	1\35	34.29	-0.69	-2.01
36	1\36	33.33	-1.64	-4.93
37	1\37	32.43	-2.54	-7.84
66	2\66	36.36	+1.39	+7.63
67	2\67	35.82	+0.85	+4.72
68	2\68	35.29	+0.32	+1.80
69	2\69	34.78	-0.19	-1.11
70	2\70	34.29	-0.69	-4.02
71	2\71	33.80	-1.17	-6.94
72	2\72	33.33	-1.64	-9.85

Etymology

The name jubilisma is likely a reference to the 50-year biblical jubilee cycle.

See also

• List of superparticular intervals
• 49/48 – the large septimal sixth-tone