49/48

Interval information

Ratio	49/48
Factorization	2-4 × 3-1 × 72
Monzo	[-4 -1 0 2⟩
Size in cents	35.69681¢
Names	large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma
Color name	zz2, zozo 2nd, Zozo comma
FJS name	[math]\displaystyle{ \text{m2}^{7,7} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	11.1997
Weil norm (log2 max(n, d))	11.2294
Wilson norm (sopfr(nd))	25
Comma size	medium
S-expression	S7
[sound info]
Open this interval in xen-calc

English Wikipedia has an article on:

Septimal diesis

49/48, the large septimal diesis (a.k.a. large septimal sixth-tone or slendro diesis), is a 7-limit superparticular ratio spanning the small distance between a subminor third (7/6) and a supermajor second (8/7) or between the supermajor sixth (12/7) and the harmonic seventh (7/4). Measuring about 35.7 ¢, it is a medium comma; however, in classical Western music, this interval is not known as a comma as it is not tempered out in 12tet.

Temperaments

49/48 is tempered out in 15edo and 19edo, where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 subgroup, this is known as the semaphore temperament, and the comma is thus known as the semaphore comma or semaphoresma.

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:

• (49/48)/(81/80) = 245/243
• (49/48)/(64/63) = 1029/1024
• (49/48)/(3125/3072) = 3136/3125
• (49/48)/(50/49) = 2401/2400
• (128/125)/(49/48) = 6144/6125
• (36/35)/(49/48) = 1728/1715

See Semaphoresmic family for the rank-3 family where it is tempered out. See Semaphoresmic clan for the rank-2 clan where it is tempered out.

Approximations

Edo approximations for 49/48 (35.70 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
2	0\2	0.00	-35.70	-5.95
3	0\3	0.00	-35.70	-8.92
31	1\31	38.71	+3.01	+7.78
32	1\32	37.50	+1.80	+4.81
33	1\33	36.36	+0.67	+1.83
34	1\34	35.29	-0.40	-1.14
35	1\35	34.29	-1.41	-4.12
36	1\36	33.33	-2.36	-7.09
64	2\64	37.50	+1.80	+9.62
65	2\65	36.92	+1.23	+6.64
66	2\66	36.36	+0.67	+3.67
67	2\67	35.82	+0.12	+0.69
68	2\68	35.29	-0.40	-2.28
69	2\69	34.78	-0.91	-5.26
70	2\70	34.29	-1.41	-8.23

See also

• Medium comma
• List of superparticular intervals
• Gallery of just intervals