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, slendro diesis
Color name	zz2, 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]
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English Wikipedia has an article on:

Septimal diesis

49/48, the large septimal diesis (or slendro diesis), is a 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 12edo.

49/48 is tempered out in 15edo and 19edo, where the two intervals are equated, and the fourth is split in a perfect half. 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 also

• Semiphore family, the rank-3 family where it is tempered out
• Slendro clan, the rank-2 clan where it is tempered out
• Medium comma
• List of superparticular intervals
• Gallery of just intervals