49/48
Ratio | 49/48 |
Factorization | 2^{-4} × 3^{-1} × 7^{2} |
Monzo | [-4 -1 0 2⟩ |
Size in cents | 35.696812¢ |
Names | large septimal diesis, slendro diesis |
Color name | zz2, zozo 2nd, Zozo comma |
FJS name | [math]\text{m2}^{7,7}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 11.1997 |
Weil height (log_{2} max(n, d)) | 11.2294 |
Wilson height (sopfr (nd)) | 25 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.62964 bits |
Comma size | medium |
S-expression | S7 |
[sound info] | |
open this interval in xen-calc |
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