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, semaphore comma, semaphoresma |
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{nd}[/math]) |
~4.52118 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.
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.