Misty comma
Ratio | 67108864/66430125 |
Factorization | 2^{26} × 3^{-12} × 5^{-3} |
Monzo | [26 -12 -3⟩ |
Size in cents | 17.598848¢ |
Name | misty comma |
Color name | ssg^{3}3, sasatrigu 3rd, Sasatrigu comma |
FJS name | [math]\text{ddd3}_{5,5,5}[/math] |
Special properties | reduced, reduced subharmonic |
Tenney height (log_{2} nd) | 51.9853 |
Weil height (log_{2} max(n, d)) | 52 |
Wilson height (sopfr (nd)) | 103 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~3.40939 bits |
Comma size | small |
open this interval in xen-calc |
The misty comma, 67108864/66430125 = [26 -12 -3⟩, is a small comma of 17.599 cents. It is the amount by which a stack of three ptolemaic diminished fourths (512/405) exceed the octave. It can be written as (81/80)/(32805/32768)^{2}, (2048/2025)/(32805/32768), (128/125)/(531441/524288). Since these are commas of 12edo, so is the misty comma. It factors into simpler commas as (393216/390625)(1600000/1594323). However, the misty temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of 87edo and 99edo. This temperament is notably in the schismic-Pythagorean equivalence continuum, with n = 3.
Etymology
The misty comma seems to have been named by Paul Erlich in 2002, referring to the fact that Carl Lumma "missed" this comma in a 5-limit comma search^{[1]}.