27/25
Ratio | 27/25 |
Factorization | 3^{3} × 5^{-2} |
Monzo | [0 3 -2⟩ |
Size in cents | 133.23757¢ |
Names | large limma, acute minor second |
Color name | gg2, gugu 2nd |
FJS name | [math]\text{m2}_{5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 9.39874 |
Weil height (log_{2} max(n, d)) | 9.50978 |
Wilson height (sopfr (nd)) | 19 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.25507 bits |
Comma size | large |
S-expressions | S6^{2} × S7, S3 / S5 |
[sound info] | |
open this interval in xen-calc |
27/25, called the large limma or acute minor second, at 133.238 cents is a large semitone interval which is a syntonic comma above the 5-limit minor second 16/15, or 2 syntonic commas above the Pythagorean minor second 256/243. It has the remarkable property of almost exactly equaling a single step of 9edo, a step of which is 133 1/3 cents. Hence, nine large limmas fall just short of an octave by the ennealimma which is [1 -27 18⟩, a comma of less than a cent in size. If all of that were not enough, two large limmas are almost exactly a subminor third, since (7/6)/(27/25)^{2} = 4375/4374. Tempering out both the ennealimma and 4375/4374, the ragisma, leads to the ennealimmal temperament. Ennealimmal is an extremely accurate temperament, while still being of a somewhat manageable complexity. Turning from microtempering to exotempering, 27/25 can be tempered out, leading to the bug family of temperaments Coincidentally, 27/25 is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively.