27/25
| Interval information |
acute minor second
(Shannon, [math]\sqrt{nd}[/math])
S3 / S5
[sound info]
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.