27/25
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.
| Interval information |
acute minor second
S3/S5
[sound info]
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 9 | 1\9 | 133.33 | +0.10 | +0.07 |
| 18 | 2\18 | 133.33 | +0.10 | +0.14 |
| 27 | 3\27 | 133.33 | +0.10 | +0.22 |
| 36 | 4\36 | 133.33 | +0.10 | +0.29 |
| 45 | 5\45 | 133.33 | +0.10 | +0.36 |
| 54 | 6\54 | 133.33 | +0.10 | +0.43 |
| 63 | 7\63 | 133.33 | +0.10 | +0.50 |
| 72 | 8\72 | 133.33 | +0.10 | +0.57 |