From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 27/25
Factorization 33 × 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 (log2 nd) 9.39874
Weil height (log2 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 S62 × 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.

See also