27/25

Interval information

Ratio	27/25
Factorization	33 × 5-2
Monzo	[0 3 -2⟩
Size in cents	133.2376¢
Names	large limma, acute minor second
Color name	gg2, gugu 2nd
FJS name	[math]\displaystyle{ \text{m2}_{5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.39874
Weil norm (log2 max(n, d))	9.50978
Wilson norm (sopfr(nd))	19
Comma size	large
S-expressions	S62⋅S7, S3/S5
[sound info]
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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.

Approximation

Edo approximations for 27/25 (133.24 ¢)
≤ 80edo, relative error ≤ 10%

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

See also

• 50/27 – its octave complement
• Gallery of just intervals
• Large comma