125edo

← 124edo

125edo

126edo →

Prime factorization	53
Step size	9.6 ¢
Fifth	73\125 (700.8 ¢)
Semitones (A1:m2)	11:10 (105.6 ¢ : 96 ¢)
Consistency limit	9
Distinct consistency limit	9

The 125 equal divisions of the octave (125edo), or the 125(-tone) equal temperament (125tet, 125et) when viewed from a regular temperament perspective, divides the octave into 125 equal parts of exactly 9.6 cents each.

Theory

125edo defines the optimal patent val for 7- and 11-limit slender temperament. It tempers out 15625/15552 in the 5-limit; 225/224 and 4375/4374 in the 7-limit; 385/384 and 540/539 in the 11-limit. In the 13-limit the 125f val ⟨125 198 290 351 432 462] does a better job, where it tempers out 169/168, 325/324, 351/350, 625/624 and 676/675, providing a good tuning for catakleismic.

Miscellaneous properties

125 is 5 cubed. Being the cube closest to division of the octave by the Germanic long hundred, 125edo has a unit step which is the cubic (fine) relative cent of 1edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-198 125⟩	[⟨125 198]]	+0.364	0.364	3.80
2.3.5	15625/15552, 17433922005/17179869184	[⟨125 198 290]]	+0.575	0.421	4.39
2.3.5.7	225/224, 4375/4374, 589824/588245	[⟨125 198 290 351]]	+0.362	0.519	5.40
2.3.5.7.11	225/224, 385/384, 1331/1323, 4375/4374	[⟨125 198 290 351 432]]	+0.528	0.570	5.94
2.3.5.7.11.13	169/168, 225/224, 325/324, 385/384, 1331/1323	[⟨125 198 290 351 432 462]] (125f)	+0.680	0.622	6.47

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	4\125	38.4	49/48	Slender
1	12\125	115.2	77/72	Semigamera
1	19\125	182.4	10/9	Minortone / mitonic
1	24\125	230.4	8/7	Gamera
1	33\125	316.8	6/5	Hanson / catakleismic
1	52\125	499.2	4/3	Gracecordial
1	61\125	585.6	7/5	Merman
5	26\125 (1\125)	249.6 (9.6)	81/70 (176/175)	Hemipental
5	52\125 (2\125)	499.2 (19.2)	4/3 (81/80)	Pental