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. 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.

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.

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	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