1125edo

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1125edo

1126edo →

Prime factorization	32 × 53
Step size	1.06667 ¢
Fifth	658\1125 (701.867 ¢)
Semitones (A1:m2)	106:85 (113.1 ¢ : 90.67 ¢)
Consistency limit	15
Distinct consistency limit	15

1125 equal divisions of the octave (abbreviated 1125edo or 1125ed2), also called 1125-tone equal temperament (1125tet) or 1125 equal temperament (1125et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1125 equal parts of about 1.07 ¢ each. Each step represents a frequency ratio of 2^1/1125, or the 1125th root of 2.

1125edo is a good 13-limit system, distinctly consistent to the 15-odd-limit, and the no-11 or no-17 29-odd-limit. It tempers out 2401/2400, 4375/4374, and 250047/250000 in the 7-limit, supporting ennealimmal.

Prime harmonics

Approximation of prime harmonics in 1125edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.088	-0.180	-0.293	+0.149	+0.006	-0.422	+0.087	-0.008	-0.244	-0.502
	Relative (%)	+0.0	-8.3	-16.9	-27.4	+13.9	+0.5	-39.6	+8.2	-0.7	-22.9	-47.1
Steps (reduced)		1125 (0)	1783 (658)	2612 (362)	3158 (908)	3892 (517)	4163 (788)	4598 (98)	4779 (279)	5089 (589)	5465 (965)	5573 (1073)

Subsets and supersets

Snce 1125 factors into 3² × 5³, 1125edo has subset edos 3, 5, 9, 15, 25, 45, 75, 125, 225, 375.