280edo

← 279edo

280edo

281edo →

Prime factorization	23 × 5 × 7
Step size	4.28571 ¢
Fifth	164\280 (702.857 ¢) (→ 41\70)
Semitones (A1:m2)	28:20 (120 ¢ : 85.71 ¢)
Consistency limit	7
Distinct consistency limit	7

280 equal divisions of the octave (abbreviated 280edo or 280ed2), also called 280-tone equal temperament (280tet) or 280 equal temperament (280et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 280 equal parts of about 4.29 ¢ each. Each step represents a frequency ratio of 2^1/280, or the 280th root of 2.

280edo is enfactored in the 7-limit, with the same tuning as 140edo. It has a consistency limit of only 7. The approximation of 11 is improved over 140edo, tempering out 3025/3024. It supplies the optimal patent val for 13-limit enki, the rank-3 temperament tempering out 325/324, 364/363, and 625/624.

Prime harmonics

Approximation of prime harmonics in 280edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.90	-0.60	-0.25	+1.54	-0.53	-2.10	-1.80	+1.73	-1.01	-0.75
	Relative (%)	+0.0	+21.0	-14.0	-5.9	+35.9	-12.3	-49.0	-42.0	+40.3	-23.5	-17.5
Steps (reduced)		280 (0)	444 (164)	650 (90)	786 (226)	969 (129)	1036 (196)	1144 (24)	1189 (69)	1267 (147)	1360 (240)	1387 (267)

Subsets and supersets

Since 280 factors into 2³ × 5 × 7, it has subset edos 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, and 140.