280edo: Difference between revisions

Revision as of 06:11, 8 March 2024

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.

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
Error	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)

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.

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 {{EDO intro|280}}
-edo is [[enfactoring|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]].
+edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as [[140edo]]. It has a [[consistency|consistency limit]] of only 7. The approximation of [[11/1|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 ===
 {{Harmonics in equal|280}}
-=== Divisors ===
+=== Subsets and supersets ===
 Since 280 factors into 2<sup>3</sup> × 5 × 7, it has subset edos {{EDOs| 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, and 140 }}.
 [[Category:Enki]]