590edo

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← 589edo590edo591edo →
Prime factorization 2 × 5 × 59
Step size 2.0339¢ 
Fifth 345\590 (701.695¢) (→69\118)
Semitones (A1:m2) 55:45 (111.9¢ : 91.53¢)
Consistency limit 15
Distinct consistency limit 15

590 equal divisions of the octave (abbreviated 590edo or 590ed2), also called 590-tone equal temperament (590tet) or 590 equal temperament (590et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 590 equal parts of about 2.03 ¢ each. Each step represents a frequency ratio of 21/590, or the 590th root of 2.

590edo has the same tuning as the 118edo in the 5-limit and provides a good correction for the harmonics 7, 11, and 13, altogether being consistent in the 15-odd-limit. Among the 118th-octave temperaments, it by definition tunes parakleischis as well as centenniamajor in the 590ee val.

Besides that, it is a tuning for the quintaschis temperament in the 7-limit.

Prime harmonics

Approximation of prime harmonics in 590edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.260 +0.127 -0.690 -0.132 -0.528 +0.807 -0.564 +0.200 -0.425 +0.049
Relative (%) +0.0 -12.8 +6.2 -33.9 -6.5 -25.9 +39.7 -27.7 +9.8 -20.9 +2.4
Steps
(reduced)
590
(0)
935
(345)
1370
(190)
1656
(476)
2041
(271)
2183
(413)
2412
(52)
2506
(146)
2669
(309)
2866
(506)
2923
(563)

Subsets and supersets

Since 590 factors into 2 × 5 × 59, 590edo has subset edos 2, 5, 10, 59, 118, and 295.