589edo

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589edo

590edo →

Prime factorization	19 × 31
Step size	2.03735 ¢
Fifth	345\589 (702.886 ¢)
Semitones (A1:m2)	59:42 (120.2 ¢ : 85.57 ¢)
Dual sharp fifth	345\589 (702.886 ¢)
Dual flat fifth	344\589 (700.849 ¢)
Dual major 2nd	100\589 (203.735 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

589et tempers out 420175/419904 in the 7-limit; 55296000/55240493, 117649/117612, 107495424/107421875, 1953125/1948617, 4302592/4296875, 85937500/85766121, 422576/421875, 3025/3024, 766656/765625, 456533/455625, 3294225/3294172, 644204/643125 and 781258401/781250000 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 589edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.931	+0.783	+0.953	-0.175	+0.804	+0.898	-0.323	+0.987	-0.060	-0.153	-0.770
	Relative (%)	+45.7	+38.4	+46.8	-8.6	+39.5	+44.1	-15.9	+48.4	-2.9	-7.5	-37.8
Steps (reduced)		934 (345)	1368 (190)	1654 (476)	1867 (100)	2038 (271)	2180 (413)	2301 (534)	2408 (52)	2502 (146)	2587 (231)	2664 (308)

Subsets and supersets

589 factors into 19 × 31 with subset edos 19, and 31. 1178edo, which doubles it, gives a good correction to the 3rd harmonic.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-1867 589⟩	⟨589 1867]	+0.0276	0.0276	1.35
2.9.5	[-37 19 -10⟩, [72 0 -31⟩	⟨589 1867 1368]	-0.0940	0.1734	8.51

Scales

• Kryptonite10
• Kryptonite19