683edo

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683edo

684edo →

Prime factorization	683 (prime)
Step size	1.75695 ¢
Fifth	400\683 (702.782 ¢)
Semitones (A1:m2)	68:49 (119.5 ¢ : 86.09 ¢)
Dual sharp fifth	400\683 (702.782 ¢)
Dual flat fifth	399\683 (701.025 ¢)
Dual major 2nd	116\683 (203.807 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

683edo is consistent to the 5-odd-limit and its harmonic 3 is about halfway its steps. It can be used in the 2.9.5.11.17.23.29.31.37 subgroup, tempering out 2025/2024, 3520/3519, 557056/556875, 5800/5797, 1332/1331, 484704/484375, 1492992/1491325 and 14384/14375.

Odd harmonics

Approximation of odd harmonics in 683edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.827	+0.216	-0.744	-0.103	+0.366	-0.703	-0.714	+0.462	-0.588	+0.083	+0.715
	Relative (%)	+47.1	+12.3	-42.3	-5.9	+20.8	-40.0	-40.6	+26.3	-33.4	+4.7	+40.7
Steps (reduced)		1083 (400)	1586 (220)	1917 (551)	2165 (116)	2363 (314)	2527 (478)	2668 (619)	2792 (60)	2901 (169)	3000 (268)	3090 (358)

Subsets and supersets

683edo is the 124th prime EDO. 1366edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-2165 683⟩	[⟨683 2165]]	+0.0163	0.0163	0.93
2.9.5	[23 3 -14⟩, [-130 52 -15⟩	[⟨683 2165 1586]]	-0.0202	0.0533	3.03