783edo

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← 782edo

783edo

784edo →

Prime factorization	33 × 29
Step size	1.53257 ¢
Fifth	458\783 (701.916 ¢)
Semitones (A1:m2)	74:59 (113.4 ¢ : 90.42 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is consistent up to the 11-limit, making it a flexible and versatile tuning. It tempers out the ennealimma and the counterschisma in the 5-limit; 2401/2400, and 4375/4374 in the 7-limit. It supports counterschismic, dodifo, ennealimmal, raider, vavoom, and francium.

Prime harmonics

Approximation of prime harmonics in 783edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.039	-0.107	-0.244	+0.406	-0.681	-0.741	-0.195	+0.078	+0.308	-0.208
	Relative (%)	+0.0	-2.6	-7.0	-15.9	+26.5	-44.4	-48.3	-12.7	+5.1	+20.1	-13.6
Steps (reduced)		783 (0)	1241 (458)	1818 (252)	2198 (632)	2709 (360)	2897 (548)	3200 (68)	3326 (194)	3542 (410)	3804 (672)	3879 (747)

Subsets and supersets

Since 783 factors into 3³ × 29, 783edo has subset edos 3, 9, 27, 29, 87, and 261.

Regular temperament properties

Rank-2 temperaments

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	73\783	111.877	16/15	Vavoom
1	224\783	343.295	8000/6561	Raider
1	233\783	357.088	768/625	Dodifo (5-limit)
1	325\783	498.084	4/3	Counterschismic
9	206\783 (32\783)	315.709 (49.042)	6/5 (36/35)	Ennealimmal
29	325\783 (1\723)	498.084 (1.533)	4/3 (32805/32768)	Copper
87	308\783 (2\783)	472.031 (3.065)	[35 1 -6 -3 -4⟩ (?)	Francium