783edo

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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

783 equal divisions of the octave (abbreviated 783edo or 783ed2), also called 783-tone equal temperament (783tet) or 783 equal temperament (783et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 783 equal parts of about 1.53 ¢ each. Each step represents a frequency ratio of 2^1/783, or the 783rd root of 2.

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-odd-limit, making it a flexible and versatile tuning. The equal temperament 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

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	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

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct