1323edo

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← 1322edo

1323edo

1324edo →

Prime factorization	33 × 72
Step size	0.907029 ¢
Fifth	774\1323 (702.041 ¢) (→ 86\147)
Semitones (A1:m2)	126:99 (114.3 ¢ : 89.8 ¢)
Consistency limit	29
Distinct consistency limit	29

Theory

1323edo is the smallest uniquely consistent EDO in the 29-odd-limit.

It provides the optimal patent val for the 11-limit trinealimmal temperament, which has a period of 1\27 octave. In additoin, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum.

1323's divisors are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, of which 441EDO is a member of the zeta edos. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three.

Prime harmonics

Approximation of prime harmonics in 1323edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.086	+0.081	-0.118	+0.156	+0.289	+0.260	-0.007	+0.297	-0.099	-0.364
	Relative (%)	+0.0	+9.5	+8.9	-13.1	+17.2	+31.8	+28.7	-0.8	+32.8	-10.9	-40.2
Steps (reduced)		1323 (0)	2097 (774)	3072 (426)	3714 (1068)	4577 (608)	4896 (927)	5408 (116)	5620 (328)	5985 (693)	6427 (1135)	6554 (1262)

Regular temperament properties

Rank-2 temperaments

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
3	177\1323	160.544	154478651796875/140737488355328	441 & 1308
27	299\1323 (5\1323)	271.201 (4.535)	1375/1176 (?)	Trinealimmal