383edo

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383edo

384edo →

Prime factorization	383 (prime)
Step size	3.13316 ¢
Fifth	224\383 (701.828 ¢)
Semitones (A1:m2)	36:29 (112.8 ¢ : 90.86 ¢)
Consistency limit	15
Distinct consistency limit	15

Theory

383edo is distinctly consistent through the 15-odd-limit with a flat tendency. The equal temperament tempers out 32805/32768 (schisma) in the 5-limit; 2401/2400 in the 7-limit; 3025/3024, 4000/3993 and 6250/6237 in the 11-limit; and 625/624, 1575/1573 and 2080/2079 in the 13-limit. It provides the optimal patent val for the countertertiaschis temperament, and a good tuning for sesquiquartififths in the higher limit.

Prime harmonics

Approximation of prime harmonics in 383edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.13	-0.94	-0.68	+0.12	-0.84	-1.56	+0.14	+1.49	+1.23	-1.43
	Relative (%)	+0.0	-4.1	-29.8	-21.7	+3.8	-26.8	-49.8	+4.4	+47.6	+39.3	-45.7
Steps (reduced)		383 (0)	607 (224)	889 (123)	1075 (309)	1325 (176)	1417 (268)	1565 (33)	1627 (95)	1733 (201)	1861 (329)	1897 (365)

Subsets and supersets

383edo is the 76th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-607 383⟩	[⟨383 607]]	+0.0402	0.0402	1.28
2.3.5	32805/32768, [-8 -55 41⟩	[⟨383 607 889]]	+0.1610	0.1741	5.55
2.3.5.7	2401/2400, 32805/32768, 68359375/68024448	[⟨383 607 889 1075]]	+0.1813	0.1548	4.94
2.3.5.7.11	2401/2400, 3025/3024, 4000/3993, 32805/32768	[⟨383 607 889 1075 1325]]	+0.1382	0.1631	5.20
2.3.5.7.11.13	625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976	[⟨383 607 889 1075 1325 1417]]	+0.1531	0.1525	4.87

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	53\383	166.06	11/10	Countertertiaschis
1	56\383	175.46	448/405	Sesquiquartififths
1	133\383	416.71	14/11	Unthirds
1	159\383	498.17	4/3	Helmholtz

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