1665edo

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1665edo

1666edo →

Prime factorization	32 × 5 × 37
Step size	0.720721 ¢
Fifth	974\1665 (701.982 ¢)
Semitones (A1:m2)	158:125 (113.9 ¢ : 90.09 ¢)
Consistency limit	15
Distinct consistency limit	15

Theory

1665edo is a very strong 5-limit (as well as 2.3.5.11 subgroup) tuning and it is consistent in the 15-odd-limit. In the 5-limit, 1665edo is a tuning for the gross temperament.

1665edo provides the optimal patent val for the rhodium temperament in the 11-limit and also in the 13-limit. In addition, it provides the optimal patent val for dzelic temperament in the 13-limit.

Prime harmonics

Approximation of prime harmonics in 1665edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.027	-0.007	-0.177	+0.033	-0.167	+0.270	+0.145	+0.194	+0.333	+0.190
	Relative (%)	+0.0	+3.7	-1.0	-24.6	+4.6	-23.2	+37.4	+20.1	+26.9	+46.2	+26.3
Steps (reduced)		1665 (0)	2639 (974)	3866 (536)	4674 (1344)	5760 (765)	6161 (1166)	6806 (146)	7073 (413)	7532 (872)	8089 (1429)	8249 (1589)

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	127\1665	91.531	[9 -32 18⟩	Gross
37	377\1665 (17\1665)	271.711 (12.252)	117/100 (?)	Dzelic
45	1301\1665 (6\1665)	937.657 (4.324)	55/32 (?)	Rhodium