742edo

← 741edo

742edo

743edo →

Prime factorization	2 × 7 × 53
Step size	1.61725 ¢
Fifth	434\742 (701.887 ¢) (→ 31\53)
Semitones (A1:m2)	70:56 (113.2 ¢ : 90.57 ¢)
Consistency limit	21
Distinct consistency limit	21

Theory

742edo is a very strong 19-limit system and a zeta peak tuning, and is uniquely consistent in the 21-odd-limit. It has a lower 19-limit relative error than any edo until 1178. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.

742 = 2 × 7 × 53, so it notably contains 53edo and 14edo. It supports silicon temperament (224 & 742) with period 14 in the 13-limit, and iodine temperament (159 & 742) with period 53 in the 17-limit.

In 5-limit, 742edo supports vishnu and fortune.

Prime harmonics

Approximation of prime harmonics in 742edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.068	+0.209	-0.093	+0.165	+0.443	+0.166	+0.061	-0.781	+0.611	-0.022
	Relative (%)	+0.0	-4.2	+12.9	-5.7	+10.2	+27.4	+10.3	+3.8	-48.3	+37.8	-1.4
Steps (reduced)		742 (0)	1176 (434)	1723 (239)	2083 (599)	2567 (341)	2746 (520)	3033 (65)	3152 (184)	3356 (388)	3605 (637)	3676 (708)

Rank-two temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	137\742	221.563	8388608/7381125	Fortune
2	44\742	71.159	25/24	Vishnu
14	434\74 (10\742)	701.886 (16.173)	3/2 (105/104)	Silicon
53	565\742 (5\742)	913.746 (8.086)	441/260 (196/195)	Iodine