700edo

← 699edo

700edo

701edo →

Prime factorization	22 × 52 × 7
Step size	1.71429 ¢
Fifth	409\700 (701.143 ¢)
Semitones (A1:m2)	63:55 (108 ¢ : 94.29 ¢)
Dual sharp fifth	410\700 (702.857 ¢) (→ 41\70)
Dual flat fifth	409\700 (701.143 ¢)
Dual major 2nd	119\700 (204 ¢) (→ 17\100)
Consistency limit	7
Distinct consistency limit	7

Theory

700edo is consistent to the 7-odd-limit, but its harmonic 3 is about halfway between its steps. It is strong in the 2.9.15.7.31 subgroup, tempering out 3969/3968, 420175/419904, 10255177611/10240000000 and 2202927104/2197265625. The equal temperament can also be used in the 2.9.5.7.13.17.23 subgroup, tempering out 1225/1224, 46000/45927, 8281/8280, 426496/426465, 31250/31213 and 262395/262144.

Odd harmonics

Approximation of odd harmonics in 700edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.812	-0.599	-0.254	+0.090	+0.682	-0.528	+0.303	-0.384	+0.773	+0.648	-0.846
	Relative (%)	-47.4	-35.0	-14.8	+5.2	+39.8	-30.8	+17.7	-22.4	+45.1	+37.8	-49.3
Steps (reduced)		1109 (409)	1625 (225)	1965 (565)	2219 (119)	2422 (322)	2590 (490)	2735 (635)	2861 (61)	2974 (174)	3075 (275)	3166 (366)

Subsets and supersets

Since 700 factors into 2² × 5² × 7, 700edo has subset edos 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, and 350. 1400edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.9	[317 -100⟩	[⟨700 2219]]	-0.0142	0.0142	0.83
2.9.5	[-65 0 28⟩, [63 -25 7⟩	[⟨700 2219 1625]]	+0.0766	0.1289	7.52
2.9.5.7	2100875/2097152, 184528125/184473632, 3500000000/3486784401	[⟨700 2219 1625 1965]]	+0.0801	0.1118	6.52