1700edo

← 1699edo

1700edo

1701edo →

Prime factorization	22 × 52 × 17
Step size	0.705882 ¢
Fifth	994\1700 (701.647 ¢) (→ 497\850)
Semitones (A1:m2)	158:130 (111.5 ¢ : 91.76 ¢)
Dual sharp fifth	995\1700 (702.353 ¢) (→ 199\340)
Dual flat fifth	994\1700 (701.647 ¢) (→ 497\850)
Dual major 2nd	289\1700 (204 ¢) (→ 17\100)
Consistency limit	5
Distinct consistency limit	5

Theory

1700edo is consistent in the 5-odd-limit, although there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, it's best usage is as a 2.9.11.21.23.31 subgroup tuning because all other harmonics up to 29th have more than 25% error. Nonetheless, it tunes the 323 & 2023 temperament leaves in the 17-limit on the patent val.

One step of 1700edo is the relative cent for 17edo. It has been named iota by Margo Schulter and George Secor.

Odd harmonics

Approximation of odd harmonics in 1700edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.308	-0.196	+0.351	+0.090	-0.024	+0.178	+0.202	+0.221	-0.337	+0.043	-0.039
	Relative (%)	-43.6	-27.8	+49.7	+12.7	-3.4	+25.2	+28.6	+31.3	-47.7	+6.0	-5.5
Steps (reduced)		2694 (994)	3947 (547)	4773 (1373)	5389 (289)	5881 (781)	6291 (1191)	6642 (1542)	6949 (149)	7221 (421)	7467 (667)	7690 (890)

Regular temperament properties

Rank-2 temperaments

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperament
17	121\1700 (21\1700)	85.412 (14.824)	1024/975 (8192/8125)	Leaves