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 only consistent in the 5-odd-limit, and there is a large relative delta on the harmonic 3. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 subgroup, or if the harmonic 5 is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 subgroup (not including either 5 or 15). 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)

Subsets and supersets

Since 1700 factors into 2² × 5² × 17, 1700edo has subset edos 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850.

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator

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

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