1700edo

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

Template:EDO intro

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.

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
Error	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.

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

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