1700edo

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← 1699edo1700edo1701edo →
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

1700 equal divisions of the octave (abbreviated 1700edo or 1700ed2), also called 1700-tone equal temperament (1700tet) or 1700 equal temperament (1700et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1700 equal parts of about 0.706 ¢ each. Each step represents a frequency ratio of 21/1700, or the 1700th root of 2.

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
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