1700edo
| ← 1699edo | 1700edo | 1701edo → |
1700 equal divisions of the octave (1700edo), or 1700-tone equal temperament (1700tet), 1700 equal temperament (1700et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1700 equal parts of about 0.706 ¢ each.
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
| 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 (%) | -44 | -28 | +50 | +13 | -3 | +25 | +29 | +31 | -48 | +6 | -6 | |
| 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 |