1700edo: Difference between revisions
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=== Rank-2 temperaments=== | === Rank-2 temperaments=== | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br>per 8ve | ! Periods<br />per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| 17 | | 17 | ||
| 121\1700<br>(21\1700) | | 121\1700<br />(21\1700) | ||
| 85.412<br>(14.824) | | 85.412<br />(14.824) | ||
| 1024/975<br>(8192/8125) | | 1024/975<br />(8192/8125) | ||
| [[Leaves]] | | [[Leaves]] | ||
|} | |} | ||
{{orf}} | |||
Revision as of 00:50, 16 November 2024
| ← 1699edo | 1700edo | 1701edo → |
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
| 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
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperament |
|---|---|---|---|---|
| 17 | 121\1700 (21\1700) |
85.412 (14.824) |
1024/975 (8192/8125) |
Leaves |