1700edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table |
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== Theory == | == Theory == | ||
1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the | 1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1|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]]. | One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]]. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|1700}} | {{Harmonics in equal|1700}} | ||
=== Subsets and supersets === | |||
Since 1700 factors into {{factorization|1700}}, 1700edo has subset edos {{EDOs| 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
=== 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 | |||
|- | |||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
Revision as of 13:31, 30 October 2023
| ← 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.
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 (%) | -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
| 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