1700edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1700}} | {{EDO intro|1700}} | ||
== Theory == | == Theory == | ||
1700edo is consistent in the 5-odd-limit, | 1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, its 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]]. | One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|1700}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments=== | === Rank-2 temperaments=== | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | ! Periods<br>per 8ve | ||
per 8ve | ! Generator* | ||
!Generator | ! Cents* | ||
! Associated<br>Ratio | |||
!Cents | ! Temperament | ||
!Associated | |||
Ratio | |||
!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]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
Revision as of 14:48, 15 October 2023
| ← 1699edo | 1700edo | 1701edo → |
Theory
1700edo is only consistent in the 5-odd-limit, and there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, its 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 (%) | -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) | |
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