783edo: Difference between revisions
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{{harmonics in equal|783}} | {{harmonics in equal|783}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per 8ve | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|1 | |||
|73\783 | |||
| | |||
|16/15 | |||
|Vavoom | |||
|- | |||
|1 | |||
|224\783 | |||
| | |||
|8000/6561 | |||
|Raider | |||
|- | |||
|1 | |||
|233\783 | |||
| | |||
|49/40 | |||
|Dodifo | |||
|- | |||
|1 | |||
|325\783 | |||
| | |||
|4/3 | |||
|Counterschismic | |||
|- | |||
|9 | |||
|206\783 | |||
(32\783) | |||
| | |||
|6/5 | |||
(36/35) | |||
|Ennealimmal | |||
|- | |||
|29 | |||
|325\783 | |||
(1\723) | |||
| | |||
|4/3 | |||
(32805/32768) | |||
|Copper | |||
|- | |||
|87 | |||
|308\783 | |||
(2\783) | |||
| | |||
|[35 1 -6 -3 -4⟩ | |||
(?) | |||
|Francium | |||
|}<!-- 3-digit number --> | |||
[[Category:Breed]] | [[Category:Breed]] | ||
[[Category:Ennealimmal]] | [[Category:Ennealimmal]] | ||
[[Category:Ragismic]] | [[Category:Ragismic]] | ||
Revision as of 21:01, 17 June 2023
| ← 782edo | 783edo | 784edo → |
It provides solid approximations of the 5-limit, the 7-limit and the 11-limit, and is consistent up to the 11-limit, making it a flexible and versatile tuning. It is a tuning for the counterschismic, dodifo, ennealimmal, raider, vavoom, and francium.
It supports the rank-3 temperaments: Breed, Landscape, Ragismic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.039 | -0.107 | -0.244 | +0.406 | -0.681 | -0.741 | -0.195 | +0.078 | +0.308 | -0.208 |
| Relative (%) | +0.0 | -2.6 | -7.0 | -15.9 | +26.5 | -44.4 | -48.3 | -12.7 | +5.1 | +20.1 | -13.6 | |
| Steps (reduced) |
783 (0) |
1241 (458) |
1818 (252) |
2198 (632) |
2709 (360) |
2897 (548) |
3200 (68) |
3326 (194) |
3542 (410) |
3804 (672) |
3879 (747) | |
Regular temperament properties
Rank-2 temperaments
| Periods
per 8ve |
Generator
(reduced) |
Cents
(reduced) |
Associated
ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 73\783 | 16/15 | Vavoom | |
| 1 | 224\783 | 8000/6561 | Raider | |
| 1 | 233\783 | 49/40 | Dodifo | |
| 1 | 325\783 | 4/3 | Counterschismic | |
| 9 | 206\783
(32\783) |
6/5
(36/35) |
Ennealimmal | |
| 29 | 325\783
(1\723) |
4/3
(32805/32768) |
Copper | |
| 87 | 308\783
(2\783) |
[35 1 -6 -3 -4⟩
(?) |
Francium |