783edo: 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" | ||
! Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 45: | Line 47: | ||
|- | |- | ||
| 9 | | 9 | ||
| 206\783<br>(32\783) | | 206\783<br />(32\783) | ||
| 315.709<br>(49.042) | | 315.709<br />(49.042) | ||
| 6/5<br>(36/35) | | 6/5<br />(36/35) | ||
| [[Ennealimmal]] | | [[Ennealimmal]] | ||
|- | |- | ||
| 29 | | 29 | ||
| 325\783<br>(1\723) | | 325\783<br />(1\723) | ||
| 498.084<br>(1.533) | | 498.084<br />(1.533) | ||
| 4/3<br>(32805/32768) | | 4/3<br />(32805/32768) | ||
| [[Copper]] | | [[Copper]] | ||
|- | |- | ||
| 87 | | 87 | ||
| 308\783<br>(2\783) | | 308\783<br />(2\783) | ||
| 472.031<br>(3.065) | | 472.031<br />(3.065) | ||
| {{monzo| 35 1 -6 -3 -4 }}<br>(?) | | {{monzo| 35 1 -6 -3 -4 }}<br />(?) | ||
| [[87th-octave temperaments #Francium|Francium]] | | [[87th-octave temperaments #Francium|Francium]] | ||
|} | |} | ||
{{orf}} | |||
Revision as of 00:49, 16 November 2024
| ← 782edo | 783edo | 784edo → |
Theory
783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is consistent up to the 11-odd-limit, making it a flexible and versatile tuning. The equal temperament tempers out the ennealimma and the counterschisma in the 5-limit; 2401/2400, and 4375/4374 in the 7-limit. It supports counterschismic, dodifo, ennealimmal, raider, vavoom, and francium.
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) | |
Subsets and supersets
Since 783 factors into 33 × 29, 783edo has subset edos 3, 9, 27, 29, 87, and 261.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 73\783 | 111.877 | 16/15 | Vavoom |
| 1 | 224\783 | 343.295 | 8000/6561 | Raider |
| 1 | 233\783 | 357.088 | 768/625 | Dodifo (5-limit) |
| 1 | 325\783 | 498.084 | 4/3 | Counterschismic |
| 9 | 206\783 (32\783) |
315.709 (49.042) |
6/5 (36/35) |
Ennealimmal |
| 29 | 325\783 (1\723) |
498.084 (1.533) |
4/3 (32805/32768) |
Copper |
| 87 | 308\783 (2\783) |
472.031 (3.065) |
[35 1 -6 -3 -4⟩ (?) |
Francium |