3776edo: 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 | !Periods<br>per 8ve | ||
per 8ve | !Generator<br>(reduced) | ||
!Generator | !Cents<br>(reduced) | ||
(reduced) | !Associated<br>ratio | ||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | !Temperaments | ||
|- | |- | ||
|118 | |118 | ||
|1781\3776 | |1781\3776<br>(21\3776) | ||
(21\3776) | |565.995<br>(6.67) | ||
|565.995 | |165/119<br>(?) | ||
(6.67) | |||
|165/119 | |||
(?) | |||
|[[Oganesson]] | |[[Oganesson]] | ||
|}<!-- 4-digit number --> | |}<!-- 4-digit number --> | ||
Revision as of 14:51, 19 January 2023
| ← 3775edo | 3776edo | 3777edo → |
Theory
3776edo is a tuning for the oganesson temperament in the 17-limit, which sets 1/118th of the octave to an interval that represents 169/168~170/169 tempered together.
It tempers out the quartisma in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.
While it does tune both 13th and 17th prime harmonic resonably, it is no longer consistent in the 15-odd-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.058 | +0.127 | +0.136 | +0.115 | +0.059 | +0.044 | -0.133 | -0.083 | -0.055 | -0.124 | +0.010 |
| Relative (%) | +18.2 | +40.0 | +42.8 | +36.3 | +18.6 | +14.0 | -41.9 | -26.0 | -17.4 | -39.1 | +3.0 | |
| Steps (reduced) |
5985 (2209) |
8768 (1216) |
10601 (3049) |
11970 (642) |
13063 (1735) |
13973 (2645) |
14752 (3424) |
15434 (330) |
16040 (936) |
16585 (1481) |
17081 (1977) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 118 | 1781\3776 (21\3776) |
565.995 (6.67) |
165/119 (?) |
Oganesson |