3776edo: Difference between revisions
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{{EDO intro|3776}} | {{EDO intro|3776}} | ||
==Theory== | ==Theory== | ||
3776edo is a tuning for the [[oganesson]] temperament in the | 3776edo is a good 2.3.11.13.19. system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val, where it is a tuning for the [[oganesson]] temperament in the 19-limit, which sets 1/118th of the octave to an interval that represents 169/168, 170/169, and 171/170 tempered together. | ||
It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament. | It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|3776}} | {{harmonics in equal|3776}} | ||
Revision as of 14:16, 10 June 2023
| ← 3775edo | 3776edo | 3777edo → |
Theory
3776edo is a good 2.3.11.13.19. system. It does not tune the 15-odd-limit consistently, though a reasonable represenation exists through the 19-limit patent val, where it is a tuning for the oganesson temperament in the 19-limit, which sets 1/118th of the octave to an interval that represents 169/168, 170/169, and 171/170 tempered together.
It tempers out the quartisma in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.
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 |