3776edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|3776}} ==Theory== 3776edo is a tuning for the oganesson temperament in the 17-limit, which sets 1/118th of the octave to an interval that repres..." |
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==Theory== | ==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. | 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]]. | While it does tune both 13th and 17th prime harmonic resonably, it is no longer consistent in the [[15-odd-limit]]. | ||
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[[Category:Equal divisions of the octave|####]] | [[Category:Equal divisions of the octave|####]] | ||
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== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per 8ve | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|118 | |||
|1781\3776 | |||
(21\3776) | |||
|565.995 | |||
(6.67) | |||
|165/119 | |||
(?) | |||
|[[Oganesson]] | |||
|}<!-- 4-digit number --> | |||
Revision as of 14:50, 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 |