3476edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|3476}} 3476edo is consistent to the 7-odd-limit, though it has large errors on harmonics 3 and 7. Aside from this, it is a strong 2.5.11.17.23..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
3476edo is consistent to the [[7-odd-limit]], though it has large errors on harmonics 3 and 7. Aside from this, it is a strong 2.5.11.17.23 subgroup tuning. | 3476edo is consistent to the [[7-odd-limit]], though it has large errors on harmonics 3 and 7. In the 7-limit, it tempers out the [[scheme comma]]. Aside from this, it is a strong 2.5.11.17.23 subgroup tuning. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|3476}} | {{harmonics in equal|3476}} | ||
=== Subsets and supersets === | |||
Since 3476 factors as {{Factorization|3476}}, 3476edo has nontrivial subset edos {{EDOs|2, 4, 11, 22, 44, 79, 158, 316, 869, 1738}}. | |||
[[10428edo]], which divides the edostep in three, is consistent in the [[21-odd-limit]] and corrects the harmonics 3 and 7. | |||
Latest revision as of 01:14, 20 October 2025
| ← 3475edo | 3476edo | 3477edo → |
3476 equal divisions of the octave (abbreviated 3476edo or 3476ed2), also called 3476-tone equal temperament (3476tet) or 3476 equal temperament (3476et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3476 equal parts of about 0.345 ¢ each. Each step represents a frequency ratio of 21/3476, or the 3476th root of 2.
3476edo is consistent to the 7-odd-limit, though it has large errors on harmonics 3 and 7. In the 7-limit, it tempers out the scheme comma. Aside from this, it is a strong 2.5.11.17.23 subgroup tuning.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.114 | -0.008 | -0.126 | +0.118 | +0.005 | +0.094 | -0.121 | -0.007 | +0.070 | +0.105 | +0.034 |
| Relative (%) | -33.0 | -2.2 | -36.6 | +34.1 | +1.6 | +27.2 | -35.2 | -2.1 | +20.4 | +30.5 | +9.9 | |
| Steps (reduced) |
5509 (2033) |
8071 (1119) |
9758 (2806) |
11019 (591) |
12025 (1597) |
12863 (2435) |
13580 (3152) |
14208 (304) |
14766 (862) |
15268 (1364) |
15724 (1820) | |
Subsets and supersets
Since 3476 factors as 22 × 11 × 79, 3476edo has nontrivial subset edos 2, 4, 11, 22, 44, 79, 158, 316, 869, 1738.
10428edo, which divides the edostep in three, is consistent in the 21-odd-limit and corrects the harmonics 3 and 7.