3395edo
| ← 3394edo | 3395edo | 3396edo → |
3395 equal divisions of the octave (abbreviated 3395edo or 3395ed2), also called 3395-tone equal temperament (3395tet) or 3395 equal temperament (3395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3395 equal parts of about 0.353 ¢ each. Each step represents a frequency ratio of 21/3395, or the 3395th root of 2.
Theory
3395edo is an extremely strong 17- and 19-limit system, and a zeta peak, integral and gap edo. It has a lower 17-limit TE relative error than any edo until 7033, and a lower 19-limit relative error than any edo until 8269. Besides, it provides the optimal patent val for the 13-limit rank-5 temperament tempering out 6656/6655, the jacobin comma, and for quartismic, which also tempers out 123201/123200. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.018 | +0.019 | +0.011 | +0.081 | +0.003 | +0.022 | +0.101 | -0.174 | +0.055 | -0.175 |
| relative (%) | +0 | +5 | +5 | +3 | +23 | +1 | +6 | +29 | -49 | +15 | -50 | |
| Steps (reduced) |
3395 (0) |
5381 (1986) |
7883 (1093) |
9531 (2741) |
11745 (1560) |
12563 (2378) |
13877 (297) |
14422 (842) |
15357 (1777) |
16493 (2913) |
16819 (3239) | |
Subsets and supersets
Since 3395 factors into 5 × 7 × 97, 3395edo has subset edos 5, 7, 35, 97, 485, and 679.
Regular temperament properties
3395edo has a lower 17-limit TE relative error than any edo until 7033, and a lower 19-limit relative error than any edo until 8269.
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 2319\3395 | 819.676 | 55115776/34328125 | Genojacobin |
| 35 | 1409\3395 (51\3395) |
498.027 (18.026) |
4/3 (?) |
Bromine |
| 97 | 1409\3395 (9\3395) |
498.027 (3.181) |
4/3 (?) |
Berkelium |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct