336edo
| ← 335edo | 336edo | 337edo → |
336 equal divisions of the octave (abbreviated 336edo or 336ed2), also called 336-tone equal temperament (336tet) or 336 equal temperament (336et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 336 equal parts of about 3.57 ¢ each. Each step represents a frequency ratio of 21/336, or the 336th root of 2.
336edo has poor approximation for harmonic 3, therefore it naturally yields a 2.9 subgroup interpretation. In the 2.9.5.7 subgroup, it tempers out the schisma and the landscape comma.
Nonetheless, there are a number of mappings to be considered. Using the 336d val in the 7-limit, 336edo tempers out the octagar comma, 4000/3969, and 336def val tunes the slithy temperament in the 13-limit. 336cefg val is a tuning for the catamite temperament in the 19-limit. 336b val uses the 12edo mapping for 3/2 and tunes the 24th-octave rabic temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +1.62 | -0.60 | -0.97 | -0.34 | -1.32 | -1.24 | +1.02 | -1.38 | -1.08 | +0.65 | +0.30 |
| relative (%) | +45 | -17 | -27 | -9 | -37 | -35 | +28 | -39 | -30 | +18 | +8 | |
| Steps (reduced) |
533 (197) |
780 (108) |
943 (271) |
1065 (57) |
1162 (154) |
1243 (235) |
1313 (305) |
1373 (29) |
1427 (83) |
1476 (132) |
1520 (176) | |