14348edo
← 14347edo | 14348edo | 14349edo → |
14348 equal divisions of the octave (abbreviated 14348edo or 14348ed2), also called 14348-tone equal temperament (14348tet) or 14348 equal temperament (14348et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 14348 equal parts of about 0.0836 ¢ each. Each step represents a frequency ratio of 21/14348, or the 14348th root of 2.
14348edo is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from 7033. It is also distinctly consistent in the 29-odd-limit, and has a lower 23-limit relative error than any lower equal temperaments aside from 2460, 8269, 8539 and 11664. Besides all that, it is a zeta peak, integral and gap edo, which has to do with its higher limit capability – it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond.
Prime harmonics
Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | absolute (¢) | +0.0000 | -0.0035 | -0.0020 | +0.0060 | +0.0063 | +0.0076 | +0.0070 | -0.0221 | -0.0056 | -0.0260 | +0.0160 | -0.0198 | -0.0131 | -0.0039 | -0.0201 |
relative (%) | +0 | -4 | -2 | +7 | +8 | +9 | +8 | -26 | -7 | -31 | +19 | -24 | -16 | -5 | -24 | |
Steps (reduced) |
14348 (0) |
22741 (8393) |
33315 (4619) |
40280 (11584) |
49636 (6592) |
53094 (10050) |
58647 (1255) |
60949 (3557) |
64904 (7512) |
69702 (12310) |
71083 (13691) |
74745 (3005) |
76870 (5130) |
77856 (6116) |
79697 (7957) |
Subsets and supersets
It factors as 22 × 17 × 211, so 17, 34, 68 and 422 are all divisors.