34691edo
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Prime factorization
113 × 307
Step size
0.0345911¢
Fifth
20293\34691 (701.957¢)
Semitones (A1:m2)
3287:2608 (113.7¢ : 90.21¢)
Consistency limit
41
Distinct consistency limit
41
Special properties
| ← 34690edo | 34691edo | 34692edo → |
34691 equal divisions of the octave (abbreviated 34691edo or 34691ed2), also called 34691-tone equal temperament (34691tet) or 34691 equal temperament (34691et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 34691 equal parts of about 0.0346 ¢ each. Each step represents a frequency ratio of 21/34691, or the 34691st root of 2.
34691edo is a zeta peak edo and zeta peak integer edo, consistent in the 41-odd-limit with a lower relative error than any previous equal temperaments in the 41-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00228 | -0.00026 | +0.00174 | -0.00492 | +0.00158 | -0.00600 | +0.00507 | +0.00388 | -0.00757 | -0.00084 | -0.00507 | +0.00565 |
| Relative (%) | +0.0 | +6.6 | -0.8 | +5.0 | -14.2 | +4.6 | -17.3 | +14.7 | +11.2 | -21.9 | -2.4 | -14.7 | +16.3 | |
| Steps (reduced) |
34691 (0) |
54984 (20293) |
80550 (11168) |
97390 (28008) |
120011 (15938) |
128372 (24299) |
141798 (3034) |
147365 (8601) |
156927 (18163) |
168528 (29764) |
171866 (33102) |
180721 (7266) |
185859 (12404) | |