User:Overthink/36269edo
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Prime factorization
36269 (prime)
Step size
0.0330861 ¢
Fifth
21216\36269 (701.955 ¢)
Semitones (A1:m2)
3436:2727 (113.7 ¢ : 90.23 ¢)
Consistency limit
29
Distinct consistency limit
29
| ← 36268edo | 36269edo | 36270edo → |
36269 equal divisions of the octave (abbreviated 36269edo or 36269ed2), also called 36269-tone equal temperament (36269tet) or 36269 equal temperament (36269et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 36269 equal parts of about 0.0331 ¢ each. Each step represents a frequency ratio of 21/36269, or the 36269th root of 2.
Theory
36269edo holds the record of lowest absolute error in the 19-, 23-, 29-, and 31-limit.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0002 | -0.0003 | +0.0015 | -0.0041 | -0.0082 | -0.0063 | -0.0027 | -0.0023 | -0.0037 | +0.0084 |
| Relative (%) | +0.0 | -0.5 | -1.0 | +4.4 | -12.5 | -24.8 | -19.0 | -8.3 | -6.9 | -11.3 | +25.4 | |
| Steps (reduced) |
36269 (0) |
57485 (21216) |
84214 (11676) |
101820 (29282) |
125470 (16663) |
134211 (25404) |
148248 (3172) |
154068 (8992) |
164065 (18989) |
176194 (31118) |
179684 (34608) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0111 | -0.0018 | -0.0065 | -0.0127 | +0.0018 | +0.0139 | +0.0029 | +0.0004 | -0.0059 | +0.0084 | +0.0058 |
| Relative (%) | +33.6 | -5.4 | -19.6 | -38.3 | +5.3 | +41.9 | +8.8 | +1.1 | -17.8 | +25.3 | +17.6 | |
| Steps (reduced) |
188942 (7597) |
194313 (12968) |
196805 (15460) |
201459 (20114) |
207746 (26401) |
213358 (32013) |
215102 (33757) |
220011 (2397) |
223045 (5431) |
224499 (6885) |
228632 (11018) | |