72569edo
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| ← 72568edo | 72569edo | 72570edo → |
72569 equal divisions of the octave (abbreviated 72569edo or 72569ed2), also called 72569-tone equal temperament (72569tet) or 72569 equal temperament (72569et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 72569 equal parts of about 0.0165 ¢ each. Each step represents a frequency ratio of 21/72569, or the 72569th root of 2.
Theory
72569edo is notable for having a very accurate 5th harmonic. It is also notable for having an accurate 1/4-comma meantone fifth, being only about 0.00000034 cents sharp. 72569edo approximates the 2.5.7 subgroup very well, and is also generally good as a 7-limit system.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00238 | +0.00000 | +0.00100 | -0.00815 | -0.00347 | -0.00150 | +0.00245 | -0.00608 | +0.00293 | -0.00119 |
| Relative (%) | +0.0 | -14.4 | +0.0 | +6.1 | -49.3 | -21.0 | -9.1 | +14.8 | -36.8 | +17.7 | -7.2 | |
| Steps (reduced) |
72569 (0) |
115019 (42450) |
168500 (23362) |
203727 (58589) |
251047 (33340) |
268537 (50830) |
296623 (6347) |
308268 (17992) |
328270 (37994) |
352539 (62263) |
359521 (69245) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00296 | -0.00317 | +0.00650 | +0.00069 | -0.00760 | +0.00788 | +0.00533 | -0.00044 | +0.00002 | -0.00626 | -0.00108 |
| Relative (%) | +17.9 | -19.1 | +39.3 | +4.2 | -45.9 | +47.7 | +32.2 | -2.6 | +0.1 | -37.8 | -6.5 | |
| Steps (reduced) |
378045 (15200) |
388792 (25947) |
393779 (30934) |
403091 (40246) |
415669 (52824) |
426898 (64053) |
430388 (67543) |
440210 (4796) |
446281 (10867) |
449189 (13775) |
457459 (22045) | |
Subsets and supersets
Since 72569 factorizes into 72 × 1481, 72569edo has subset edos 7, 49, 1481, and 10367.