10729edo
| ← 10728edo | 10729edo | 10730edo → |
10729 equal divisions of the octave (abbreviated 10729edo or 10729ed2), also called 10729-tone equal temperament (10729tet) or 10729 equal temperament (10729et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 10729 equal parts of about 0.112 ¢ each. Each step represents a frequency ratio of 21/10729, or the 10729th root of 2.
10729edo is a fairly strong 23- and 29-limit system, consistent to the 29-odd-limit. Some of the simpler commas it tempers out include 123201/123200 and 1990656/1990625 in the 13-limit; 194481/194480 and 336141/336140 in the 17-limit; 23409/23408, 27456/27455, 43681/43680, 89376/89375 in the 19-limit; and 21505/21504, 23276/23275, and 25921/25920 in the 23-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0070 | +0.0037 | -0.0124 | -0.0270 | -0.0020 | -0.0435 | -0.0016 | -0.0331 |
| Relative (%) | +0.0 | -6.3 | +3.3 | -11.1 | -24.2 | -1.8 | -38.9 | -1.4 | -29.6 | |
| Steps (reduced) |
10729 (0) |
17005 (6276) |
24912 (3454) |
30120 (8662) |
37116 (4929) |
39702 (7515) |
43854 (938) |
45576 (2660) |
48533 (5617) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0311 | +0.0478 | -0.0252 | -0.0196 | -0.0441 | -0.0206 | +0.0158 | +0.0137 | +0.0133 |
| Relative (%) | -27.8 | +42.8 | -22.5 | -17.5 | -39.5 | -18.4 | +14.1 | +12.3 | +11.9 | |
| Steps (reduced) |
52121 (9205) |
53154 (10238) |
55892 (2247) |
57481 (3836) |
58218 (4573) |
59595 (5950) |
61455 (7810) |
63115 (9470) |
63631 (9986) | |
Subsets and supersets
10729edo is the 1308th prime edo.