17461edo
17461 equal divisions of the octave (abbreviated 17461edo or 17461ed2), also called 17461-tone equal temperament (17461tet) or 17461 equal temperament (17461et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 17461 equal parts of about 0.0687 ¢ each. Each step represents a frequency ratio of 21/17461, or the 17461st root of 2.
| ← 17460edo | 17461edo | 17462edo → |
17461edo is a remarkable very high-limit system, distinctly consistent through the 45-odd-limit, and has a lower relative error than any previous equal temperaments in the 41-limit. It tempers out 33670/33669, 67425/67424, 81549/81548, 101270/101269, 115885/115884, 120745/120744, 127281/127280, 203320/203319, 355725/355718, 728365/728364, 730639/730620, 2942775/2942758, and 7172253/7172228 in the 43-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0021 | -0.0128 | -0.0154 | -0.0093 | -0.0260 | -0.0130 | -0.0043 | +0.0058 | -0.0142 | -0.0152 |
| Relative (%) | +0.0 | -3.0 | -18.6 | -22.4 | -13.5 | -37.8 | -18.9 | -6.2 | +8.5 | -20.6 | -22.2 | |
| Steps (reduced) |
17461 (0) |
27675 (10214) |
40543 (5621) |
49019 (14097) |
60405 (8022) |
64613 (12230) |
71371 (1527) |
74173 (4329) |
78986 (9142) |
84825 (14981) |
86505 (16661) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0182 | -0.0148 | -0.0006 | +0.0223 | -0.0151 | +0.0117 | +0.0272 | +0.0011 | +0.0182 | +0.0325 | -0.0217 |
| Relative (%) | -26.5 | -21.6 | -0.9 | +32.4 | -21.9 | +17.0 | +39.5 | +1.7 | +26.6 | +47.3 | -31.6 | |
| Steps (reduced) |
90962 (3657) |
93548 (6243) |
94748 (7443) |
96989 (9684) |
100015 (12710) |
102717 (15412) |
103557 (16252) |
105920 (1154) |
107381 (2615) |
108081 (3315) |
110070 (5304) | |