6181edt
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6181 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 6181edt or 6181ed3), is a nonoctave tuning system that divides the interval of 3/1 into 6181 equal parts of about 0.308 ¢ each. Each step represents a frequency ratio of 31/6181, or the 6181st root of 3.
6181edt supports Izar, being a nearly optimal tuning of that temperament. It is consistent to the no-evens 35-throdd limit, and excluding the high primes 37, 47, 53, and 61, to the 65-throdd limit as well.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.069 | +0.000 | -0.000 | -0.018 | -0.003 | +0.034 | -0.059 | +0.009 | +0.036 |
| Relative (%) | +22.3 | +0.0 | -0.1 | -5.8 | -1.1 | +11.1 | -19.3 | +3.1 | +11.8 | |
| Steps (reduced) |
3900 (3900) |
6181 (0) |
9055 (2874) |
10948 (4767) |
13491 (1129) |
14431 (2069) |
15940 (3578) |
16566 (4204) |
17641 (5279) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.001 | +0.000 | -0.013 | -0.080 | -0.003 | -0.018 | +0.091 | +0.034 | -0.079 |
| Relative (%) | -0.3 | +0.0 | -4.2 | -26.0 | -1.1 | -5.9 | +29.5 | +11.1 | -25.7 | |
| Steps (reduced) |
18110 (5748) |
18543 (0) |
18945 (402) |
19320 (777) |
19672 (1129) |
20003 (1460) |
20316 (1773) |
20612 (2069) |
20893 (2350) | |
| Harmonic | 43 | 45 | 47 | 49 | 51 | 53 | 55 | 57 | 59 | 61 | 63 | 65 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.068 | -0.000 | +0.106 | -0.035 | -0.059 | +0.120 | -0.004 | +0.009 | +0.002 | +0.138 | -0.018 | +0.034 |
| Relative (%) | -22.1 | -0.1 | +34.3 | -11.5 | -19.3 | +38.9 | -1.3 | +3.1 | +0.5 | +44.8 | -5.8 | +11.0 | |
| Steps (reduced) |
21161 (2618) |
21417 (2874) |
21662 (3119) |
21896 (3353) |
22121 (3578) |
22338 (3795) |
22546 (4003) |
22747 (4204) |
22941 (4398) |
23129 (4586) |
23310 (4767) |
23486 (4943) | |
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