1213edt
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Prime factorization
1213 (prime)
Step size
1.56798¢
Octave
765\1213edt (1199.5¢)
Consistency limit
2
Distinct consistency limit
2
| ← 1212edt | 1213edt | 1214edt → |
1213 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 1213edt or 1213ed3), is a nonoctave tuning system that divides the interval of 3/1 into 1213 equal parts of about 1.57 ¢ each. Each step represents a frequency ratio of 31/1213, or the 1213th root of 3. It corresponds to 765.31779edo.
Theory
1213edt is strong in the 3.5.13.19.23.29 subgroup, tempering out 12675/12673, 318573/318565, 7421875/7420491, 22024249/22021875 and 7993758375/7992538801. Using the 3.5.13.17.19.23 subgroup, it tempers out 8075/8073.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.498 | +0.000 | +0.571 | -0.020 | -0.498 | +0.755 | +0.073 | +0.000 | -0.518 | +0.683 | +0.571 |
| Relative (%) | -31.8 | +0.0 | +36.4 | -1.3 | -31.8 | +48.1 | +4.7 | +0.0 | -33.1 | +43.5 | +36.4 | |
| Steps (reduced) |
765 (765) |
1213 (0) |
1531 (318) |
1777 (564) |
1978 (765) |
2149 (936) |
2296 (1083) |
2426 (0) |
2542 (116) |
2648 (222) |
2744 (318) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.019 | +0.256 | -0.020 | -0.425 | -0.326 | -0.498 | -0.023 | +0.551 | +0.755 | +0.184 | +0.059 | +0.073 | -0.040 | -0.518 | +0.000 |
| Relative (%) | -1.2 | +16.4 | -1.3 | -27.1 | -20.8 | -31.8 | -1.5 | +35.2 | +48.1 | +11.8 | +3.8 | +4.7 | -2.6 | -33.0 | +0.0 | |
| Steps (reduced) |
2832 (406) |
2914 (488) |
2990 (564) |
3061 (635) |
3128 (702) |
3191 (765) |
3251 (825) |
3308 (882) |
3362 (936) |
3413 (987) |
3462 (1036) |
3509 (1083) |
3554 (1128) |
3597 (1171) |
3639 (0) | |