229edt
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Prime factorization
229 (prime)
Step size
8.30548¢
Octave
144\229edt (1195.99¢)
Consistency limit
2
Distinct consistency limit
2
 |
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229 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 229edt or 229ed3), is a nonoctave tuning system that divides the interval of 3/1 into 229 equal parts of about 8.31 ¢ each. Each step represents a frequency ratio of 31/229, or the 229th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.01 | +0.00 | +0.28 | -3.98 | -4.01 | +3.20 | -3.73 | +0.00 | +0.32 | +1.42 | +0.28 |
| Relative (%) | -48.3 | +0.0 | +3.4 | -47.9 | -48.3 | +38.5 | -44.9 | +0.0 | +3.8 | +17.1 | +3.4 | |
| Steps (reduced) |
144 (144) |
229 (0) |
289 (60) |
335 (106) |
373 (144) |
406 (177) |
433 (204) |
458 (0) |
480 (22) |
500 (42) |
518 (60) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.90 | -0.81 | -3.98 | +0.57 | +3.58 | -4.01 | +2.05 | -3.69 | +3.20 | -2.59 | +3.51 |
| Relative (%) | +35.0 | -9.8 | -47.9 | +6.8 | +43.1 | -48.3 | +24.7 | -44.5 | +38.5 | -31.2 | +42.3 | |
| Steps (reduced) |
535 (77) |
550 (92) |
564 (106) |
578 (120) |
591 (133) |
602 (144) |
614 (156) |
624 (166) |
635 (177) |
644 (186) |
654 (196) | |