231edt
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Prime factorization
3 × 7 × 11
Step size
8.23357¢
Octave
146\231edt (1202.1¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 230edt | 231edt | 232edt → |
231 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 231edt or 231ed3), is a nonoctave tuning system that divides the interval of 3/1 into 231 equal parts of about 8.23 ¢ each. Each step represents a frequency ratio of 31/231, or the 231st root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.10 | +0.00 | -4.03 | -3.37 | +2.10 | -1.30 | -1.93 | +0.00 | -1.27 | -1.60 | -4.03 |
| Relative (%) | +25.5 | +0.0 | -49.0 | -40.9 | +25.5 | -15.7 | -23.4 | +0.0 | -15.4 | -19.4 | -49.0 | |
| Steps (reduced) |
146 (146) |
231 (0) |
291 (60) |
338 (107) |
377 (146) |
409 (178) |
437 (206) |
462 (0) |
484 (22) |
504 (42) |
522 (60) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +0.81 | -3.37 | +0.17 | +2.25 | +2.10 | -0.93 | +0.84 | -1.30 | +0.50 | -2.35 |
| Relative (%) | -32.0 | +9.8 | -40.9 | +2.1 | +27.4 | +25.5 | -11.3 | +10.2 | -15.7 | +6.1 | -28.6 | |
| Steps (reduced) |
539 (77) |
555 (93) |
569 (107) |
583 (121) |
596 (134) |
608 (146) |
619 (157) |
630 (168) |
640 (178) |
650 (188) |
659 (197) | |