88edf
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Prime factorization
23 × 11
Step size
7.97676¢
Octave
150\88edf (1196.51¢) (→75\44edf)
Twelfth
238\88edf (1898.47¢) (→119\44edf)
Consistency limit
2
Distinct consistency limit
2
| ← 87edf | 88edf | 89edf → |
88 equal divisions of the perfect fifth (abbreviated 88edf or 88ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 88 equal parts of about 7.98 ¢ each. Each step represents a frequency ratio of (3/2)1/88, or the 88th root of 3/2.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.49 | -3.49 | +1.01 | -2.42 | +1.01 | -2.63 | -2.48 | +1.01 | +2.07 | -3.40 | -2.48 |
| Relative (%) | -43.7 | -43.7 | +12.6 | -30.4 | +12.6 | -33.0 | -31.1 | +12.6 | +25.9 | -42.6 | -31.1 | |
| Steps (reduced) |
150 (62) |
238 (62) |
301 (37) |
349 (85) |
389 (37) |
422 (70) |
451 (11) |
477 (37) |
500 (60) |
520 (80) |
539 (11) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.53 | +1.86 | +2.07 | +2.01 | +0.75 | -2.48 | -0.36 | -1.42 | +1.86 | +1.09 | +3.90 |
| Relative (%) | +31.7 | +23.3 | +25.9 | +25.2 | +9.4 | -31.1 | -4.5 | -17.8 | +23.3 | +13.7 | +48.9 | |
| Steps (reduced) |
557 (29) |
573 (45) |
588 (60) |
602 (74) |
615 (87) |
627 (11) |
639 (23) |
650 (34) |
661 (45) |
671 (55) |
681 (65) | |
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