User:Lériendil/76ed81/5
| ← 4edo | 5 | 6edo → |
(convergent)
76 equal divisions of 81/5 (abbreviated 76ed81/5) is a nonoctave tuning system that divides the interval of 81/5 into 76 equal parts of about 63.4 ¢ each. Each step represents a frequency ratio of (81/5)1/76, or the 76th root of 81/5.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 100 | 15/14, 16/15, 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 | D♯, E♭ |
| 2 | 200 | 9/8, 10/9, 17/15, 19/17, 21/19 | E |
| 3 | 300 | 6/5, 19/16, 20/17 | F |
| 4 | 400 | 5/4, 14/11, 19/15, 23/18 | F♯, G♭ |
| 5 | 500 | 4/3, 23/17 | G |
| 6 | 600 | 7/5, 10/7, 17/12, 23/16 | G♯, A♭ |
| 7 | 700 | 3/2 | A |
| 8 | 800 | 8/5, 11/7, 19/12 | A♯, B♭ |
| 9 | 900 | 5/3, 17/10 | B |
| 10 | 1000 | 9/5, 16/9, 23/13 | C |
| 11 | 1100 | 15/8, 17/9, 19/10, 21/11, 23/12 | C♯, D♭ |
| 12 | 1200 | 2/1 | D |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.4 | +1.3 | +10.8 | +5.1 | +6.6 | -6.5 | +16.1 | +2.5 | +10.5 | -27.7 | +12.0 |
| Relative (%) | +8.5 | +2.0 | +16.9 | +8.0 | +10.5 | -10.2 | +25.4 | +4.0 | +16.5 | -43.6 | +19.0 | |
| Steps (reduced) |
19 (19) |
30 (30) |
38 (38) |
44 (44) |
49 (49) |
53 (53) |
57 (57) |
60 (60) |
63 (63) |
65 (65) |
68 (68) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.3 | -1.1 | +6.4 | +21.5 | -20.0 | +7.9 | -22.2 | +15.8 | -5.2 | -22.3 | +27.6 |
| Relative (%) | +0.5 | -1.7 | +10.0 | +33.9 | -31.5 | +12.5 | -35.1 | +25.0 | -8.2 | -35.1 | +43.6 | |
| Steps (reduced) |
70 (70) |
72 (72) |
74 (74) |
76 (0) |
77 (1) |
79 (3) |
80 (4) |
82 (6) |
83 (7) |
84 (8) |
86 (10) | |
|
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