50ed7/3
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Prime factorization
2 × 52
Step size
29.3374¢
Octave
41\50ed7/3 (1202.83¢)
Twelfth
65\50ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit
12
Distinct consistency limit
8
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| ← 49ed7/3 | 50ed7/3 | 51ed7/3 → |
50 equal divisions of 7/3 (abbreviated 50ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 50 equal parts of about 29.3 ¢ each. Each step represents a frequency ratio of (7/3)1/50, or the 50th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 29.3 | |
| 2 | 58.7 | 28/27, 29/28, 30/29, 31/30, 32/31 |
| 3 | 88 | 20/19, 21/20 |
| 4 | 117.3 | 15/14, 31/29 |
| 5 | 146.7 | 12/11, 25/23 |
| 6 | 176 | 21/19, 31/28 |
| 7 | 205.4 | 9/8 |
| 8 | 234.7 | 8/7, 31/27 |
| 9 | 264 | 7/6 |
| 10 | 293.4 | 19/16, 32/27 |
| 11 | 322.7 | 29/24 |
| 12 | 352 | 11/9, 27/22 |
| 13 | 381.4 | 5/4 |
| 14 | 410.7 | 19/15 |
| 15 | 440.1 | 9/7, 31/24 |
| 16 | 469.4 | 17/13, 21/16 |
| 17 | 498.7 | 4/3 |
| 18 | 528.1 | 19/14, 23/17 |
| 19 | 557.4 | 29/21 |
| 20 | 586.7 | 7/5 |
| 21 | 616.1 | 10/7 |
| 22 | 645.4 | 16/11, 29/20 |
| 23 | 674.8 | 28/19, 31/21 |
| 24 | 704.1 | 3/2 |
| 25 | 733.4 | 26/17, 29/19, 32/21 |
| 26 | 762.8 | 14/9, 31/20 |
| 27 | 792.1 | 19/12, 30/19 |
| 28 | 821.4 | 29/18 |
| 29 | 850.8 | 18/11, 31/19 |
| 30 | 880.1 | 5/3 |
| 31 | 909.5 | 27/16 |
| 32 | 938.8 | 31/18 |
| 33 | 968.1 | 7/4 |
| 34 | 997.5 | 16/9 |
| 35 | 1026.8 | 29/16 |
| 36 | 1056.1 | |
| 37 | 1085.5 | 15/8, 28/15 |
| 38 | 1114.8 | 19/10, 21/11 |
| 39 | 1144.2 | 29/15, 31/16 |
| 40 | 1173.5 | |
| 41 | 1202.8 | 2/1 |
| 42 | 1232.2 | |
| 43 | 1261.5 | 29/14, 31/15 |
| 44 | 1290.8 | 19/9 |
| 45 | 1320.2 | 15/7 |
| 46 | 1349.5 | 24/11 |
| 47 | 1378.9 | 20/9, 31/14 |
| 48 | 1408.2 | 9/4 |
| 49 | 1437.5 | 23/10 |
| 50 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.8 | +5.0 | +5.7 | +0.7 | +7.8 | +5.0 | +8.5 | +10.0 | +3.6 | +14.6 | +10.6 |
| Relative (%) | +9.7 | +17.0 | +19.3 | +2.5 | +26.6 | +17.0 | +29.0 | +33.9 | +12.2 | +49.8 | +36.3 | |
| Steps (reduced) |
41 (41) |
65 (15) |
82 (32) |
95 (45) |
106 (6) |
115 (15) |
123 (23) |
130 (30) |
136 (36) |
142 (42) |
147 (47) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.6 | +7.8 | +5.7 | +11.3 | -5.6 | +12.8 | +7.2 | +6.4 | +10.0 | -11.9 | -0.9 |
| Relative (%) | -36.1 | +26.6 | +19.5 | +38.6 | -19.1 | +43.6 | +24.5 | +21.8 | +33.9 | -40.6 | -2.9 | |
| Steps (reduced) |
151 (1) |
156 (6) |
160 (10) |
164 (14) |
167 (17) |
171 (21) |
174 (24) |
177 (27) |
180 (30) |
182 (32) |
185 (35) | |