51ed4: Difference between revisions
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== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 51 | |||
| num = 4 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 51 | |||
| num = 4 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 02:23, 5 October 2024
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| ← 49ed4 | 51ed4 | 53ed4 → |
51 equal divisions of the 4th harmonic (abbreviated 51ed4) is a nonoctave tuning system that divides the interval of 4/1 into 51 equal parts of about 47.1 ¢ each. Each step represents a frequency ratio of 41/51, or the 51st root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 47.1 | |
| 2 | 94.1 | 18/17, 19/18 |
| 3 | 141.2 | 25/23 |
| 4 | 188.2 | 19/17, 29/26 |
| 5 | 235.3 | |
| 6 | 282.4 | |
| 7 | 329.4 | 23/19 |
| 8 | 376.5 | 31/25 |
| 9 | 423.5 | 23/18 |
| 10 | 470.6 | 25/19 |
| 11 | 517.6 | 31/23 |
| 12 | 564.7 | 18/13, 25/18 |
| 13 | 611.8 | |
| 14 | 658.8 | 19/13 |
| 15 | 705.9 | |
| 16 | 752.9 | 17/11 |
| 17 | 800 | |
| 18 | 847.1 | 31/19 |
| 19 | 894.1 | |
| 20 | 941.2 | 19/11, 31/18 |
| 21 | 988.2 | 23/13, 30/17 |
| 22 | 1035.3 | 31/17 |
| 23 | 1082.4 | |
| 24 | 1129.4 | 25/13 |
| 25 | 1176.5 | |
| 26 | 1223.5 | |
| 27 | 1270.6 | |
| 28 | 1317.6 | |
| 29 | 1364.7 | 11/5 |
| 30 | 1411.8 | |
| 31 | 1458.8 | |
| 32 | 1505.9 | 31/13 |
| 33 | 1552.9 | |
| 34 | 1600 | |
| 35 | 1647.1 | |
| 36 | 1694.1 | |
| 37 | 1741.2 | 30/11 |
| 38 | 1788.2 | |
| 39 | 1835.3 | |
| 40 | 1882.4 | |
| 41 | 1929.4 | |
| 42 | 1976.5 | |
| 43 | 2023.5 | |
| 44 | 2070.6 | |
| 45 | 2117.6 | 17/5 |
| 46 | 2164.7 | 7/2 |
| 47 | 2211.8 | |
| 48 | 2258.8 | |
| 49 | 2305.9 | 19/5 |
| 50 | 2352.9 | |
| 51 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +23.5 | -19.6 | +0.0 | -9.8 | +3.9 | +19.4 | +23.5 | +7.9 | +13.7 | -10.1 | -19.6 |
| Relative (%) | +50.0 | -41.7 | +0.0 | -20.9 | +8.3 | +41.2 | +50.0 | +16.7 | +29.1 | -21.6 | -41.7 | |
| Steps (reduced) |
26 (26) |
40 (40) |
51 (0) |
59 (8) |
66 (15) |
72 (21) |
77 (26) |
81 (30) |
85 (34) |
88 (37) |
91 (40) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.0 | -4.1 | +17.6 | +0.0 | -10.8 | -15.7 | -15.2 | -9.8 | -0.2 | +13.4 | -16.5 |
| Relative (%) | -36.1 | -8.8 | +37.4 | +0.0 | -23.0 | -33.3 | -32.2 | -20.9 | -0.4 | +28.4 | -35.1 | |
| Steps (reduced) |
94 (43) |
97 (46) |
100 (49) |
102 (0) |
104 (2) |
106 (4) |
108 (6) |
110 (8) |
112 (10) |
114 (12) |
115 (13) | |