62ed6
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Prime factorization
2 × 31
Step size
50.0315¢
Octave
24\62ed6 (1200.76¢) (→12\31ed6)
Twelfth
38\62ed6 (1901.2¢) (→19\31ed6)
Consistency limit
5
Distinct consistency limit
5
| ← 61ed6 | 62ed6 | 63ed6 → |
62 equal divisions of the 6th harmonic (abbreviated 62ed6) is a nonoctave tuning system that divides the interval of 6/1 into 62 equal parts of about 50 ¢ each. Each step represents a frequency ratio of 61/62, or the 62nd root of 6.
62ED6 is related to 24edo (quarter-tone tuning), but with the 6/1 rather than the 2/1 being just, which stretches the octave by about 0.76 cents. It is consistent to the 6-integer-limit.
Lookalikes: 14edf, 24edo, 38edt, 56ed5
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 50 | 33/32, 34/33, 35/34 |
| 2 | 100.1 | 18/17, 35/33 |
| 3 | 150.1 | 12/11 |
| 4 | 200.1 | 9/8 |
| 5 | 250.2 | 15/13, 22/19 |
| 6 | 300.2 | 19/16, 31/26 |
| 7 | 350.2 | 11/9, 27/22 |
| 8 | 400.3 | 24/19, 34/27 |
| 9 | 450.3 | 13/10, 22/17, 35/27 |
| 10 | 500.3 | 4/3 |
| 11 | 550.3 | 11/8 |
| 12 | 600.4 | 17/12, 24/17 |
| 13 | 650.4 | 16/11, 35/24 |
| 14 | 700.4 | 3/2 |
| 15 | 750.5 | 17/11 |
| 16 | 800.5 | 27/17, 35/22 |
| 17 | 850.5 | 18/11, 31/19 |
| 18 | 900.6 | 32/19 |
| 19 | 950.6 | 26/15 |
| 20 | 1000.6 | |
| 21 | 1050.7 | 11/6 |
| 22 | 1100.7 | 17/9 |
| 23 | 1150.7 | 33/17, 35/18 |
| 24 | 1200.8 | 2/1 |
| 25 | 1250.8 | 33/16, 35/17 |
| 26 | 1300.8 | 17/8 |
| 27 | 1350.9 | 24/11, 35/16 |
| 28 | 1400.9 | 9/4 |
| 29 | 1450.9 | 30/13 |
| 30 | 1500.9 | 19/8, 31/13 |
| 31 | 1551 | 22/9, 27/11 |
| 32 | 1601 | |
| 33 | 1651 | 13/5 |
| 34 | 1701.1 | 8/3 |
| 35 | 1751.1 | 11/4 |
| 36 | 1801.1 | 17/6 |
| 37 | 1851.2 | 32/11, 35/12 |
| 38 | 1901.2 | 3/1 |
| 39 | 1951.2 | 34/11 |
| 40 | 2001.3 | 35/11 |
| 41 | 2051.3 | |
| 42 | 2101.3 | |
| 43 | 2151.4 | |
| 44 | 2201.4 | |
| 45 | 2251.4 | 11/3 |
| 46 | 2301.5 | 34/9 |
| 47 | 2351.5 | 35/9 |
| 48 | 2401.5 | 4/1 |
| 49 | 2451.5 | 33/8 |
| 50 | 2501.6 | 17/4 |
| 51 | 2551.6 | 35/8 |
| 52 | 2601.6 | 9/2 |
| 53 | 2651.7 | |
| 54 | 2701.7 | 19/4 |
| 55 | 2751.7 | |
| 56 | 2801.8 | |
| 57 | 2851.8 | 26/5 |
| 58 | 2901.8 | 16/3 |
| 59 | 2951.9 | 11/2 |
| 60 | 3001.9 | 17/3 |
| 61 | 3051.9 | 35/6 |
| 62 | 3102 | 6/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.8 | -0.8 | +1.5 | +15.5 | +0.0 | -16.7 | +2.3 | -1.5 | +16.2 | +1.3 | +0.8 |
| Relative (%) | +1.5 | -1.5 | +3.0 | +30.9 | +0.0 | -33.4 | +4.5 | -3.0 | +32.4 | +2.6 | +1.5 | |
| Steps (reduced) |
24 (24) |
38 (38) |
48 (48) |
56 (56) |
62 (0) |
67 (5) |
72 (10) |
76 (14) |
80 (18) |
83 (21) |
86 (24) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.3 | -16.0 | +14.7 | +3.0 | -1.9 | -0.8 | +5.7 | +17.0 | -17.5 | +2.1 | -24.9 |
| Relative (%) | +24.5 | -31.9 | +29.4 | +6.1 | -3.7 | -1.5 | +11.4 | +33.9 | -34.9 | +4.1 | -49.7 | |
| Steps (reduced) |
89 (27) |
91 (29) |
94 (32) |
96 (34) |
98 (36) |
100 (38) |
102 (40) |
104 (42) |
105 (43) |
107 (45) |
108 (46) | |
|
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