47edt
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Prime factorization
47 (prime)
Step size
40.4671¢
Octave
30\47edt (1214.01¢)
Consistency limit
2
Distinct consistency limit
2
| ← 46edt | 47edt | 48edt → |
47 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 47edt or 47ed3), is a nonoctave tuning system that divides the interval of 3/1 into 47 equal parts of about 40.5 ¢ each. Each step represents a frequency ratio of 31/47, or the 47th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 40.5 | 27.7 | |
| 2 | 80.9 | 55.3 | |
| 3 | 121.4 | 83 | 15/14, 29/27, 31/29 |
| 4 | 161.9 | 110.6 | 11/10, 23/21 |
| 5 | 202.3 | 138.3 | |
| 6 | 242.8 | 166 | 15/13, 31/27 |
| 7 | 283.3 | 193.6 | 13/11, 27/23 |
| 8 | 323.7 | 221.3 | |
| 9 | 364.2 | 248.9 | 21/17 |
| 10 | 404.7 | 276.6 | 19/15, 29/23 |
| 11 | 445.1 | 304.3 | |
| 12 | 485.6 | 331.9 | |
| 13 | 526.1 | 359.6 | 19/14, 23/17 |
| 14 | 566.5 | 387.2 | 18/13, 25/18 |
| 15 | 607 | 414.9 | 27/19 |
| 16 | 647.5 | 442.6 | |
| 17 | 687.9 | 470.2 | |
| 18 | 728.4 | 497.9 | 29/19 |
| 19 | 768.9 | 525.5 | 14/9 |
| 20 | 809.3 | 553.2 | |
| 21 | 849.8 | 580.9 | 18/11, 31/19 |
| 22 | 890.3 | 608.5 | 5/3 |
| 23 | 930.7 | 636.2 | |
| 24 | 971.2 | 663.8 | |
| 25 | 1011.7 | 691.5 | 9/5 |
| 26 | 1052.1 | 719.1 | 11/6 |
| 27 | 1092.6 | 746.8 | |
| 28 | 1133.1 | 774.5 | 25/13, 27/14 |
| 29 | 1173.5 | 802.1 | |
| 30 | 1214 | 829.8 | |
| 31 | 1254.5 | 857.4 | 31/15 |
| 32 | 1294.9 | 885.1 | 19/9 |
| 33 | 1335.4 | 912.8 | 13/6 |
| 34 | 1375.9 | 940.4 | 31/14 |
| 35 | 1416.3 | 968.1 | 25/11 |
| 36 | 1456.8 | 995.7 | |
| 37 | 1497.3 | 1023.4 | |
| 38 | 1537.8 | 1051.1 | 17/7 |
| 39 | 1578.2 | 1078.7 | |
| 40 | 1618.7 | 1106.4 | 23/9, 28/11 |
| 41 | 1659.2 | 1134 | 13/5 |
| 42 | 1699.6 | 1161.7 | |
| 43 | 1740.1 | 1189.4 | 30/11 |
| 44 | 1780.6 | 1217 | 14/5 |
| 45 | 1821 | 1244.7 | |
| 46 | 1861.5 | 1272.3 | |
| 47 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +14.0 | +0.0 | -12.4 | +5.9 | +14.0 | -10.1 | +1.6 | +0.0 | +19.9 | +16.8 | -12.4 |
| Relative (%) | +34.6 | +0.0 | -30.7 | +14.6 | +34.6 | -24.8 | +3.9 | +0.0 | +49.3 | +41.5 | -30.7 | |
| Steps (reduced) |
30 (30) |
47 (0) |
59 (12) |
69 (22) |
77 (30) |
83 (36) |
89 (42) |
94 (0) |
99 (5) |
103 (9) |
106 (12) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.9 | +4.0 | +5.9 | +15.6 | -8.4 | +14.0 | +1.3 | -6.5 | -10.1 | -9.7 | -5.7 |
| Relative (%) | +26.8 | +9.8 | +14.6 | +38.5 | -20.8 | +34.6 | +3.3 | -16.1 | -24.8 | -23.9 | -14.0 | |
| Steps (reduced) |
110 (16) |
113 (19) |
116 (22) |
119 (25) |
121 (27) |
124 (30) |
126 (32) |
128 (34) |
130 (36) |
132 (38) |
134 (40) | |
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