33edt
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Prime factorization
3 × 11
Step size
57.635¢
Octave
21\33edt (1210.34¢) (→7\11edt)
Consistency limit
4
Distinct consistency limit
4
| ← 32edt | 33edt | 34edt → |
33EDT is the equal division of the third harmonic into 33 parts of 57.6350 cents each, corresponding to 20.8207 edo. It has a distinct flat tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, 19, and 23 are all flat. It is consistent to the no-twos 23-limit, tempering out 3125/3087 and 588245/531441 in the 7-limit; 125/121, 3087/3025, and 3773/3645 in the 11-limit; 147/143, 175/169, 847/845, and 2197/2187 in the 13-limit; 119/117, 189/187, 225/221, and 1105/1089 in the 17-limit; 171/169, 175/171, 247/243, and 325/323 in the 19-limit; 209/207, 255/253, and 299/297 in the 23-limit (no-twos subgroup).
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 57.6 | 39.4 | 27/26, 28/27 |
| 2 | 115.3 | 78.8 | 15/14 |
| 3 | 172.9 | 118.2 | 11/10, 21/19 |
| 4 | 230.5 | 157.6 | |
| 5 | 288.2 | 197 | 13/11, 20/17 |
| 6 | 345.8 | 236.4 | 11/9, 27/22, 28/23 |
| 7 | 403.4 | 275.8 | 19/15 |
| 8 | 461.1 | 315.2 | 13/10, 17/13 |
| 9 | 518.7 | 354.5 | 23/17, 27/20 |
| 10 | 576.4 | 393.9 | 7/5 |
| 11 | 634 | 433.3 | 13/9 |
| 12 | 691.6 | 472.7 | |
| 13 | 749.3 | 512.1 | 17/11, 20/13 |
| 14 | 806.9 | 551.5 | 27/17 |
| 15 | 864.5 | 590.9 | 23/14, 28/17 |
| 16 | 922.2 | 630.3 | 17/10 |
| 17 | 979.8 | 669.7 | 23/13 |
| 18 | 1037.4 | 709.1 | 20/11 |
| 19 | 1095.1 | 748.5 | 17/9 |
| 20 | 1152.7 | 787.9 | |
| 21 | 1210.3 | 827.3 | |
| 22 | 1268 | 866.7 | 23/11, 27/13 |
| 23 | 1325.6 | 906.1 | 15/7, 28/13 |
| 24 | 1383.2 | 945.5 | 20/9 |
| 25 | 1440.9 | 984.8 | 23/10 |
| 26 | 1498.5 | 1024.2 | |
| 27 | 1556.1 | 1063.6 | 22/9, 27/11 |
| 28 | 1613.8 | 1103 | 28/11 |
| 29 | 1671.4 | 1142.4 | |
| 30 | 1729.1 | 1181.8 | 19/7 |
| 31 | 1786.7 | 1221.2 | 14/5 |
| 32 | 1844.3 | 1260.6 | 26/9 |
| 33 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | +20.7 | -19.8 | +10.3 | -26.0 | -26.6 | +0.0 | -9.5 | -1.6 | +20.7 |
| Relative (%) | +17.9 | +0.0 | +35.9 | -34.4 | +17.9 | -45.1 | -46.2 | +0.0 | -16.5 | -2.8 | +35.9 | |
| Steps (reduced) |
21 (21) |
33 (0) |
42 (9) |
48 (15) |
54 (21) |
58 (25) |
62 (29) |
66 (0) |
69 (3) |
72 (6) |
75 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | -15.7 | -19.8 | -16.3 | -6.0 | +10.3 | -25.6 | +0.8 | -26.0 | +8.7 | -10.6 |
| Relative (%) | -4.6 | -27.2 | -34.4 | -28.3 | -10.4 | +17.9 | -44.5 | +1.5 | -45.1 | +15.2 | -18.4 | |
| Steps (reduced) |
77 (11) |
79 (13) |
81 (15) |
83 (17) |
85 (19) |
87 (21) |
88 (22) |
90 (24) |
91 (25) |
93 (27) |
94 (28) | |
|
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