32edf
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Prime factorization
25
Step size
21.9361¢
Octave
55\32edf (1206.49¢)
Twelfth
87\32edf (1908.44¢)
Consistency limit
2
Distinct consistency limit
2
| ← 31edf | 32edf | 33edf → |
32 equal divisions of the perfect fifth (abbreviated 32edf or 32ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 32 equal parts of about 21.9 ¢ each. Each step represents a frequency ratio of (3/2)1/32, or the 32nd root of 3/2.
Theory
32edf corresponds to 54.7044edo, similar to every seventh step of 383edo. It is related to the regular temperament which tempers out [127 -127 32⟩ in the 5-limit, which is supported by 164-, 383-, 547-, 711-, 875-, and 1258edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.49 | +6.49 | -8.97 | -0.43 | -8.97 | +9.33 | -2.48 | -8.97 | +6.06 | -5.40 | -2.48 |
| Relative (%) | +29.6 | +29.6 | -40.9 | -2.0 | -40.9 | +42.5 | -11.3 | -40.9 | +27.6 | -24.6 | -11.3 | |
| Steps (reduced) |
55 (23) |
87 (23) |
109 (13) |
127 (31) |
141 (13) |
154 (26) |
164 (4) |
173 (13) |
182 (22) |
189 (29) |
196 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.44 | -6.12 | +6.06 | +4.00 | +8.73 | -2.48 | -8.34 | -9.40 | -6.12 | +1.09 | -10.06 |
| Relative (%) | -43.0 | -27.9 | +27.6 | +18.3 | +39.8 | -11.3 | -38.0 | -42.8 | -27.9 | +5.0 | -45.9 | |
| Steps (reduced) |
202 (10) |
208 (16) |
214 (22) |
219 (27) |
224 (0) |
228 (4) |
232 (8) |
236 (12) |
240 (16) |
244 (20) |
247 (23) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 21.9361 | 81/80 | |
| 2 | 43.8722 | 40/39 | |
| 3 | 65.8083 | 27/26, 28/27 | |
| 4 | 87.7444 | ||
| 5 | 109.6805 | 49/46, 16/15 | |
| 6 | 131.6166 | 41/38 | |
| 7 | 153.5527 | 59/54, 18/11 | |
| 8 | 175.4888 | ||
| 9 | 197.4248 | 65/58 | |
| 10 | 219.3609 | 42/37 | |
| 11 | 241.297 | (23/20) | |
| 12 | 263.2331 | 7/6 | |
| 13 | 285.1692 | ||
| 14 | 307.1053 | 117/98 | |
| 15 | 329.0414 | 52/43 | |
| 16 | 350.9775 | 60/49, 49/40 | |
| 17 | 372.9136 | 129/104 | |
| 18 | 394.8497 | 49/39 | |
| 19 | 416.7858 | 14/11 | |
| 20 | 438.7219 | 9/7 | |
| 21 | 460.6580 | (30/23) | |
| 22 | 482.5941 | 37/28 | |
| 23 | 504.5302 | 87/65 | pseudo-4/3 |
| 24 | 526.4663 | 61/45 | |
| 25 | 548.4023 | 81/59 | |
| 26 | 570.3384 | 57/41 | |
| 27 | 592.2745 | 69/49 | |
| 28 | 614.2106 | 10/7 | |
| 29 | 636.1467 | 13/9 | |
| 30 | 658.0828 | 117/80 | |
| 31 | 680.0189 | 40/27 | |
| 32 | 701.9550 | exact 3/2 | just perfect fifth |
| 33 | 723.8911 | 243/160 | |
| 34 | 745.8372 | 20/13 | |
| 35 | 766.7633 | 81/52, 14/9 | |
| 36 | 790.6994 | ||
| 37 | 811.6355 | 147/92, 8/5 | |
| 38 | 833.5716 | 123/76 | |
| 39 | 855.5077 | 59/36, 18/11 | |
| 40 | 877.4438 | ||
| 41 | 899.3798 | 195/116 | |
| 42 | 922.3159 | 63/37 | |
| 43 | 943.252 | 69/40 | |
| 44 | 965.1881 | 7/4 | |
| 45 | 987.1242 | ||
| 46 | 1009.0603 | 351/196 | |
| 47 | 1030.9964 | 78/43 | |
| 48 | 1052.9325 | 90/49, 147/80 | |
| 49 | 1076.8686 | 387/208 | |
| 50 | 1096.847 | 147/78 | |
| 51 | 1118.7408 | 21/11 | |
| 52 | 1140.6769 | 27/14 | |
| 53 | 1162.613 | 45/23 | |
| 54 | 1184.5451 | 111/56 | |
| 55 | 1206.4852 | 261/130 | pseudo-2/1 |
| 56 | 1228.4213 | 61/30 | |
| 57 | 1250.3575 | 243/118 | |
| 58 | 1272.2934 | 171/82 | |
| 59 | 1294.2395 | 207/98 | |
| 60 | 1316.1656 | 15/7 | |
| 61 | 1338.1017 | 13/6 | |
| 62 | 1360.0378 | 351/160 | |
| 63 | 1381.9739 | 20/9 | |
| 64 | 1403.91 | exact 9/4 | |