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 → |
32EDF is the equal division of the just perfect fifth into 32 parts of 21.9361 cents each, corresponding to 54.7044 edo (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 1258 EDOs.
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 | |