71edo
| ← 70edo | 71edo | 72edo → |
The 71 equal temperament or 71-EDO divides the octave into 71 equal parts of 16.901 cents each.
71edo is the 20th prime EDO.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.90 | +2.42 | -5.45 | -1.09 | +6.43 | +4.54 | -6.58 | -3.55 | +6.71 | +2.46 | -2.92 |
| Relative (%) | +46.8 | +14.3 | -32.2 | -6.5 | +38.0 | +26.9 | -38.9 | -21.0 | +39.7 | +14.5 | -17.3 | |
| Steps (reduced) |
113 (42) |
165 (23) |
199 (57) |
225 (12) |
246 (33) |
263 (50) |
277 (64) |
290 (6) |
302 (18) |
312 (28) |
321 (37) | |
It tempers out 20480/19683 and 393216/390625 in the 5-limit, 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242 and 100/99 in the 11-limit, and 91/90 in the 13-limit. In the 13-limit it supplies the optimal patent val for the 29&71 and 34&37 temperaments.
Intervals
| # | Cents | Diatonic interval category |
|---|---|---|
| 0 | 0.0 | perfect unison |
| 1 | 17.1 | superunison |
| 2 | 34.3 | superunison |
| 3 | 51.4 | subminor second |
| 4 | 68.6 | subminor second |
| 5 | 85.7 | minor second |
| 6 | 102.9 | minor second |
| 7 | 120.0 | supraminor second |
| 8 | 137.1 | supraminor second |
| 9 | 154.3 | neutral second |
| 10 | 171.4 | submajor second |
| 11 | 188.6 | major second |
| 12 | 205.7 | major second |
| 13 | 222.9 | supermajor second |
| 14 | 240.0 | ultramajor second |
| 15 | 257.1 | ultramajor second |
| 16 | 274.3 | subminor third |
| 17 | 291.4 | minor third |
| 18 | 308.6 | minor third |
| 19 | 325.7 | supraminor third |
| 20 | 342.9 | neutral third |
| 21 | 360.0 | submajor third |
| 22 | 377.1 | submajor third |
| 23 | 394.3 | major third |
| 24 | 411.4 | major third |
| 25 | 428.6 | supermajor third |
| 26 | 445.7 | ultramajor third |
| 27 | 462.9 | subfourth |
| 28 | 480.0 | perfect fourth |
| 29 | 497.1 | perfect fourth |
| 30 | 514.3 | perfect fourth |
| 31 | 531.4 | superfourth |
| 32 | 548.6 | superfourth |
| 33 | 565.7 | low tritone |
| 34 | 582.9 | low tritone |
| 35 | 600.0 | high tritone |
| 36 | 617.1 | high tritone |
| 37 | 634.3 | high tritone |
| 38 | 651.4 | subfifth |
| 39 | 668.6 | subfifth |
| 40 | 685.7 | perfect fifth |
| 41 | 702.9 | perfect fifth |
| 42 | 720.0 | superfifth |
| 43 | 737.1 | superfifth |
| 44 | 754.3 | ultrafifth |
| 45 | 771.4 | subminor sixth |
| 46 | 788.6 | minor sixth |
| 47 | 805.7 | minor sixth |
| 48 | 822.9 | supraminor sixth |
| 49 | 840.0 | neutral sixth |
| 50 | 857.1 | neutral sixth |
| 51 | 874.3 | submajor sixth |
| 52 | 891.4 | major sixth |
| 53 | 908.6 | major sixth |
| 54 | 925.7 | supermajor sixth |
| 55 | 942.9 | ultramajor sixth |
| 56 | 960.0 | subminor seventh |
| 57 | 977.1 | subminor seventh |
| 58 | 994.3 | minor seventh |
| 59 | 1011.4 | minor seventh |
| 60 | 1028.6 | supraminor seventh |
| 61 | 1045.7 | neutral seventh |
| 62 | 1062.9 | submajor seventh |
| 63 | 1080.0 | major seventh |
| 64 | 1097.1 | major seventh |
| 65 | 1114.3 | major seventh |
| 66 | 1131.4 | supermajor seventh |
| 67 | 1148.6 | ultramajor seventh |
| 68 | 1165.7 | suboctave |
| 69 | 1182.9 | suboctave |
| 70 | 1200.0 | perfect octave |