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.
71edo is, quite unusually for an EDO this large, a dual-fifth system, with the flat fifth (which is near the fifths of 26edo and 45edo) supporting flattone temperament, and the sharp fifth (which is near 22edo's fifth) supporting superpyth and archy. Unlike small dual-fifth systems such as 18edo, both fifths are close approximations of 3/2.
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 | 16.9 | superunison |
| 2 | 33.8 | superunison |
| 3 | 50.7 | subminor second |
| 4 | 67.6 | subminor second |
| 5 | 84.5 | minor second |
| 6 | 101.4 | minor second |
| 7 | 118.3 | minor second |
| 8 | 135.2 | supraminor second |
| 9 | 152.1 | neutral second |
| 10 | 169.0 | submajor second |
| 11 | 185.9 | major second |
| 12 | 202.8 | major second |
| 13 | 219.7 | major second |
| 14 | 236.6 | supermajor second |
| 15 | 253.5 | ultramajor second |
| 16 | 270.4 | subminor third |
| 17 | 287.3 | minor third |
| 18 | 304.2 | minor third |
| 19 | 321.1 | supraminor third |
| 20 | 338.0 | supraminor third |
| 21 | 354.9 | neutral third |
| 22 | 371.8 | submajor third |
| 23 | 388.7 | major third |
| 24 | 405.6 | major third |
| 25 | 422.5 | supermajor third |
| 26 | 439.4 | supermajor third |
| 27 | 456.3 | ultramajor third |
| 28 | 473.2 | subfourth |
| 29 | 490.1 | perfect fourth |
| 30 | 507.0 | perfect fourth |
| 31 | 523.9 | superfourth |
| 32 | 540.8 | superfourth |
| 33 | 557.7 | superfourth |
| 34 | 574.6 | low tritone |
| 35 | 591.5 | low tritone |
| 36 | 608.5 | high tritone |
| 37 | 625.4 | high tritone |
| 38 | 642.3 | subfifth |
| 39 | 659.2 | subfifth |
| 40 | 676.1 | subfifth |
| 41 | 693.0 | perfect fifth |
| 42 | 709.9 | perfect fifth |
| 43 | 726.8 | superfifth |
| 44 | 743.7 | ultrafifth |
| 45 | 760.6 | subminor sixth |
| 46 | 777.5 | subminor sixth |
| 47 | 794.4 | minor sixth |
| 48 | 811.3 | minor sixth |
| 49 | 828.2 | supraminor sixth |
| 50 | 845.1 | neutral sixth |
| 51 | 862.0 | submajor sixth |
| 52 | 878.9 | submajor sixth |
| 53 | 895.8 | major sixth |
| 54 | 912.7 | major sixth |
| 55 | 929.6 | supermajor sixth |
| 56 | 946.5 | ultramajor sixth |
| 57 | 963.4 | subminor seventh |
| 58 | 980.3 | minor seventh |
| 59 | 997.2 | minor seventh |
| 60 | 1014.1 | minor seventh |
| 61 | 1031.0 | supraminor seventh |
| 62 | 1047.9 | neutral seventh |
| 63 | 1064.8 | submajor seventh |
| 64 | 1081.7 | major seventh |
| 65 | 1098.6 | major seventh |
| 66 | 1115.5 | major seventh |
| 67 | 1132.4 | supermajor seventh |
| 68 | 1149.3 | ultramajor seventh |
| 69 | 1166.2 | suboctave |
| 70 | 1183.1 | suboctave |
| 71 | 1200.0 | perfect octave |