51edo
| ← 50edo | 51edo | 52edo → |
51 EDO divides the octave into 51 equal parts of 23.5 cents each, which is about the size of the Pythagorean comma (even though this comma itself is mapped to a different interval).
Theory
Script error: No such module "primes_in_edo". 51 EDO tempers out 250/243 in the 5-limit, 225/224 and 2401/2400 in the 7-limit, and 55/54 and 100/99 in the 11-limit. It is the optimal patent val for sonic, the rank three temperament tempering out 250/243, 55/54 and 100/99, and also for the rank four temperament tempering out 55/54. It provides an alternative tuning to 22edo for porcupine temperament, with a nice fifth but a rather flat major third, and the optimal patent val for 7 and 11-limit porky temperament, which is sonic plus 225/224. 51 contains an Archeotonic scale based on repetitions of 8\51, creating a scale with a whole tone-like drive towards the tonic through the 17edo semitone at the top.
Intervals
| Degrees | Cents | Ups and Downs Notation | ||
|---|---|---|---|---|
| 0 | 0.000 | Perfect 1sn | P1 | D |
| 1 | 23.529 | Up 1sn | ^1 | ^D |
| 2 | 47.059 | Downminor 2nd | vm2 | vEb |
| 3 | 70.588 | Minor 2nd | m2 | Eb |
| 4 | 94.118 | Upminor 2nd | ^m2 | ^Eb |
| 5 | 117.647 | Downmid 2nd | v~2 | ^^Eb |
| 6 | 141.176 | Mid 2nd | ~2 | vvvE, ^^^Eb |
| 7 | 164.706 | Upmid 2nd | ^~2 | vvE |
| 8 | 188.235 | Downmajor 2nd | vM2 | vE |
| 9 | 211.765 | Major 2nd | M2 | E |
| 10 | 235.294 | Upmajor 2nd | ^M2 | ^E |
| 11 | 258.824 | Downminor 3rd | vm3 | vF |
| 12 | 282.353 | Minor 3rd | m3 | F |
| 13 | 305.882 | Upminor 3rd | ^m3 | ^F |
| 14 | 329.412 | Downmid 3rd | v~3 | ^^F |
| 15 | 352.941 | Mid 3rd | ~3 | ^^^F, vvvF# |
| 16 | 376.471 | Upmid 3rd | ^~3 | vvF# |
| 17 | 400.000 | Downmajor 3rd | vM3 | vF# |
| 18 | 423.529 | Major 3rd | M3 | F# |
| 19 | 447.509 | Upmajor 3rd | ^M3 | ^F# |
| 20 | 470.588 | Down 4th | v4 | vG |
| 21 | 494.118 | Perfect 4th | P4 | G |
| 22 | 517.647 | Up 4th | ^1 | ^G |
| 23 | 541.176 | Downdim 5th | vd5 | vAb |
| 24 | 564.706 | Dim 5th | d5 | Ab |
| 25 | 588.235 | Updim 5th | ^d5 | ^Ab |
| 26 | 611.765 | Downaug 4th | vA4 | vG# |
| 27 | 635.294 | Aug 4th | A4 | G# |
| 28 | 658.824 | Upaug 4th | ^A4 | ^G# |
| 29 | 682.353 | Down 5th | v5 | vA |
| 30 | 705.882 | Perfect 5th | P5 | A |
| 31 | 729.412 | Up 5th | ^5 | ^A |
| 32 | 752.941 | Downminor 6th | vm6 | vBb |
| 33 | 776.471 | Minor 6th | m6 | Bb |
| 34 | 800.000 | Upminor 6th | ^m6 | ^Bb |
| 35 | 823.529 | Downmid 6th | v~6 | ^^Bb |
| 36 | 847.059 | Mid 6th | ~6 | vvvB, ^^^Bb |
| 37 | 870.588 | Upmid 6th | ^~6 | vvB |
| 38 | 894.118 | Downmajor 6th | vM6 | vB |
| 39 | 917.647 | Major 6th | M6 | B |
| 40 | 941.176 | Upmajor 6th | ^M6 | ^B |
| 41 | 964.706 | Downminor 7th | vm7 | vC |
| 42 | 988.235 | Minor 7th | m7 | C |
| 43 | 1011.765 | Upminor 7th | ^m7 | ^C |
| 44 | 1035.294 | Downmid 7th | v~7 | ^^C |
| 45 | 1058.824 | Mid 7th | ~7 | ^^^C, vvvC# |
| 46 | 1082.353 | Upmid 7th | ^~7 | vvC# |
| 47 | 1105.882 | Downmajor 7th | vM7 | vC# |
| 48 | 1129.412 | Major 7th | M7 | C# |
| 49 | 1152.941 | Upmajor 7th | ^M7 | ^C# |
| 50 | 1176.471 | Down 8ve | v8 | vD |
| 51 | 1200.000 | Perfect 8ve | P8 | D |
Music
- James Mulvale (FAST-fast) - STARS (Thoughts and Prayers) (51 EDO for 51 States)