52edo
| ← 51edo | 52edo | 53edo → |
52edo divides the octave into 52 equal parts of 23.077 cents each. It has 26edo's very flat meantone fifth and a very sharp fifth close to 1/2 septimal comma superpyth.
Theory
Script error: No such module "primes_in_edo". The 52 equal division divides the octave into 52 equal parts of 23.077 cents each. The patent val has the same mapping for 3, 7, 11 and 13 as 26 does, but its 5 is sharp rather than flat. From this it tempers out 648/625 rather than 81/80 in the 5-limit, and 225/224 and 1029/1024 in the 7-limit, showing it supports miracle, albeit badly, and may be defined by the tempering out of both 648/625 and miracle. In the 11-limit it tempers out 99/98 and 176/175 and in the 13-limit 78/77, 144/143 and 169/168. It supplies the optimal patent val for then 12&40 temperament of the diminished family in the 7- and 11-limits, and also in the 13-limit where it can be defined as tempering out 78/77, 99/98, 176/175, 567/550 rather than by two patent vals. It also gives the 13-limit patent val for the 21&52 variant of miracle.
Using the sharp fifth rather than the flat fifth (that is, using the 52b val), it contains a version of porcupine temperament, and combining 30\52 with 31\52 leads to a whole tone of 9\52, or 208 cents, which can be used inconsistently.
Intervals
| Degrees | Cents | Ups and Downs Notation | ||
|---|---|---|---|---|
| 0 | 0.000 | Perfect 1sn | P1 | D |
| 1 | 23.077 | Up 1sn | ^1 | ^D |
| 2 | 46.154 | Aug 1sn | A1 | D# |
| 3 | 69.231 | Downdim 2nd, Upaug 1sn | vd2, ^A1 | vEbb, ^D# |
| 4 | 92.308 | Dim 2nd | d2 | Ebb |
| 5 | 115.358 | Downminor 2nd | vm2 | vEb |
| 6 | 138.462 | Minor 2nd | m2 | Eb |
| 7 | 161.538 | Mid 2nd | ~2 | vE, ^Eb |
| 8 | 184.615 | Major 2nd | M2 | E |
| 9 | 207.692 | Upmajor 2nd | ^M2 | ^E |
| 10 | 230.769 | Aug 2nd | A2 | E# |
| 11 | 253.846 | Downdim 3rd, Upaug 2nd | vd3, ^A2 | vFb, ^E# |
| 12 | 276.923 | Dim 3rd | d3 | Fb |
| 13 | 300.000 | Downminor 3rd | vm3 | vF |
| 14 | 323.077 | Minor 3rd | m3 | F |
| 15 | 346.154 | Mid 3rd | ~3 | ^F, vF# |
| 16 | 369.231 | Major 3rd | M3 | F# |
| 17 | 392.308 | Upmajor 3rd | ^M3 | ^F# |
| 18 | 415.385 | Aug 3rd | A3 | Fx |
| 19 | 438.462 | Downdim 4th, Upaug 3rd | vd4, ^A4 | vGb, ^Fx |
| 20 | 461.538 | Dim 4th | d4 | Gb |
| 21 | 484.615 | Down 4th | v4 | vG |
| 22 | 507.692 | Perfect 4th | P4 | G |
| 23 | 530.769 | Up 4th | ^4 | ^G |
| 24 | 553.846 | Aug 4th | A4 | G# |
| 25 | 576.293 | Upaug 4th | ^A4 | ^G# |
| 26 | 600.000 | Double-aug 4th, Double-dim 5th | AA4, dd5 | Gx, Abb |
| 27 | 623.077 | Downdim 5th | vd5 | vAb |
| 28 | 646.154 | Dim 5th | d5 | Ab |
| 29 | 669.231 | Down 5th | v5 | vA |
| 30 | 692.308 | Perfect 5th | P5 | A |
| 31 | 715.385 | Up 5th | ^5 | ^A |
| 32 | 738.462 | Aug 5th | A5 | A# |
| 33 | 761.538 | Downdim 6th, Upaug 5th | vd6, ^A5 | vBbb, ^A# |
| 34 | 784.615 | Dim 6th | d6 | Bbb |
| 35 | 807.692 | Downminor 6th | vm6 | vBb |
| 36 | 830.769 | Minor 6th | m6 | Bb |
| 37 | 853.846 | Mid 6th | ~6 | vB, ^Bb |
| 38 | 876.923 | Major 6th | M6 | B |
| 39 | 900.000 | Upmajor 6th | ^M6 | ^B |
| 40 | 923.077 | Aug 6th | A6 | B# |
| 41 | 946.154 | Downdim 7th, Upaug 6th | vd7, ^A6 | vCb, ^B# |
| 42 | 969.231 | Dim 7th | d7 | Cb |
| 43 | 992.308 | Downminor 7th | vm7 | vC |
| 44 | 1015.385 | Minor 7th | m7 | C |
| 45 | 1038.462 | Mid 7th | ~7 | ^C, vC# |
| 46 | 1061.538 | Major 7th | M7 | C# |
| 47 | 1084.615 | Upmajor 7th | ^M7 | ^C# |
| 48 | 1107.692 | Aug 7th | A7 | Cx |
| 49 | 1130.769 | Downdim 8ve, Upaug 7th | vd8, ^A7 | vDb, ^Cx |
| 50 | 1153.846 | Dim 8ve | d8 | Db |
| 51 | 1176.923 | Down 8ve | v8 | vD |
| 52 | 1200.000 | Perfect 8ve | P8 | D |