User:MisterShafXen/64edo
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Prime factorization
26
Step size
18.75 ¢
Fifth
37\64 (693.75 ¢)
Semitones (A1:m2)
3:7 (56.25 ¢ : 131.3 ¢)
Dual sharp fifth
38\64 (712.5 ¢) (→ 19\32)
Dual flat fifth
37\64 (693.75 ¢)
Dual major 2nd
11\64 (206.25 ¢)
Consistency limit
3
Distinct consistency limit
3
| ← 63edo | 64edo | 65edo → |
64 equal divisions of the octave (abbreviated 64edo or 64ed2), also called 64-tone equal temperament (64tet) or 64 equal temperament (64et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 64 equal parts of about 18.8 ¢ each. Each step represents a frequency ratio of 21/64, or the 64th root of 2.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation (Dual flat fifth 37\64) |
Ups and downs notation (Dual sharp fifth 38\64) |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D | D |
| 1 | 18.8 | ^D, E♭♭♭ | ^D, vE♭ | |
| 2 | 37.5 | vD♯, ^E♭♭♭ | ^^D, E♭ | |
| 3 | 56.3 | 30/29, 31/30, 32/31 | D♯, vE♭♭ | ^3D, ^E♭ |
| 4 | 75 | ^D♯, E♭♭ | ^4D, ^^E♭ | |
| 5 | 93.8 | vD𝄪, ^E♭♭ | ^5D, ^3E♭ | |
| 6 | 112.5 | 16/15, 31/29 | D𝄪, vE♭ | v4D♯, ^4E♭ |
| 7 | 131.3 | 14/13 | ^D𝄪, E♭ | v3D♯, v5E |
| 8 | 150 | 12/11 | vD♯𝄪, ^E♭ | vvD♯, v4E |
| 9 | 168.8 | 32/29 | D♯𝄪, vE | vD♯, v3E |
| 10 | 187.5 | 29/26 | E | D♯, vvE |
| 11 | 206.3 | ^E, F♭♭ | ^D♯, vE | |
| 12 | 225 | vE♯, ^F♭♭ | E | |
| 13 | 243.8 | 15/13, 23/20 | E♯, vF♭ | ^E, vF |
| 14 | 262.5 | ^E♯, F♭ | F | |
| 15 | 281.3 | 20/17 | vE𝄪, ^F♭ | ^F, vG♭ |
| 16 | 300 | 19/16 | E𝄪, vF | ^^F, G♭ |
| 17 | 318.8 | F | ^3F, ^G♭ | |
| 18 | 337.5 | 17/14, 28/23 | ^F, G♭♭♭ | ^4F, ^^G♭ |
| 19 | 356.3 | 16/13 | vF♯, ^G♭♭♭ | ^5F, ^3G♭ |
| 20 | 375 | F♯, vG♭♭ | v4F♯, ^4G♭ | |
| 21 | 393.8 | ^F♯, G♭♭ | v3F♯, v5G | |
| 22 | 412.5 | 19/15 | vF𝄪, ^G♭♭ | vvF♯, v4G |
| 23 | 431.3 | F𝄪, vG♭ | vF♯, v3G | |
| 24 | 450 | ^F𝄪, G♭ | F♯, vvG | |
| 25 | 468.8 | 21/16 | vF♯𝄪, ^G♭ | ^F♯, vG |
| 26 | 487.5 | F♯𝄪, vG | G | |
| 27 | 506.2 | G | ^G, vA♭ | |
| 28 | 525 | 19/14, 23/17 | ^G, A♭♭♭ | ^^G, A♭ |
| 29 | 543.8 | 26/19 | vG♯, ^A♭♭♭ | ^3G, ^A♭ |
| 30 | 562.5 | 29/21 | G♯, vA♭♭ | ^4G, ^^A♭ |
| 31 | 581.3 | 7/5 | ^G♯, A♭♭ | ^5G, ^3A♭ |
| 32 | 600 | vG𝄪, ^A♭♭ | v4G♯, ^4A♭ | |
| 33 | 618.8 | 10/7 | G𝄪, vA♭ | v3G♯, v5A |
| 34 | 637.5 | ^G𝄪, A♭ | vvG♯, v4A | |
| 35 | 656.3 | 19/13 | vG♯𝄪, ^A♭ | vG♯, v3A |
| 36 | 675 | 28/19, 31/21, 34/23 | G♯𝄪, vA | G♯, vvA |
| 37 | 693.8 | A | ^G♯, vA | |
| 38 | 712.5 | ^A, B♭♭♭ | A | |
| 39 | 731.3 | 29/19, 32/21 | vA♯, ^B♭♭♭ | ^A, vB♭ |
| 40 | 750 | A♯, vB♭♭ | ^^A, B♭ | |
| 41 | 768.8 | ^A♯, B♭♭ | ^3A, ^B♭ | |
| 42 | 787.5 | 30/19 | vA𝄪, ^B♭♭ | ^4A, ^^B♭ |
| 43 | 806.3 | A𝄪, vB♭ | ^5A, ^3B♭ | |
| 44 | 825 | ^A𝄪, B♭ | v4A♯, ^4B♭ | |
| 45 | 843.7 | 13/8, 31/19 | vA♯𝄪, ^B♭ | v3A♯, v5B |
| 46 | 862.5 | 23/14, 28/17 | A♯𝄪, vB | vvA♯, v4B |
| 47 | 881.2 | B | vA♯, v3B | |
| 48 | 900 | 32/19 | ^B, C♭♭ | A♯, vvB |
| 49 | 918.8 | 17/10 | vB♯, ^C♭♭ | ^A♯, vB |
| 50 | 937.5 | B♯, vC♭ | B | |
| 51 | 956.3 | 26/15 | ^B♯, C♭ | ^B, vC |
| 52 | 975 | vB𝄪, ^C♭ | C | |
| 53 | 993.8 | B𝄪, vC | ^C, vD♭ | |
| 54 | 1012.5 | C | ^^C, D♭ | |
| 55 | 1031.3 | 29/16 | ^C, D♭♭♭ | ^3C, ^D♭ |
| 56 | 1050 | 11/6 | vC♯, ^D♭♭♭ | ^4C, ^^D♭ |
| 57 | 1068.8 | 13/7 | C♯, vD♭♭ | ^5C, ^3D♭ |
| 58 | 1087.5 | 15/8 | ^C♯, D♭♭ | v4C♯, ^4D♭ |
| 59 | 1106.3 | vC𝄪, ^D♭♭ | v3C♯, v5D | |
| 60 | 1125 | C𝄪, vD♭ | vvC♯, v4D | |
| 61 | 1143.8 | 29/15, 31/16 | ^C𝄪, D♭ | vC♯, v3D |
| 62 | 1162.5 | vC♯𝄪, ^D♭ | C♯, vvD | |
| 63 | 1181.3 | C♯𝄪, vD | ^C♯, vD | |
| 64 | 1200 | 2/1 | D | D |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 | 179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 | 233 | 239 | 241 | 251 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -8.21 | +7.44 | +6.17 | -7.57 | +3.22 | +7.54 | +2.49 | +9.23 | +1.67 | -1.29 | -7.59 | +2.19 | -5.27 | -9.26 | +7.75 | -9.17 | +8.12 | -4.31 | +7.80 | -2.79 | -8.29 | -0.05 | -8.38 | -7.40 | -2.35 | +1.20 | -8.51 | -3.07 | -9.21 | -5.17 | -2.61 | -5.14 | +7.27 | -0.50 | -4.84 | +2.71 | -5.97 | +8.30 | +3.45 | +0.67 | +0.18 | +0.84 | +1.55 | +3.54 | +4.80 | -2.82 | -4.83 | +1.89 | +5.46 | -5.77 | +6.46 | -7.97 | -3.35 |
| Relative (%) | +0.0 | -43.8 | +39.7 | +32.9 | -40.4 | +17.2 | +40.2 | +13.3 | +49.2 | +8.9 | -6.9 | -40.5 | +11.7 | -28.1 | -49.4 | +41.3 | -48.9 | +43.3 | -23.0 | +41.6 | -14.9 | -44.2 | -0.3 | -44.7 | -39.4 | -12.6 | +6.4 | -45.4 | -16.4 | -49.1 | -27.6 | -13.9 | -27.4 | +38.8 | -2.7 | -25.8 | +14.4 | -31.9 | +44.3 | +18.4 | +3.6 | +1.0 | +4.5 | +8.3 | +18.9 | +25.6 | -15.0 | -25.8 | +10.1 | +29.1 | -30.8 | +34.5 | -42.5 | -17.9 | |
| Steps (reduced) |
64 (0) |
101 (37) |
149 (21) |
180 (52) |
221 (29) |
237 (45) |
262 (6) |
272 (16) |
290 (34) |
311 (55) |
317 (61) |
333 (13) |
343 (23) |
347 (27) |
355 (35) |
367 (47) |
376 (56) |
380 (60) |
388 (4) |
394 (10) |
396 (12) |
403 (19) |
408 (24) |
414 (30) |
422 (38) |
426 (42) |
428 (44) |
431 (47) |
433 (49) |
436 (52) |
447 (63) |
450 (2) |
454 (6) |
456 (8) |
462 (14) |
463 (15) |
467 (19) |
470 (22) |
473 (25) |
476 (28) |
479 (31) |
480 (32) |
485 (37) |
486 (38) |
488 (40) |
489 (41) |
494 (46) |
499 (51) |
501 (53) |
502 (54) |
503 (55) |
506 (58) |
506 (58) |
510 (62) | |