63edo: Difference between revisions
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63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 736/729. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to [[17edo]], but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7. | 63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 736/729. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to [[17edo]], but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7. | ||
{{ | {{Harmonics in equal|63}} | ||
== Interval table == | == Interval table == | ||
Revision as of 06:48, 21 January 2024
| ← 62edo | 63edo | 64edo → |
The 63 equal division or 63-EDO divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 540/539. In the 13-limit it tempers out 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.
63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 736/729. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +2.81 | -5.36 | +2.60 | +1.06 | -2.43 | +9.33 | +7.25 | +0.30 | -1.01 | -2.18 |
| Relative (%) | +0.0 | +14.7 | -28.1 | +13.7 | +5.6 | -12.8 | +49.0 | +38.1 | +1.6 | -5.3 | -11.4 | |
| Steps (reduced) |
63 (0) |
100 (37) |
146 (20) |
177 (51) |
218 (29) |
233 (44) |
258 (6) |
268 (16) |
285 (33) |
306 (54) |
312 (60) | |
Interval table
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 19 | ^D, v3E♭ | |
| 2 | 38.1 | ^^D, vvE♭ | |
| 3 | 57.1 | 29/28, 30/29, 31/30, 32/31, 33/32 | ^3D, vE♭ |
| 4 | 76.2 | 23/22, 24/23 | v3D♯, E♭ |
| 5 | 95.2 | 18/17, 19/18 | vvD♯, ^E♭ |
| 6 | 114.3 | 16/15, 31/29 | vD♯, ^^E♭ |
| 7 | 133.3 | D♯, ^3E♭ | |
| 8 | 152.4 | 12/11, 35/32 | ^D♯, v3E |
| 9 | 171.4 | 21/19, 32/29 | ^^D♯, vvE |
| 10 | 190.5 | 19/17, 29/26 | ^3D♯, vE |
| 11 | 209.5 | 26/23, 35/31 | E |
| 12 | 228.6 | 8/7 | ^E, v3F |
| 13 | 247.6 | 15/13 | ^^E, vvF |
| 14 | 266.7 | 7/6 | ^3E, vF |
| 15 | 285.7 | 13/11, 33/28 | F |
| 16 | 304.8 | 31/26 | ^F, v3G♭ |
| 17 | 323.8 | 29/24, 35/29 | ^^F, vvG♭ |
| 18 | 342.9 | 28/23 | ^3F, vG♭ |
| 19 | 361.9 | 16/13, 21/17 | v3F♯, G♭ |
| 20 | 381 | vvF♯, ^G♭ | |
| 21 | 400 | 29/23, 34/27 | vF♯, ^^G♭ |
| 22 | 419 | 14/11 | F♯, ^3G♭ |
| 23 | 438.1 | 9/7 | ^F♯, v3G |
| 24 | 457.1 | 13/10, 30/23 | ^^F♯, vvG |
| 25 | 476.2 | 29/22 | ^3F♯, vG |
| 26 | 495.2 | 4/3 | G |
| 27 | 514.3 | 31/23, 35/26 | ^G, v3A♭ |
| 28 | 533.3 | 15/11 | ^^G, vvA♭ |
| 29 | 552.4 | 11/8 | ^3G, vA♭ |
| 30 | 571.4 | 32/23 | v3G♯, A♭ |
| 31 | 590.5 | 31/22 | vvG♯, ^A♭ |
| 32 | 609.5 | 27/19 | vG♯, ^^A♭ |
| 33 | 628.6 | 23/16, 33/23 | G♯, ^3A♭ |
| 34 | 647.6 | 16/11 | ^G♯, v3A |
| 35 | 666.7 | 22/15 | ^^G♯, vvA |
| 36 | 685.7 | ^3G♯, vA | |
| 37 | 704.8 | 3/2 | A |
| 38 | 723.8 | 35/23 | ^A, v3B♭ |
| 39 | 742.9 | 20/13, 23/15 | ^^A, vvB♭ |
| 40 | 761.9 | 14/9, 31/20 | ^3A, vB♭ |
| 41 | 781 | 11/7 | v3A♯, B♭ |
| 42 | 800 | 27/17, 35/22 | vvA♯, ^B♭ |
| 43 | 819 | vA♯, ^^B♭ | |
| 44 | 838.1 | 13/8, 34/21 | A♯, ^3B♭ |
| 45 | 857.1 | 23/14 | ^A♯, v3B |
| 46 | 876.2 | ^^A♯, vvB | |
| 47 | 895.2 | ^3A♯, vB | |
| 48 | 914.3 | 22/13 | B |
| 49 | 933.3 | 12/7 | ^B, v3C |
| 50 | 952.4 | 26/15, 33/19 | ^^B, vvC |
| 51 | 971.4 | 7/4 | ^3B, vC |
| 52 | 990.5 | 23/13 | C |
| 53 | 1009.5 | 34/19 | ^C, v3D♭ |
| 54 | 1028.6 | 29/16 | ^^C, vvD♭ |
| 55 | 1047.6 | 11/6 | ^3C, vD♭ |
| 56 | 1066.7 | v3C♯, D♭ | |
| 57 | 1085.7 | 15/8 | vvC♯, ^D♭ |
| 58 | 1104.8 | 17/9 | vC♯, ^^D♭ |
| 59 | 1123.8 | 23/12 | C♯, ^3D♭ |
| 60 | 1142.9 | 29/15, 31/16 | ^C♯, v3D |
| 61 | 1161.9 | ^^C♯, vvD | |
| 62 | 1181 | ^3C♯, vD | |
| 63 | 1200 | 2/1 | D |
Music
Cam Taylor
- Seconds and Otonal Shifts
- those early dreams
- Early Dreams 2
- Improvisation in 12-tone fifths chain in 63EDO