29edt
| ← 28edt | 29edt | 30edt → |
29EDT is the equal division of the third harmonic into 29 parts of 65.5847 cents each, corresponding to 18.2970 edo. It is related to the luminal temperament.
While not possessing good approximations to most integer harmonics, it does have a few very good rational intervals: notably 27/26, 17/10, 45/32, and 11/6.
Intervals
| steps | cents | hekts | corresponding JI intervals |
comments |
|---|---|---|---|---|
| 0 | 1/1 | |||
| 1 | 65.5847 | 44.8276 | 27/26 | |
| 2 | 131.1693 | 89.6552 | 14/13, 27/25, 55/51 | |
| 3 | 196.7540 | 134.4828 | 9/8, 28/25 | pseudo-10/9 |
| 4 | 262.3386 | 179.3103 | 7/6 | |
| 5 | 327.9233 | 224.1379 | pseudo-6/5 | |
| 6 | 393.5079 | 268.9655 | 64/51 | pseudo-5/4 |
| 7 | 459.0926 | 313.7931 | 13/10 | |
| 8 | 524.6772 | 358.6206 | 65/48, 27/20 | |
| 9 | 590.2619 | 403.4483 | 45/32 | |
| 10 | 655.8466 | 448.2759 | 16/11 | |
| 11 | 721.4312 | 493.1034 | pseudo-3/2 | |
| 12 | 787.0159 | 537.9310 | 63/40, 52/33 | pseudo-8/5 |
| 13 | 852.6005 | 582.7586 | 18/11 | flat pseudo-5/3 |
| 14 | 918.1852 | 627.5862 | 17/10 | sharp pseudo-5/3 |
| 15 | 983.7698 | 672.4138 | 30/17 | flat pseudo-9/5 |
| 16 | 1049.3545 | 717.2414 | 11/6 | sharp pseudo-9/5 |
| 17 | 1114.9391 | 772.0690 | 99/52, 40/21 | pseudo-15/8 |
| 18 | 1180.5238 | 806.8966 | pseudooctave | |
| 19 | 1246.1084 | 851.7241 | 33/16 | |
| 20 | 1311.6931 | 896.5517 | 32/15 | |
| 21 | 1377.2778 | 941.3794 | 144/65, 20/9 | |
| 22 | 1442.8624 | 986.2069 | 30/13 | pseudo-7/3 (7/6 plus pseudooctave) |
| 23 | 1508.4471 | 1031.0345 | 153/64 | pseudo-12/5 |
| 24 | 1574.0317 | 1075.8621 | pseudo-5/2 | |
| 25 | 1639.6164 | 1120.6897 | 18/7 | |
| 26 | 1705.2010 | 1165.5172 | 8/3, 75/28 | pseudo-27/10 |
| 27 | 1770.7857 | 1210.3448 | 39/14, 25/9, 153/55 | |
| 28 | 1836.3703 | 1255.1724 | 26/9 | |
| 29 | 1901.9550 | 1300.0000 | 3/1 | just perfect fifth plus an octave |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -19.5 | +0.0 | +26.6 | -31.8 | -19.5 | -24.0 | +7.2 | +0.0 | +14.4 | -19.5 | +26.6 |
| Relative (%) | -29.7 | +0.0 | +40.6 | -48.4 | -29.7 | -36.6 | +10.9 | +0.0 | +21.9 | -29.7 | +40.6 | |
| Steps (reduced) |
18 (18) |
29 (0) |
37 (8) |
42 (13) |
47 (18) |
51 (22) |
55 (26) |
58 (0) |
61 (3) |
63 (5) |
66 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.2 | +22.1 | -31.8 | -12.3 | +13.9 | -19.5 | +18.1 | -5.1 | -24.0 | +26.6 | +15.3 |
| Relative (%) | +29.3 | +33.7 | -48.4 | -18.8 | +21.2 | -29.7 | +27.6 | -7.8 | -36.6 | +40.6 | +23.3 | |
| Steps (reduced) |
68 (10) |
70 (12) |
71 (13) |
73 (15) |
75 (17) |
76 (18) |
78 (20) |
79 (21) |
80 (22) |
82 (24) |
83 (25) | |