22edt
22edt is the equal division of the third harmonic (edt) into 22 tones, each 86.4525 cents in size.
| ← 21edt | 22edt | 23edt → |
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics. It also has the 4L+5s MOS with L=3 and s=2 approximating 5/3 somewhat fuzzily.
Like 11edt, both the octave and small whole tone (10/9) are about 10c off (sharp and flat respectively) dissonant but recognizable. Like 16edt and Blackwood, admitting the octave induces an interpretation into a tritave-based version of Whitewood temperament.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | -19.8 | +2.8 | -1.6 | -31.5 | +22.8 | +3.2 | +18.2 | -37.3 | +20.2 | -26.8 | -31.6 | -27.6 | -8.7 |
| Relative (%) | +12.0 | +0.0 | -22.9 | +3.3 | -1.8 | -36.4 | +26.4 | +3.7 | +21.1 | -43.1 | +23.4 | -31.0 | -36.5 | -31.9 | -10.0 | |
| Steps (reduced) |
14 (14) |
22 (0) |
32 (10) |
39 (17) |
48 (4) |
51 (7) |
57 (13) |
59 (15) |
63 (19) |
67 (1) |
69 (3) |
72 (6) |
74 (8) |
75 (9) |
77 (11) | |
Intervals
| Steps | Cents | hekts |
|---|---|---|
| 1 | 86.453 | 59.091 |
| 2 | 172.905 | 118.182 |
| 3 | 259.358 | 177.273 |
| 4 | 345.81 | 236.364 |
| 5 | 432.263 | 295.4545 |
| 6 | 518.715 | 354.5455 |
| 7 | 605.168 | 413.636 |
| 8 | 691.620 | 472.727 |
| 9 | 778.073 | 531.818 |
| 10 | 864.525 | 590.909 |
| 11 | 950.978 | 650 |
| 12 | 1037.430 | 709.091 |
| 13 | 1123.883 | 768.182 |
| 14 | 1210.335 | 827.273 |
| 15 | 1296.788 | 886.364 |
| 16 | 1383.24 | 945.4545 |
| 17 | 1469.693 | 1004.5455 |
| 18 | 1556.145 | 1063.636 |
| 19 | 1642.598 | 1122.727 |
| 20 | 1729.05 | 1181.818 |
| 21 | 1815.503 | 1240.909 |
| 22 | 1901.955 | 1300 |