14edt
| ← 13edt | 14edt | 15edt → |
14 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 14edt or 14ed3), is a nonoctave tuning system that divides the interval of 3/1 into 14 equal parts of about 136 ¢ each. Each step represents a frequency ratio of 31/14, or the 14th root of 3.
Theory
14edt is the simplest edt with a distinct form for each rotation of the antilambda scale. It can be seen as 9edo with significantly stretched octaves (~23 ¢) and may be used as a tuning for Pelog.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +22.7 | +0.0 | +45.4 | +66.6 | +22.7 | +27.5 | -67.8 | +0.0 | -46.5 | +60.2 | +45.4 |
| Relative (%) | +16.7 | +0.0 | +33.4 | +49.0 | +16.7 | +20.3 | -49.9 | +0.0 | -34.3 | +44.3 | +33.4 | |
| Steps (reduced) |
9 (9) |
14 (0) |
18 (4) |
21 (7) |
23 (9) |
25 (11) |
26 (12) |
28 (0) |
29 (1) |
31 (3) |
32 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +42.7 | +50.2 | +66.6 | -45.1 | -14.2 | +22.7 | +64.9 | -23.9 | +27.5 | -53.0 | +5.9 | -67.8 |
| Relative (%) | +31.4 | +37.0 | +49.0 | -33.2 | -10.5 | +16.7 | +47.8 | -17.6 | +20.3 | -39.0 | +4.3 | -49.9 | |
| Steps (reduced) |
33 (5) |
34 (6) |
35 (7) |
35 (7) |
36 (8) |
37 (9) |
38 (10) |
38 (10) |
39 (11) |
39 (11) |
40 (12) |
40 (12) | |
Intervals
| # | Cents | Hekts | Notation[clarification needed] |
|---|---|---|---|
| 1 | 136 | 93 | Cp/D\\ |
| 2 | 272 | 186 | D |
| 3 | 408 | 279 | E |
| 4 | 543 | 371 | Ep/F\\ |
| 5 | 679 | 464 | F |
| 6 | 815 | 557 | G |
| 7 | 951 | 650 | Gp/H\\ |
| 8 | 1087 | 743 | H |
| 9 | 1223 | 836 | J |
| 10 | 1359 | 929 | Jp/A\\ |
| 11 | 1494 | 1021 | A |
| 12 | 1630 | 1114 | Ap/B\\ |
| 13 | 1766 | 1207 | B |
| 14 | 1902 | 1300 | C |
|
Todo: expand |