18edt
| ← 17edt | 18edt | 19edt → |
18edt is the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.
Temperaments
As the double of 9edt, it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like 8edt, is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.
18edt can also be used for the Electra temperament based on 15/11, although in this case its approximation to 13/11 is very sharp.
Intervals
| Step | Cents | Hekts | Approximated interval | Electra notation (J = 1/1) |
|---|---|---|---|---|
| 0 | 1/1 | J | ||
| 1 | 105.664 | 72.222 | 16/15 | J#, Kbb |
| 2 | 211.328 | 144.444 | 9/8 | Jx, Kb |
| 3 | 316.993 | 216.667 | 6/5 | K |
| 4 | 422.657 | 288.889 | 9/7 | K#, Lb |
| 5 | 528.321 | 361.111 | 27/20 | L |
| 6 | 633.985 | 433.333 | 13/9 | L#, Mbb |
| 7 | 739.649 | 505.556 | 17/13 | Lx, Mb |
| 8 | 845.313 | 577.778 | 5/3 | M |
| 9 | 950.978 | 650 | 19/11 | M#, Nbb |
| 10 | 1056.642 | 722.222 | 9/5 | Mx, Nb |
| 11 | 1162.306 | 794.444 | 49/25 | N |
| 12 | 1267.97 | 866.667 | 27/13 | N#, Ob |
| 13 | 1373.634 | 938.889 | 20/9 | O |
| 14 | 1479.298 | 1011.111 | 7/3 | O#, Pbb |
| 15 | 1584.963 | 1083.333 | 5/2 | Ox, Pb |
| 16 | 1690.627 | 1155.556 | 8/3 | P |
| 17 | 1806.291 | 1227.778 | 45/16 | P#, Jb |
| 18 | 1901.955 | 1300 | 3/1 | J |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.7 | +0.0 | +30.3 | -39.0 | -37.7 | +12.4 | -7.4 | +0.0 | +28.9 | -30.4 | +30.3 |
| Relative (%) | -35.7 | +0.0 | +28.7 | -37.0 | -35.7 | +11.8 | -7.0 | +0.0 | +27.4 | -28.8 | +28.7 | |
| Steps (reduced) |
11 (11) |
18 (0) |
23 (5) |
26 (8) |
29 (11) |
32 (14) |
34 (16) |
36 (0) |
38 (2) |
39 (3) |
41 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | -25.3 | -39.0 | -45.1 | -44.4 | -37.7 | -25.6 | -8.8 | +12.4 | +37.6 | -39.4 |
| Relative (%) | -2.5 | -23.9 | -37.0 | -42.7 | -42.0 | -35.7 | -24.3 | -8.3 | +11.8 | +35.5 | -37.3 | |
| Steps (reduced) |
42 (6) |
43 (7) |
44 (8) |
45 (9) |
46 (10) |
47 (11) |
48 (12) |
49 (13) |
50 (14) |
51 (15) |
51 (15) | |