19edt
| ← 18edt | 19edt | 20edt → |
(convergent)
Division of the third harmonic into 19 equal parts (19ED3) is related to 12 EDO, but with the 3/1 rather than the 2/1 being just. It is also known as Stopper tuning. The octave is about 1.2347 cents stretched and the step size is about 100.1029 cents.
Properties
Bernhard Stopper's OnlyPure tuning [dead link] 19 equal divisions of the tritave is not a "real" xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal 12-tone scale. Although it is really just the normal 12edo tuning framed in a tritave equivalence, it can still be used as a temperament with no twos like other tritave tunings, alithough limited accuracy, with 5/3 approximated as 9 steps and 7/3 approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, 11/9.
This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0-600-1100 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a “macro-godzilla" temperament (with a generator of 400.4 cents and a 3:1 ratio 5L 4s scale, weird coincidence how 17edt and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of meantone temperament (with a generator of 700.7 or 1201.2 cents), producing a basic Obikhod scale.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +0.0 | +2.5 | +16.6 | +1.2 | +34.7 | +3.7 | +0.0 | +17.8 | -47.1 | +2.5 |
| Relative (%) | +1.2 | +0.0 | +2.5 | +16.6 | +1.2 | +34.6 | +3.7 | +0.0 | +17.8 | -47.1 | +2.5 | |
| Steps (reduced) |
12 (12) |
19 (0) |
24 (5) |
28 (9) |
31 (12) |
34 (15) |
36 (17) |
38 (0) |
40 (2) |
41 (3) |
43 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -36.0 | +35.9 | +16.6 | +4.9 | +0.1 | +1.2 | +7.7 | +19.0 | +34.7 | -45.9 | -22.7 |
| Relative (%) | -36.0 | +35.9 | +16.6 | +4.9 | +0.1 | +1.2 | +7.7 | +19.0 | +34.6 | -45.8 | -22.7 | |
| Steps (reduced) |
44 (6) |
46 (8) |
47 (9) |
48 (10) |
49 (11) |
50 (12) |
51 (13) |
52 (14) |
53 (15) |
53 (15) |
54 (16) | |