19edt
| ← 18edt | 19edt | 20edt → |
(convergent)
19 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 19edt or 19ed3), is a nonoctave tuning system that divides the interval of 3/1 into 19 equal parts of about 100 ¢ each. Each step represents a frequency ratio of 31/19, or the 19th root of 3. It is also known as Stopper tuning.
Theory
19edt is not a truly 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 framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in 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, and it is an interesting 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 8L 3s 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 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -36.0 | +35.9 | +16.6 | +4.9 | +0.1 | +1.2 | +7.7 | +19.0 | +34.7 | -45.9 | -22.7 | +3.7 |
| Relative (%) | -36.0 | +35.9 | +16.6 | +4.9 | +0.1 | +1.2 | +7.7 | +19.0 | +34.6 | -45.8 | -22.7 | +3.7 | |
| Steps (reduced) |
44 (6) |
46 (8) |
47 (9) |
48 (10) |
49 (11) |
50 (12) |
51 (13) |
52 (14) |
53 (15) |
53 (15) |
54 (16) |
55 (17) | |
Subsets and supersets
19edt is the 8th prime edt, following 17edt and before 23edt.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 100.1 | 16/15, 17/16, 18/17, 19/18, 20/19, 21/20 |
| 2 | 200.2 | 9/8, 17/15, 19/17 |
| 3 | 300.3 | 6/5, 13/11, 19/16 |
| 4 | 400.4 | 5/4, 19/15, 24/19 |
| 5 | 500.5 | 4/3 |
| 6 | 600.6 | 10/7, 17/12, 24/17 |
| 7 | 700.7 | 3/2 |
| 8 | 800.8 | 8/5, 19/12 |
| 9 | 900.9 | 5/3, 22/13 |
| 10 | 1001 | 9/5, 16/9, 23/13 |
| 11 | 1101.1 | 15/8, 17/9, 19/10 |
| 12 | 1201.2 | 2/1 |
| 13 | 1301.3 | 17/8, 19/9, 21/10 |
| 14 | 1401.4 | 9/4 |
| 15 | 1501.5 | 12/5, 19/8 |
| 16 | 1601.6 | 5/2 |
| 17 | 1701.7 | 8/3 |
| 18 | 1801.9 | 17/6, 20/7 |
| 19 | 1902 | 3/1 |
See also
- 7edf – relative edf
- 12edo – relative edo
- 28ed5 – relative ed5
- 31ed6 – relative ed6
- 34ed7 – relative ed7
- 40ed10 – relative ed10
- 43ed12 – relative ed12