19edo
19edo is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.
19edo is interesting as a flatter Meantone system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has interordinals and supports Semaphore, which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a very consonant 9-note MOS semiquartal (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of
- Kleismic (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all
- Magic (five 5/4's = 3/1)
An early use of 19edo was in the mid-1500s by French composer Guillaume Costeley in his chanson "Seigneur Dieu ta pitie", in which he uses mostly the standard consonances from the diatonic scale (perfect fifth, major third, etc.) as contrapuntal consonances, but incorporates motions by a third of a tone that are outside the diatonic scale generated by the perfect fifth. A keyboard rendition of the chanson can be heard on YouTube.
Basic theory
Edostep interpretations
19edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup:
- 25/24 (the interval between 6/5 and 5/4)
- 26/25 (the interval between 25/16 and 13/8)
- 27/26 (the interval between 13/8 and 27/16)
- 28/27 (the interval between 9/8 and 7/6)
25/24 ~ 26/25 ~ 27/26 is the characteristic equivalence of 2.3.5.13 Kleismic.
Prime harmonic approximations
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -7.2 | -7.4 | -21.5 | +17.1 | -19.5 | +21.4 | +18.3 | +3.3 |
| Relative (%) | 0.0 | -11.4 | -11.7 | -34.0 | +27.1 | -30.8 | +33.8 | +28.9 | +5.2 | |
| Steps
(reduced) |
19
(0) |
30
(11) |
44
(6) |
53
(15) |
66
(9) |
70
(13) |
78
(2) |
81
(5) |
86
(10) | |
