19edo: Difference between revisions
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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 [[interordinal]]s 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 | 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 [[interordinal]]s 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]] | * [[Kleismic]] (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all | ||
* [[Magic]] | * [[Magic]] (five 5/4's = 3/1) | ||
== Basic theory == | == Basic theory == | ||
Revision as of 22:33, 22 January 2026
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)
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) | |
