17edo: Difference between revisions
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'''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1. | '''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1. | ||
17edo is the smallest edo that has a sharper-than-just diatonic fifth (705.8c, compared to just 3/2 = 702.0c), not counting the degenerate case 5edo. 17edo has discordant diatonic major thirds and provides no good approximation of 5/4, which to some extent forces | 17edo is the smallest edo that has a sharper-than-just diatonic fifth (705.8c, compared to just 3/2 = 702.0c), not counting the degenerate case 5edo. 17edo has discordant diatonic major thirds and provides no good approximation of 5/4, which to some extent forces one to use nonfunctional and modal harmony instead of standard functional harmony. | ||
== Tuning theory == | == Tuning theory == | ||
Revision as of 00:52, 26 January 2026
17edo, or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1.
17edo is the smallest edo that has a sharper-than-just diatonic fifth (705.8c, compared to just 3/2 = 702.0c), not counting the degenerate case 5edo. 17edo has discordant diatonic major thirds and provides no good approximation of 5/4, which to some extent forces one to use nonfunctional and modal harmony instead of standard functional harmony.
Tuning theory
Prime approximations
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +3.9 | -33.4 | +19.4 | +13.4 | +6.5 | -34.4 | -15.2 | +7.0 |
| Relative (%) | 0.0 | +5.6 | -47.3 | +27.5 | +19.0 | +9.3 | -48.7 | -21.5 | +9.9 | |
| Steps
(reduced) |
17
(0) |
27
(10) |
39
(5) |
48
(14) |
59
(8) |
63
(12) |
69
(1) |
72
(4) |
77
(9) | |
