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 (not counting the degenerate case 5edo). This makes major thirds discordant and forces reliance on nonfunctional and modal harmony. | 17edo is the smallest edo that has a sharper than just diatonic fifth (not counting the degenerate case 5edo). This makes major thirds discordant and to some extent forces reliance on nonfunctional and modal harmony. | ||
== Tuning theory == | == Tuning theory == | ||
Revision as of 00:25, 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 (not counting the degenerate case 5edo). This makes major thirds discordant and to some extent forces reliance on nonfunctional and modal 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) | |
