Pi-edo: Difference between revisions
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{{harmonics in cet|title=Approximation of harmonics in pi-EDO|381.971863421|prec=1|columns=11}} | {{harmonics in cet|title=Approximation of harmonics in pi-EDO|381.971863421|prec=1|columns=11}} | ||
[[Category:Non-integer edos | [[Category:Non-integer edos]] | ||
Revision as of 00:36, 28 February 2024
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Pi-EDO, or 3.141...EDO is a nonoctave equal-step tuning in which pi number of steps occur per octave. It does not approximate any simple harmonics well, except for the 3rd harmonic. This lends the tuning to use with custom inharmonic timbres. It has the potential to facilitate music far removed from any conventional harmonic or melodic traditions.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -54.1 | +7.9 | -108.2 | -112.5 | -46.2 | +68.9 | -162.3 | +15.8 | -166.6 | +50.4 | -100.3 |
| Relative (%) | -14.2 | +2.1 | -28.3 | -29.5 | -12.1 | +18.0 | -42.5 | +4.1 | -43.6 | +13.2 | -26.2 | |
| Step | 3 | 5 | 6 | 7 | 8 | 9 | 9 | 10 | 10 | 11 | 11 | |