Pi-edo: Difference between revisions
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m FloraC moved page Πedo to Pi-edo over redirect: Move back. Wikipedia article on the mathematical constant is simply "pi" |
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{{ | {{Novelty}} | ||
{{#invoke:Infobox_ET|infobox_ET|tuning=1ed697/559|Prime factorization=|Zeta=|Consistency=|Distinct consistency=|debug= }} | |||
'''π-edo''', '''1ed2<sup>1/π</sup>''', or '''APS(1/π oct)''' is a nonoctave [[equal-step tuning]] in which π steps occur per [[octave]]. It does not approximate any simple [[harmonic]]s well, except for the [[3/1|3rd harmonic]]. In fact, it is nearly identical to [[5edt]]. 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 == | ||
{{Harmonics in cet|title=Approximation of harmonics in π-edo|381.971863420548806|prec=1|columns=11}} | |||
[[Category:Edonoi]] | |||
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Latest revision as of 14:20, 11 August 2024
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
| ← 0ed697/559 | 1ed697/559 | 2ed697/559 → |
π-edo, 1ed21/π, or APS(1/π oct) is a nonoctave equal-step tuning in which π steps occur per octave. It does not approximate any simple harmonics well, except for the 3rd harmonic. In fact, it is nearly identical to 5edt. 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 | |