20edo: Difference between revisions
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== Theory == | == Theory == | ||
20edo contains smaller edos {{EDOs| 2, 4, 5, and 10 }} and is part of the 5''n'' family of equal divisions of the octave. It fairly approximates the harmonics 7 (from [[5edo]]), 11, 13, 15 (from [[10edo]]), 19, 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20edo does a reasonably convincing approximation of harmonics 4:7:11:13:15. | 20edo contains smaller edos {{EDOs| 2, 4, 5, and 10 }} and is part of the 5''n'' family of equal divisions of the octave. It fairly approximates the harmonics 7 (from [[5edo]]), 11, 13, 15 (from [[10edo]]), 19, 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20edo does a reasonably convincing approximation of harmonics 4:7:11:13:15. | ||
20edo is around the point where 5edo's 3rd harmonic starts to become notably inaccurate relative to the size of the edo (that is, it is over 25 relative cents off). It thus inherits 5edo's crude [[archy]] temperament, with its particularly accurate approximation of 7/4 at 960 cents. | |||
As 7, 11 and 15 are all flat by approximately 10 cents, their flatness cancels out when combined in composite ratios, making an 11:14:15 chord (0–7–9 steps) and its utonal inversion particularly precise. Using 9/20 as the generator and treating these as the primary major and minor triads produces [[Balzano]] nonatonic and undecatonic scales, which is probably the clearest arrangement for the black/white keys on a 20-tone keyboard. | As 7, 11 and 15 are all flat by approximately 10 cents, their flatness cancels out when combined in composite ratios, making an 11:14:15 chord (0–7–9 steps) and its utonal inversion particularly precise. Using 9/20 as the generator and treating these as the primary major and minor triads produces [[Balzano]] nonatonic and undecatonic scales, which is probably the clearest arrangement for the black/white keys on a 20-tone keyboard. | ||
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* 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six" | * 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six" | ||
For a more complete list, see [[Ups and | For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]]. Because many intervals have several names, many chords do too. | ||
== Modes == | == Modes == | ||
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* [https://www.youtube.com/watch?v=duJHUo_ACgk ''Composition for cello and clavier in 20-tone equal temperament''] (2017) | * [https://www.youtube.com/watch?v=duJHUo_ACgk ''Composition for cello and clavier in 20-tone equal temperament''] (2017) | ||
* [https://www.youtube.com/watch?v=u6k4lgCnHqs ''5 compositions for violin and clavier in 20-tone equal temperament''] (2017) | * [https://www.youtube.com/watch?v=u6k4lgCnHqs ''5 compositions for violin and clavier in 20-tone equal temperament''] (2017) | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025) | |||
* [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025) | |||
; [[E8 Heterotic]] | ; [[E8 Heterotic]] | ||