5edf: Difference between revisions
+subsets and supersets; cleanup |
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== Theory == | == Theory == | ||
5edf is close to the [[bleu]] [[generator]] chain and every second step of [[17edo]] | 5edf is close to the [[bleu]] [[generator]] chain and every second step of [[17edo]] (also known as [[17ed4]]) 5edf has an extremely accurate approximation of the seventh harmonic for its size. | ||
5edf is notable as a relatively basic and easy-to-use nonoctave system. Traditional harmony using major and minor triads is accessible in 5edf, although they are not 5-limit but rather septimal/undecimal in flavor. One must be wary of the 3/2-equivalence paradigm-there is no dominant, and major and minor triads, seventh chords, ninth chords, etc. are all merely voicings of major and minor dyads. Diminished chords also play a more important role than they do traditionally, as unlike the conventional triads, they are not equivalent to dyads, and are somewhat more consonant than in [[12edo]] due to the laxer subtritone. | |||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|5|3|2|columns=15}} | {{Harmonics in equal|5|3|2|columns=15}} | ||
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| 8 | | 8 | ||
| 1123 | | 1123 | ||
| | | 44/23 | ||
| major seventh, minor octave | | major seventh, minor octave | ||
| E, Fb | | E, Fb | ||
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| 9 | | 9 | ||
| 1264 | | 1264 | ||
| | | 83/40 | ||
| major octave | | major octave | ||
| F | | F | ||
| Line 82: | Line 83: | ||
| 1404 | | 1404 | ||
| [[9/4]] | | [[9/4]] | ||
| | | major ninth | ||
| C | | C | ||
|} | |} | ||
{{Todo|expand}} | {{Todo|expand}} | ||