5edf: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} It corresponds to 8.5476 [[edo]]. | |||
[[ | == Theory == | ||
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 in equal|5|3|2|columns=15}} | |||
=== Subsets and supersets === | |||
5edf is the 3rd [[prime equal division|prime edf]], after [[3edf]] and before [[7edf]]. | |||
== Intervals == | |||
{| class="wikitable center-1 right-2" | |||
|- | |||
! # | |||
! Cents | |||
! Approximate ratios | |||
! colspan="2"| [[1L 3s (fifth-equivalent)|Neptunian]] notation | |||
|- | |||
| 0 | |||
| 0.0 | |||
| [[1/1]] | |||
| perfect unison | |||
| C | |||
|- | |||
| 1 | |||
| 140 | |||
| [[13/12]], [[49/45]] | |||
| augmented unison, minor second | |||
| C#, Db | |||
|- | |||
| 2 | |||
| 281 | |||
| [[13/11]], [[20/17]], [[75/64]] | |||
| major second, minor third | |||
| D, Eb | |||
|- | |||
| 3 | |||
| 421 | |||
| [[14/11]], [[23/18]] | |||
| major third, diminished fourth | |||
| E, Fb | |||
|- | |||
| 4 | |||
| 562 | |||
| [[11/8]], [[18/13]], [[25/18]] | |||
| perfect fourth | |||
| F | |||
|- | |||
| 5 | |||
| 702 | |||
| [[3/2]] | |||
| perfect fifth | |||
| C | |||
|- | |||
| 6 | |||
| 842 | |||
| [[13/8]], [[18/11]], [[21/13]] | |||
| augmented fifth, minor sixth | |||
| C#, Db | |||
|- | |||
| 7 | |||
| 983 | |||
| [[7/4]], [[30/17]] | |||
| major sixth, minor seventh | |||
| D, Eb | |||
|- | |||
| 8 | |||
| 1123 | |||
| 44/23 | |||
| major seventh, minor octave | |||
| E, Fb | |||
|- | |||
| 9 | |||
| 1264 | |||
| 83/40 | |||
| major octave | |||
| F | |||
|- | |||
| 10 | |||
| 1404 | |||
| [[9/4]] | |||
| major ninth | |||
| C | |||
|} | |||
{{Todo|expand}} | |||