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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}} | {{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 == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
! | ! # | ||
! | ! Cents | ||
! | ! Approximate ratios | ||
! colspan="2"| [[1L 3s (fifth-equivalent)|Neptunian]] notation | |||
!colspan="2"|[[1L 3s (fifth-equivalent)|Neptunian]] notation | |||
|- | |- | ||
| 0 | |||
| | | 0.0 | ||
|[[1/1]] | | [[1/1]] | ||
|perfect unison | | perfect unison | ||
|C | | C | ||
|- | |- | ||
|1 | | 1 | ||
|140 | | 140 | ||
| [[13/12]], [[49/45]] | |||
|[[13/12]], [[49/45]] | | augmented unison, minor second | ||
|augmented unison, minor second | | C#, Db | ||
|C#, Db | |||
|- | |- | ||
|2 | | 2 | ||
| | | 281 | ||
| [[13/11]], [[20/17]], [[75/64]] | |||
|[[ | | major second, minor third | ||
|major second, minor third | | D, Eb | ||
|D, Eb | |||
|- | |- | ||
|3 | | 3 | ||
|421 | | 421 | ||
| [[14/11]], [[23/18]] | |||
|[[14/11]], [[23/18]] | | major third, diminished fourth | ||
|major third, diminished fourth | | E, Fb | ||
|E, Fb | |||
|- | |- | ||
|4 | | 4 | ||
| | | 562 | ||
| [[11/8]], [[18/13]], [[25/18]] | |||
|[[11/8]], [[18/13]], [[25/18]] | | perfect fourth | ||
|perfect fourth | | F | ||
|F | |||
|- | |- | ||
|5 | | 5 | ||
| | | 702 | ||
| [[3/2]] | |||
|[[3/2]] | | perfect fifth | ||
|perfect fifth | | C | ||
|C | |||
|- | |- | ||
|6 | | 6 | ||
|842 | | 842 | ||
| [[13/8]], [[18/11]], [[21/13]] | |||
|[[ | | augmented fifth, minor sixth | ||
|augmented fifth, minor sixth | | C#, Db | ||
|C#, Db | |||
|- | |- | ||
|7 | | 7 | ||
| | | 983 | ||
| [[7/4]], [[30/17]] | |||
|[[7/4]], [[30/17]] | | major sixth, minor seventh | ||
|major sixth, minor seventh | | D, Eb | ||
|D, Eb | |||
|- | |- | ||
|8 | | 8 | ||
|1123 | | 1123 | ||
| 44/23 | |||
| | | major seventh, minor octave | ||
|major seventh, minor octave | | E, Fb | ||
|E, Fb | |||
|- | |- | ||
|9 | | 9 | ||
| | | 1264 | ||
| 83/40 | |||
| | | major octave | ||
|major octave | | F | ||
|F | |||
|- | |- | ||
|10 | | 10 | ||
| | | 1404 | ||
| [[9/4]] | |||
| major ninth | |||
| C | |||
| | |||
| | |||
|C | |||
|} | |} | ||
{{Todo|expand}} | |||