5edf: Difference between revisions
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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 == | ||
| Line 13: | Line 17: | ||
! # | ! # | ||
! Cents | ! Cents | ||
! Approximate | ! Approximate ratios | ||
! colspan="2"| [[1L 3s (fifth-equivalent)|Neptunian]] | ! colspan="2"| [[1L 3s (fifth-equivalent)|Neptunian]] notation | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 23: | Line 27: | ||
|- | |- | ||
| 1 | | 1 | ||
| 140 | | 140 | ||
| [[13/12]], [[49/45]] | | [[13/12]], [[49/45]] | ||
| augmented unison, minor second | | augmented unison, minor second | ||
| Line 29: | Line 33: | ||
|- | |- | ||
| 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 | ||
| Line 41: | Line 45: | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 562 | ||
| [[11/8]], [[18/13]], [[25/18]] | | [[11/8]], [[18/13]], [[25/18]] | ||
| perfect fourth | | perfect fourth | ||
| Line 47: | Line 51: | ||
|- | |- | ||
| 5 | | 5 | ||
| 702 | | 702 | ||
| [[3/2]] | | [[3/2]] | ||
| perfect fifth | | perfect fifth | ||
| Line 53: | Line 57: | ||
|- | |- | ||
| 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 | ||
| Line 65: | Line 69: | ||
|- | |- | ||
| 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}} | ||