5edf: Difference between revisions
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{{Infobox ET}} | |||
==Intervals== | {{ED intro}} It corresponds to 8.5476 [[edo]]. | ||
{| class="wikitable" | |||
== 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 | | 0.0 | ||
| | | [[1/1]] | ||
| perfect unison | |||
| C | |||
|- | |- | ||
|1 | | 1 | ||
|140 | | 140 | ||
| | | [[13/12]], [[49/45]] | ||
| augmented unison, minor second | |||
| C#, Db | |||
|- | |- | ||
|2 | | 2 | ||
| | | 281 | ||
| | | [[13/11]], [[20/17]], [[75/64]] | ||
| major second, minor third | |||
| D, Eb | |||
|- | |- | ||
|3 | | 3 | ||
|421 | | 421 | ||
| | | [[14/11]], [[23/18]] | ||
| major third, diminished fourth | |||
| E, Fb | |||
|- | |- | ||
|4 | | 4 | ||
| | | 562 | ||
| | | [[11/8]], [[18/13]], [[25/18]] | ||
| perfect fourth | |||
| F | |||
|- | |- | ||
|5 | | 5 | ||
| | | 702 | ||
| | | [[3/2]] | ||
| perfect fifth | |||
| C | |||
|- | |- | ||
|6 | | 6 | ||
|842 | | 842 | ||
| | | [[13/8]], [[18/11]], [[21/13]] | ||
| augmented fifth, minor sixth | |||
| C#, Db | |||
|- | |- | ||
|7 | | 7 | ||
| | | 983 | ||
| | | [[7/4]], [[30/17]] | ||
| major sixth, minor seventh | |||
| D, Eb | |||
|- | |- | ||
|8 | | 8 | ||
|1123 | | 1123 | ||
| | | 44/23 | ||
| major seventh, minor octave | |||
| E, Fb | |||
|- | |- | ||
| 9 | |||
| 1264 | |||
| 83/40 | |||
| major octave | |||
| F | |||
|- | |- | ||
| 10 | |||
| 1404 | |||
| [[9/4]] | |||
| major ninth | |||
|10 | | C | ||
| | |||
| | |||
| | |||
| | |||
|} | |} | ||
{{Todo|expand}} | |||