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5edf: Difference between revisions

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**Imported revision 288517210 - Original comment: **
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}} It corresponds to 8.5476 [[edo]].
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-12-26 16:29:41 UTC</tt>.<br>
 
: The original revision id was <tt>288517210</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
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, a fact which is exploited by the octave-repeating [[navy]] temperament.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
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.
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Close to the [[Bleu]] generator chain and 17ed4.</pre></div>
=== Harmonics ===
<h4>Original HTML content:</h4>
{{Harmonics in equal|5|3|2|columns=15}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;5edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Close to the &lt;a class="wiki_link" href="/Bleu"&gt;Bleu&lt;/a&gt; generator chain and 17ed4.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== 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}}
Retrieved from "https://en.xen.wiki/w/5edf"