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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.
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}}
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