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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}}
: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-09 20:09:59 UTC</tt>.<br>
: The original revision id was <tt>318907828</tt>.<br>
: The revision comment was: <tt></tt><br>
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>
<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">=**Intrevals**=
|| 1 || 43.872 cents ||
|| 2 || 87.744 ||
|| 3 || 131.61656 ||
|| 4 || 175.48875 ||
|| 5 || 219.3609 ||
|| 6 || 263.233 ||
|| 7 || 307.105 ||
|| 8 || 350.9775 ||
|| 9 || 394.84969 ||
|| 10 || 438.72188 ||
|| 11 || 482.594 ||
|| 12 || 526.466 ||
|| 13 || 570.338 ||
|| 14 || 614.2106 ||
|| 15 || 658.0828 ||
|| 16 || 701.955 ||
|| 17 || 745.827 ||
|| 18 || 789.699 ||
|| 19 || 833.57156 ||
|| 20 || 877.44375 ||
|| 21 || 921.3159 ||
|| 22 || 965.188 ||
|| 23 || 1009.0603 ||
|| 24 || 1052.932 ||
|| 25 || 1096.80469 ||
|| 26 || 1140.67688 ||
|| 27 || 1184.549 ||


=Compositions=  
== Theory ==
16edf corresponds to 27.3522…[[edo]]. It is similar to every third step of [[82edo]] but not quite similar to [[27edo]]; the octave is compressed by 15.45{{c}}, a small but significant deviation. It contains good approximations of the [[7/1|7th]] and [[13/1|13th]] [[harmonic]]s.


[[http://www.youtube.com/watch?v=-RUeO6hJLBY|schizophrenic lullaby fugue]]</pre></div>
It serves as a good approximation to [[halftone]] temperament, containing the [[~]][[7/5]] generator at 13 steps.
<h4>Original HTML content:</h4>
<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;16edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intrevals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;strong&gt;Intrevals&lt;/strong&gt;&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
=== Harmonics ===
    &lt;tr&gt;
{{Harmonics in equal|16|3|2}}
        &lt;td&gt;1&lt;br /&gt;
{{Harmonics in equal|16|3|2|start=12|columns=12|collapsed=true|title=Approximation of harmonics in 16edf (continued)}}
&lt;/td&gt;
        &lt;td&gt;43.872 cents&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;87.744&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;131.61656&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;175.48875&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;219.3609&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;263.233&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;307.105&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350.9775&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;394.84969&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;438.72188&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;482.594&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;526.466&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;570.338&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;614.2106&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;658.0828&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;745.827&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;789.699&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;833.57156&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;877.44375&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;921.3159&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;965.188&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1009.0603&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1052.932&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1096.80469&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1140.67688&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1184.549&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
=== Subsets and supersets ===
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Compositions&lt;/h1&gt;
Since 16 factors into primes as 2<sup>4</sup>, 16edf contains subset edfs {{EDs|equave=f| 2, 4, and 8 }}.
&lt;br /&gt;
 
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=-RUeO6hJLBY" rel="nofollow"&gt;schizophrenic lullaby fugue&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{| class="wikitable center-1 right-2 mw-collapsible"
|+ Intervals of 16edf
|-
! #
! Cents
! Approximate ratios
! Halftone[6] notation<br>(using [[ups and downs notation|ups and downs]])
! Comments
|-
| 0
| 0.0
| [[1/1]]
| C
|
|-
| 1
| 43.9
| 40/39, 39/38
| ^C
|
|-
| 2
| 87.7
| [[20/19]]
| Db
|
|-
| 3
| 131.6
| 55/51, ([[27/25]])
| vD
|
|-
| 4
| 175.5
| ([[21/19]])
| D
|
|-
| 5
| 219.4
|
| vE
|
|-
| 6
| 263.2
| ([[7/6]])
| E
|
|-
| 7
| 307.1
|
| Fb
|
|-
| 8
| 351.0
| 60/49, 49/40
| vF
|
|-
| 9
| 394.8
| (44/35)
| F
|
|-
| 10
| 438.7
| ([[9/7]])
| Ab
|
|-
| 11
| 482.6
|
| vA
|
|-
| 12
| 526.5
| ([[19/14]])
| A
|
|-
| 13
| 570.3
| ([[25/18]]), 153/110, 112/81
| B
|
|-
| 14
| 614.2
| ([[10/7]])
| Cb
|
|-
| 15
| 658.1
| [[19/13]]
| vC
|
|-
| 16
| 702.0
| [[3/2]]
| C
| Just perfect fifth
|-
| 17
| 745.8
| [[20/13]]
|
|
|-
| 18
| 789.7
| [[30/19]]
|
|
|-
| 19
| 833.6
| 55/34
|
|
|-
| 20
| 877.4
|
|
|
|-
| 21
| 921.3
|
|
|
|-
| 22
| 965.2
| [[7/4]]
|
|
|-
| 23
| 1009.0
|
|
|
|-
| 24
| 1052.9
| 90/49, ([[11/6]])
|
|
|-
| 25
| 1096.8
| (66/35)
|
|
|-
| 26
| 1140.7
|
|
|
|-
| 27
| 1184.5
|
|
|
|-
| 28
| 1228.4
| 128/63
|
|
|-
| 29
| 1272.3
| 25/12
|
|
|-
| 30
| 1316.2
| 15/7
|
|
|-
| 31
| 1360.0
| 57/26
|
|
|-
| 32
| 1403.9
| [[9/4]]
|
| Pythagorean major ninth
|}
 
== Music ==
; [[Nae Ayy]]
* [https://www.youtube.com/watch?v=8YegsoiO1Co ''Neptune''] (2021)
 
; [[nationalsolipsism]]
* [https://www.youtube.com/watch?v=-RUeO6hJLBY ''schizophrenic lullaby fugue''] (2011)
 
== See also ==
* [[27edo]] – relative edo
* [[43edt]] – relative edt
* [[70ed6]] – relative ed6
* [[90ed10]] – relative ed10
* [[97ed12]] – relative ed12
 
{{Todo|expand}}
 
[[Category:27edo]]
Retrieved from "https://en.xen.wiki/w/16edf"