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13edf: Difference between revisions

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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 19:54:44 UTC</tt>.<br>
: The original revision id was <tt>318904740</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">Intervals
|| 1 || 53.9965 cents ||
|| 2 || 107.993 ||
|| 3 || 161.9896 ||
|| 4 || 215.986 ||
|| 5 || 269.98269 ||
|| 6 || 323.979 ||
|| 7 || 377.97577 ||
|| 8 || 431.972 ||
|| 9 || 485.9688 ||
|| 10 || 539.965 ||
|| 11 || 593.9619 ||
|| 12 || 647.958 ||
|| 13 || 701.955 ||
|| 14 || 755.9515 ||
|| 15 || 809.948 ||
|| 16 || 863.9446 ||
|| 17 || 917.941 ||
|| 18 || 971.93769 ||
|| 19 || 1025.934 ||
|| 20 || 1079.93077 ||
|| 21 || 1133.927 ||
|| 22 || 1187.9238 ||</pre></div>
<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;13edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Intervals&lt;br /&gt;


== Theory ==
13edf corresponds to 22.2236[[edo]]. It is nearly identical to every ninth step of [[200edo]], but not quite similar to [[22edo]]; the octave is compressed by 12.076{{c}}, a deviation that is small but significant enough to create a discrepancy for the [[7/1|7th]] and [[11/1|11th]] harmonics.


&lt;table class="wiki_table"&gt;
== Harmonics ==
    &lt;tr&gt;
{{Harmonics in equal|13|3|2|intervals=prime|columns=8}}
        &lt;td&gt;1&lt;br /&gt;
{{Harmonics in equal|13|3|2|start=9|intervals=prime|columns=8}}
&lt;/td&gt;
        &lt;td&gt;53.9965 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;107.993&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;161.9896&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;215.986&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;269.98269&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;323.979&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;377.97577&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;431.972&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;485.9688&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;539.965&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;593.9619&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;647.958&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;701.955&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;755.9515&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;809.948&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;863.9446&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;917.941&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;971.93769&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;1025.934&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;1079.93077&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;1133.927&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;1187.9238&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{| class="wikitable mw-collapsible"
|+ style="font-size: 105%;" | Intervals of 13edf
|-
! Degree
! Cents
! Corresponding<br />JI intervals
! Comments
|-
! colspan="2" | 0
| '''exact [[1/1]]'''
|
|-
| 1
| 53.9965
| 33/32
| pseudo-[[25/24]]
|-
| 2
| 107.9931
| [[17/16]], 117/110, [[16/15]]
|
|-
| 3
| 161.9896
| [[11/10]]
|
|-
| 4
| 215.9862
| [[17/15]]
|
|-
| 5
| 269.9827
| [[7/6]]
|
|-
| 6
| 323.9792
| [[77/64]]
| pseudo-[[6/5]]
|-
| 7
| 377.9758
| 56/45
| pseudo-[[5/4]]
|-
| 8
| 431.9723
| [[9/7]]
|
|-
| 9
| 485.9688
| 45/34
| pseudo-[[4/3]]
|-
| 10
| 539.9654
| [[15/11]]
|
|-
| 11
| 593.9619
| 55/39, [[24/17]]
|
|-
| 12
| 647.9585
| [[16/11]]
|
|-
| 13
| 701.9550
| '''exact [[3/2]]'''
| just perfect fifth
|-
| 14
| 755.9515
| 99/64
|
|-
| 15
| 809.9481
| 51/32, [[8/5]]
|
|-
| 16
| 863.9446
| 33/20
|
|-
| 17
| 917.9412
| [[17/10]]
|
|-
| 18
| 971.9377
| [[7/4]]
|
|-
| 19
| 1025.9342
| [[29/16]]
| pseudo-[[9/5]]
|-
| 20
| 1079.9308
| [[28/15]]
| pseudo-[[15/8]]
|-
| 21
| 1133.9273
| 52/27, [[27/14]]
|
|-
| 22
| 1187.9238
| 135/68
| pseudo-[[octave]]
|-
| 23
| 1241.9204
| [[45/44|45/22]]
|
|-
| 24
| 1295.9169
| [[19/18|19/9]], [[18/17|36/17]]
|
|-
| 25
| 1349.9135
| [[12/11|24/11]]
|
|-
| 26
| 1403.9100
| '''exact [[9/4]]'''
| pythagorean major ninth
|}
 
{{stub}}
 
[[Category:22edo]]
Retrieved from "https://en.xen.wiki/w/13edf"