14edt: Difference between revisions

Wikispaces>JosephRuhf
**Imported revision 595263774 - Original comment: **
+subsets and supersets; +see also
 
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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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-13 12:27:26 UTC</tt>.<br>
: The original revision id was <tt>595263774</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">This is the simplest edt with a distinct form for each rotation of the Anti-Lambda scale. It is 9edo with ~23 cent stretched octaves and so is a stretched octave pelog scale.


||~ Degree ||~ cents ||~ notation ||
== Theory ==
|| 1/14 || 135.85 || Cp/D@ ||
14edt is the simplest [[edt]] with a distinct form for each rotation of the [[5L 4s (3/1-equivalent)|antilambda]] scale. It can be seen as [[9edo]] with significantly [[stretched and compressed tuning|stretched]] [[octave]]s (~23{{c}}) and may be used as a tuning for [[Pelog]].
|| 2/14 || 271.71 || D ||
|| 3/14 || 407.56 || E ||
|| 4/14 || 543.42 || Ep/F@ ||
|| 5/14 || 679.27 || F ||
|| 6/14 || 815.12 || G ||
|| 7/14 || 950.98 || Gp/H@ ||
|| 8/14 || 1086.83 || H ||
|| 9/14 || 1222.685 || J ||
|| 10/14 || 1358.54 || Jp/A@ ||
|| 11/14 || 1494.39 || A ||
|| 12/14 || 1630.25 || Ap/B@ ||
|| 13/14 || 1766.10 || B ||
|| 14/14 || 1901.955 || C ||</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;14edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the simplest edt with a distinct form for each rotation of the Anti-Lambda scale. It is 9edo with ~23 cent stretched octaves and so is a stretched octave pelog scale. &lt;br /&gt;
&lt;br /&gt;


=== Harmonics ===
{{Harmonics in equal|14|3|1|intervals=integer|columns=11}}
{{Harmonics in equal|14|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 14edt (continued)}}


&lt;table class="wiki_table"&gt;
=== Subsets and supersets ===
    &lt;tr&gt;
Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edt has subset edts [[2edt]] and [[7edt]].  
        &lt;th&gt;Degree&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notation&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;135.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cp/D@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;407.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ep/F@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;679.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;815.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;950.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gp/H@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1086.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1222.685&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1358.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jp/A@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1494.39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1630.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ap/B@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1766.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
! #
! [[Cent]]s
! [[Hekt]]s
! Notation{{clarify}}
|-
| 1
| 136
| 93
| Cp/D\\
|-
| 2
| 272
| 186
| D
|-
| 3
| 408
| 279
| E
|-
| 4
| 543
| 371
| Ep/F\\
|-
| 5
| 679
| 464
| F
|-
| 6
| 815
| 557
| G
|-
| 7
| 951
| 650
| Gp/H\\
|-
| 8
| 1087
| 743
| H
|-
| 9
| 1223
| 836
| J
|-
| 10
| 1359
| 929
| Jp/A\\
|-
| 11
| 1494
| 1021
| A
|-
| 12
| 1630
| 1114
| Ap/B\\
|-
| 13
| 1766
| 1207
| B
|-
| 14
| 1902
| 1300
| C
|}
 
== See also ==
* [[9edo]] – relative edo
* [[23ed6]] – relative ed6
* [[32ed12]] – relative ed12
 
 
{{Todo|inline=1|expand}}
[[Category:Pelog]]