16edt: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
=Properties=
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
As the double of [[8edt|8edt]], this division of the tritave is harmonically fraternal to [[10edo|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13|13:21]] and a decent [[13/7|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 10:06:04 UTC</tt>.<br>
: The original revision id was <tt>602892288</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">=Properties=  
As the double of [[8edt]], this division of the tritave is harmonically fraternal to [[10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21_13|13:21]] and a decent [[13_7|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.


=Intervals=  
=Intervals=
||~ Degree ||~ Size in [[cent|Cents]] ||
||= 1  ||&gt;  118.87219 ||
||= 2  ||&gt;  237.74438 ||
||= 3  ||&gt;  356.61656 ||
||= 4  ||&gt;  475.48875 ||
||= 5  ||&gt;  594.36094 ||
||= 6  ||&gt;  713.23312 ||
||= 7  ||&gt;  832.10531 ||
||= 8  ||&gt;  950.97750 ||
||= 9  ||&gt; 1069.84969 ||
||= 10 ||&gt; 1188.72188 ||
||= 11 ||&gt; 1307.59406 ||
||= 12 ||&gt; 1426.46625 ||
||= 13 ||&gt; 1545.33844 ||
||= 14 ||&gt; 1664.21063 ||
||= 15 ||&gt; 1783.08281 ||
||= 16 ||&gt; 1901.95500 ||


=Music=
{| class="wikitable"
[[@http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3|A Short Tune in 16EDT]] by [[@Peter 'Rush' Kosmorsky]]</pre></div>
|-
<h4>Original HTML content:</h4>
! | Degree
<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;16edt&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="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Properties&lt;/h1&gt;
! | Size in [[cent|Cents]]
As the double of &lt;a class="wiki_link" href="/8edt"&gt;8edt&lt;/a&gt;, this division of the tritave is harmonically fraternal to &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent &lt;a class="wiki_link" href="/21_13"&gt;13:21&lt;/a&gt; and a decent &lt;a class="wiki_link" href="/13_7"&gt;7:13&lt;/a&gt;. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.&lt;br /&gt;
|-
&lt;br /&gt;
| style="text-align:center;" | 1
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h1&gt;
| style="text-align:right;" | 118.87219
|-
| style="text-align:center;" | 2
| style="text-align:right;" | 237.74438
|-
| style="text-align:center;" | 3
| style="text-align:right;" | 356.61656
|-
| style="text-align:center;" | 4
| style="text-align:right;" | 475.48875
|-
| style="text-align:center;" | 5
| style="text-align:right;" | 594.36094
|-
| style="text-align:center;" | 6
| style="text-align:right;" | 713.23312
|-
| style="text-align:center;" | 7
| style="text-align:right;" | 832.10531
|-
| style="text-align:center;" | 8
| style="text-align:right;" | 950.97750
|-
| style="text-align:center;" | 9
| style="text-align:right;" | 1069.84969
|-
| style="text-align:center;" | 10
| style="text-align:right;" | 1188.72188
|-
| style="text-align:center;" | 11
| style="text-align:right;" | 1307.59406
|-
| style="text-align:center;" | 12
| style="text-align:right;" | 1426.46625
|-
| style="text-align:center;" | 13
| style="text-align:right;" | 1545.33844
|-
| style="text-align:center;" | 14
| style="text-align:right;" | 1664.21063
|-
| style="text-align:center;" | 15
| style="text-align:right;" | 1783.08281
|-
| style="text-align:center;" | 16
| style="text-align:right;" | 1901.95500
|}


&lt;table class="wiki_table"&gt;
=Music=
    &lt;tr&gt;
[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky|Peter 'Rush' Kosmorsky]]
        &lt;th&gt;Degree&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Size in &lt;a class="wiki_link" href="/cent"&gt;Cents&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;118.87219&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;237.74438&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;356.61656&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;475.48875&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;594.36094&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;713.23312&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;832.10531&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;950.97750&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1069.84969&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1188.72188&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1307.59406&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1426.46625&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1545.33844&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1664.21063&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1783.08281&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1901.95500&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Music&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3" rel="nofollow" target="_blank"&gt;A Short Tune in 16EDT&lt;/a&gt; by &lt;a class="wiki_link" href="/Peter%20%27Rush%27%20Kosmorsky" target="_blank"&gt;Peter 'Rush' Kosmorsky&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Properties

As the double of 8edt, this division of the tritave is harmonically fraternal to 10edo. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent 13:21 and a decent 7:13. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.

Intervals

Degree Size in Cents
1 118.87219
2 237.74438
3 356.61656
4 475.48875
5 594.36094
6 713.23312
7 832.10531
8 950.97750
9 1069.84969
10 1188.72188
11 1307.59406
12 1426.46625
13 1545.33844
14 1664.21063
15 1783.08281
16 1901.95500

Music

A Short Tune in 16EDT by Peter 'Rush' Kosmorsky