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10edt: 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:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-16 13:35:12 UTC</tt>.<br>
: The original revision id was <tt>246268983</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">
&lt;span style="font-size: 18px; line-height: 27px;"&gt;**10 Equal Divisions of the Tritave**&lt;/span&gt;


|| Degrees || Cents || Approximate Ratios ||
== Theory ==
|| 0 || 0 || &lt;span style="color: #660000;"&gt;[[1_1|1/1]]&lt;/span&gt; ||
10edt has very accurate 5-limit harmony for such a small number of steps per tritave, most notably the [[5/4]] inherited from 5edt. 10edt introduces some new harmonic properties though — such as the 571 cent tritone, which can function as [[7/5]]. We can use this to readily construct chords such as 4:5:7:12, although the [[7/4]], being 18 cents flat, does considerable damage to the consonance of this chord.  
|| 1 || 190.196 || [[10_9|10/9]], 28/25 ||
|| 2 || 380.391 || &lt;span style="color: #660000;"&gt;[[5_4|5/4]]&lt;/span&gt; ||
|| 3 || 570.587 || [[7_5|7/5]] ||
|| 4 || 760.782 || &lt;span style="color: #660000;"&gt;[[14_9|14/9]]&lt;/span&gt; ||
|| 5 || 950.978 || 19/11? ||
|| 6 || 1141.173 || &lt;span style="color: #660000;"&gt;[[27_14|27/14]]&lt;/span&gt; ||
|| 7 || 1331.369 || 15/7 ([[15_14|15/14]] plus an octave) ||
|| 8 || 1521.564 || 12/5 (&lt;span style="color: #660000;"&gt;[[6_5|6/5]]&lt;/span&gt; plus an octave) ||
|| 9 || 1711.760 || 27/10 ||
|| 10 || 1901.955 || 3/1 ||


10edt also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.
One step of 10edt can serve as the generator for [[pocus]] temperament, a [[Temperament merging|merge]] of [[sensamagic]] and 2.3.5.7.13 [[catakleismic]], which tempers out [[169/168]], [[225/224]], and [[245/243]] in the 2.3.5.7.13 subgroup.


10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.</pre></div>
=== Harmonics ===
<h4>Original HTML content:</h4>
{{Harmonics in equal|10|3|1}}
<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;10edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
{{Harmonics in equal|10|3|1|intervals=prime}}
&lt;span style="font-size: 18px; line-height: 27px;"&gt;&lt;strong&gt;10 Equal Divisions of the Tritave&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;


=== Interval table ===
{| class="wikitable"
|-
! Degrees
! [[Cent]]s
! [[Hekt]]s
! Approximate Ratios
|-
| colspan="3" | 0
| <span style="color: #660000;">[[1/1]]</span>
|-
| 1
| 190.196
| 130
| [[10/9]], [[28/25]]
|-
| 2
| 380.391
| 260
| <span style="color: #660000;">[[5/4]]</span>
|-
| 3
| 570.587
| 390
| [[7/5]]
|-
| 4
| 760.782
| 520
| <span style="color: #660000;">[[14/9]]</span>
|-
| 5
| 950.978
| 650
| 45/26, [[26/15]]
|-
| 6
| 1141.173
| 780
| <span style="color: #660000;">[[27/14]]</span>
|-
| 7
| 1331.369
| 910
| [[15/7]] ([[15/14]] plus an octave)
|-
| 8
| 1521.564
| 1040
| [[12/5]] (<span style="color: #660000;">[[6/5]]</span> plus an octave)
|-
| 9
| 1711.760
| 1170
| [[27/20|27/10]]
|-
| 10
| 1901.955
| 1300
| [[3/1]]
|}


&lt;table class="wiki_table"&gt;
[[Category:Macrotonal]]
    &lt;tr&gt;
        &lt;td&gt;Degrees&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Approximate Ratios&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;190.196&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;, 28/25&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;380.391&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;/span&gt;&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;570.587&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;&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;760.782&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;&lt;/span&gt;&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;950.978&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/11?&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;1141.173&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;&lt;/span&gt;&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;1331.369&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/7 (&lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt; plus an octave)&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;1521.564&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/5 (&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;/span&gt; plus an octave)&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;1711.760&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/10&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;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
10edt, like &lt;a class="wiki_link" href="/5edt"&gt;5edt&lt;/a&gt;, has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of &amp;quot;meantone&amp;quot; temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/10edt"