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8L 5s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Periods = 1
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-12 13:27:30 UTC</tt>.<br>
| nLargeSteps = 8
: The original revision id was <tt>540784162</tt>.<br>
| nSmallSteps = 5
: The revision comment was: <tt></tt><br>
| Equalized = 5
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Collapsed = 3
<h4>Original Wikitext content:</h4>
| Pattern = LLsLLsLsLLsLs
<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 MOS is the chromatic scale of Semidim, Tridec, Ammonite and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 superthird, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to phi, or even phi itself.
}}
||  ||  || cents || 2g ||
{{MOS intro}}
|| 3/8 ||  || 450 || 900 ||
|| 17/45 ||  || 453 1/3 || 906 2/3 ||
||  || 31/82 || 453 21/41 || 907 1/41 ||
|| 14/37 ||  || 454 2/37 || 908 4/37 ||
||  || 25/66 || 454 6/11 || 909 1/11 ||
||  ||  || 455.132972 || 910.265944 ||
|| 11/29 ||  || 455 5/29 || 910 10/29 ||
||  ||  || 455.212095 || 910.42419 ||
||  || 30/79 || 455 55/79 || 911 31/79 ||
||  || 19/50 || 456 || 912 ||
||  || 27/71 || 456 24/71 || 912 48/71 ||
||  || 35/92 || 456 12/23 || 913 1/23 ||
|| 8/21 ||  || 457 1/7 || 914 2/7 ||
||  || 29/76 || 457 13/19 || 915 7/19 ||
||  || 21/55 || 458 2/11 || 916 4/11 ||
|| 13/34 ||  || 458 14/17 || 917 11/17 ||
||  || 31/81 || 459 7/27 || 918 14/27 ||
|| 18/47 ||  || 459 27/47 || 919 7/47 ||
|| 23/60 ||  || 460 || 920 ||
|| 5/13 ||  || 461 7/13 || 923 1/13 ||</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;8L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS is the chromatic scale of Semidim, Tridec, Ammonite and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 superthird, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to phi, or even phi itself.&lt;br /&gt;


8L&nbsp;5s represents the chromatic scale of [[Semidim]], [[Tridec]], [[Ammonite]], and [[Petrtri]] temperaments. It represents [[tempered]] chains of the 13:10 or 17:13 [[semisixth]], thus rendering 10:13:17 as an equidistant [[triad]] and [[tempering out]] 170:169. Also, the ratio between the generator of this MOS and its inverse is close to [[logarithmic phi]], or even logarithmic phi itself; based on this relation to the golden sequence, [[User:Lériendil|Lériendil]] has proposed the name '''aureate''' for this scale.


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2g&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;450&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;900&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;453 1/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;906 2/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31/82&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;453 21/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;907 1/41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;454 2/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;908 4/37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;454 6/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;909 1/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;455.132972&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;910.265944&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;455 5/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;910 10/29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;455.212095&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;910.42419&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;30/79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;455 55/79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;911 31/79&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;456&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;912&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;456 24/71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;912 48/71&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;35/92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;456 12/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;913 1/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;457 1/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;914 2/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29/76&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;457 13/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;915 7/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;458 2/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;916 4/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;458 14/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;917 11/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;459 7/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;918 14/27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;459 27/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;919 7/47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23/60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;460&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;920&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;461 7/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;923 1/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
==Scale tree==
{{MOS tuning spectrum}}
 
{{todo|expand}}
 
[[Category:Oneirotonic]]
[[Category:13-tone scales]]
Retrieved from "https://en.xen.wiki/w/8L_5s"