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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>
{{MOS intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-11 15:11:03 UTC</tt>.<br>
: The original revision id was <tt>566086773</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 MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.
||  ||  || Cents ||
|| 0/1 ||  || 0 ||
|| 1/17 ||  || 70.588 ||
||  || 4/67 || 71.641 ||
||  || 3/50 || 72 ||
||  || 2/33 || 72.727 ||
||  || 3/49 || 73.469 ||
||  || 4/65 || 73.846 ||
||  || 5/81 || 74.074 ||
|| 1/16 ||  || 75 ||
||  || 3/47 || 76.596 ||
||  || 2/31 || 77.419 ||
||  || 3/46 || 78.261 ||
||  || 4/61 || 78.6885 ||
||  || 5/76 || 78.947 ||
||  || 6/91 || 79.121 ||
||  ||  || 1200/(12+pi) ||
|| 1/15 ||  || 80 ||
||  ||  || 1200/(12+e) ||
||  || 3/44 || 81.818 ||
||  ||  || 1200/(13+phi) ||
||  || 2/29 || 82.759 ||
||  || 3/43 || 83.721 ||
||  || 4/57 || 84.2105 ||
|| 1/14 ||  || 85.714 ||
||  || 4/55 || 86.364 ||
||  ||  || 1200/(12+sqrt(3)) ||
||  || 3/41 || 87.805 ||
||  ||  || 1200/(12+phi) ||
||  || 5/68 || 88.235 ||
||  ||  || 1200/(12+pi/2) ||
|| 2/27 ||  || 88.889 ||
||  || 5/67 || 89.552 ||
|| 3/40 ||  || 90 ||
|| 4/53 ||  || 90.556 ||
|| 1/13 ||  || 92.308 ||</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;1L 12s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.&lt;br /&gt;


This MOS, also called the '''Happy tridecatonic scale''', has its first [[harmonic entropy]] minimum at 1/[[14edo]]-3/[[40edo]], where 3:2 is +8 [[generator]]s (giving [[Octacot]]). However, the absolute harmonic entropy minimum is [[Nautilus]] ({{nowrap|3:2 ← −6 generators}}), and that is not complete until 14 tones.


&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;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;70.588&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;71.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;72&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;72.727&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;73.469&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;73.846&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;74.074&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;75&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;76.596&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;77.419&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.261&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.6885&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/76&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.947&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;79.121&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;1200/(12+pi)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;80&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;1200/(12+e)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81.818&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;1200/(13+phi)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;82.759&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;83.721&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;84.2105&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;85.714&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;86.364&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;1200/(12+sqrt(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;3/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;87.805&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;1200/(12+phi)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/68&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.235&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;1200/(12+pi/2)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.889&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89.552&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90.556&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;92.308&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
| 10/7 = [[Slithy]]
| 13/8 = Golden [[octacot]] (88.118¢)
| 12/5 = [[Marvolo]]
| 5/2 = [[Nautilus]]
| 13/5 = Unnamed golden tuning
| 3/1 = [[Nuke]]
| 10/3 = [[Valentine]]
| 9/2 = [[Slurpee]]
| 6/1 = ↓[[Unicorn]]
}}
 
{{Todo|improve synopsis|inline=1|text=Rewrite intro with the same information but worded in a way that’s easier to parse.}}
 
[[Category:13-tone scales]]
Retrieved from "https://en.xen.wiki/w/1L_12s"