9L 3s: Difference between revisions

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**Imported revision 565973167 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="font-size: 12.8000001907349px;">This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-10 18:19:52 UTC</tt>.<br>
: The original revision id was <tt>565973167</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: 12.8000001907349px;"&gt;This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.&lt;/span&gt;
|| 1/12 ||  || &lt;span style="font-size: 12.8px;"&gt;100&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8px;"&gt;5/57&lt;/span&gt; ||  || 105.263 ||
|| &lt;span style="font-size: 12.8px;"&gt;4/45&lt;/span&gt; ||  || 106.667 ||
||  || &lt;span style="font-size: 12.8px;"&gt;7/78&lt;/span&gt; || 107.5385 ||
||  || 10/111 || 108.108 ||
|| &lt;span style="font-size: 12.8px;"&gt;3/33&lt;/span&gt; ||  || 109.111 ||
||  ||  || 109.992 ||
||  || &lt;span style="font-size: 12.8px;"&gt;8/87&lt;/span&gt; || 110.345 ||
||  ||  || 110.557 ||
||  || &lt;span style="font-size: 12.8000001907349px;"&gt;5/54&lt;/span&gt; || 111.111 ||
||  ||  || 111.815 ||
||  || &lt;span style="font-size: 12.8px;"&gt;7/75&lt;/span&gt; || 112 ||
||  || 9/96 || 112.5 ||
||  || 11/117 || 112.8205 ||
||  || 13/138 || 113.0435 ||
|| 2/21 ||  || &lt;span style="font-size: 12.8000001907349px;"&gt;114.286&lt;/span&gt; ||
||  || 11/114 || 115.7895 ||
||  || 9/93 || 116.129 ||
||  || &lt;span style="font-size: 12.8px;"&gt;7/72&lt;/span&gt; || 116.667 ||
||  || &lt;span style="font-size: 12.8px;"&gt;5/51&lt;/span&gt; || 117.647 ||
||  ||  || 118.274 ||
||  || &lt;span style="font-size: 12.8px;"&gt;8/81&lt;/span&gt; || 118.5185 ||
||  ||  || 118.769 ||
||  || 11/111 || 118.919 ||
||  || 14/141 || 119.149 ||
|| &lt;span style="font-size: 12.8px;"&gt;3/30&lt;/span&gt; ||  || 120 ||
||  ||  || 120.543 ||
||  || &lt;span style="font-size: 12.8px;"&gt;7/69&lt;/span&gt; || 121.739 ||
||  || 11/108 || 122.222 ||
|| &lt;span style="font-size: 12.8px;"&gt;4/39&lt;/span&gt; ||  || 123.138 ||
||  || 9/87 || 124.138 ||
|| &lt;span style="font-size: 12.8px;"&gt;5/48&lt;/span&gt; ||  || 125 ||
|| 1/9 ||  || &lt;span style="font-size: 12.8px;"&gt;133.333&lt;/span&gt; ||</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;9L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or &amp;quot;trienthird&amp;quot;/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.&lt;/span&gt;&lt;br /&gt;


 
{| class="wikitable"
&lt;table class="wiki_table"&gt;
|-
    &lt;tr&gt;
| | 1/12
        &lt;td&gt;1/12&lt;br /&gt;
| |
&lt;/td&gt;
| | <span style="font-size: 12.8px;">100</span>
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | <span style="font-size: 12.8px;">5/57</span>
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;100&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 105.263
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | <span style="font-size: 12.8px;">4/45</span>
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;5/57&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 106.667
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;105.263&lt;br /&gt;
| | <span style="font-size: 12.8px;">7/78</span>
&lt;/td&gt;
| | 107.5385
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;4/45&lt;/span&gt;&lt;br /&gt;
| | 10/111
&lt;/td&gt;
| | 108.108
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | <span style="font-size: 12.8px;">3/33</span>
        &lt;td&gt;106.667&lt;br /&gt;
| |
&lt;/td&gt;
| | 109.111
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 109.992
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;7/78&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;107.5385&lt;br /&gt;
| | <span style="font-size: 12.8px;">8/87</span>
&lt;/td&gt;
| | 110.345
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 110.557
        &lt;td&gt;10/111&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;108.108&lt;br /&gt;
| | <span style="font-size: 12.8000001907349px;">5/54</span>
&lt;/td&gt;
| | 111.111
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;3/33&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 111.815
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;109.111&lt;br /&gt;
| | <span style="font-size: 12.8px;">7/75</span>
&lt;/td&gt;
| | 112
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 9/96
&lt;/td&gt;
| | 112.5
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;109.992&lt;br /&gt;
| | 11/117
&lt;/td&gt;
| | 112.8205
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 13/138
&lt;/td&gt;
| | 113.0435
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;8/87&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | 2/21
        &lt;td&gt;110.345&lt;br /&gt;
| |
&lt;/td&gt;
| | <span style="font-size: 12.8000001907349px;">114.286</span>
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 11/114
&lt;/td&gt;
| | 115.7895
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;110.557&lt;br /&gt;
| | 9/93
&lt;/td&gt;
| | 116.129
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | <span style="font-size: 12.8px;">7/72</span>
&lt;/td&gt;
| | 116.667
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;5/54&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;111.111&lt;br /&gt;
| | <span style="font-size: 12.8px;">5/51</span>
&lt;/td&gt;
| | 117.647
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 118.274
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;111.815&lt;br /&gt;
| | <span style="font-size: 12.8px;">8/81</span>
&lt;/td&gt;
| | 118.5185
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 118.769
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;7/75&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;112&lt;br /&gt;
| | 11/111
&lt;/td&gt;
| | 118.919
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 14/141
&lt;/td&gt;
| | 119.149
        &lt;td&gt;9/96&lt;br /&gt;
|-
&lt;/td&gt;
| | <span style="font-size: 12.8px;">3/30</span>
        &lt;td&gt;112.5&lt;br /&gt;
| |
&lt;/td&gt;
| | 120
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 120.543
        &lt;td&gt;11/117&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;112.8205&lt;br /&gt;
| | <span style="font-size: 12.8px;">7/69</span>
&lt;/td&gt;
| | 121.739
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 11/108
&lt;/td&gt;
| | 122.222
        &lt;td&gt;13/138&lt;br /&gt;
|-
&lt;/td&gt;
| | <span style="font-size: 12.8px;">4/39</span>
        &lt;td&gt;113.0435&lt;br /&gt;
| |
&lt;/td&gt;
| | 123.138
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;2/21&lt;br /&gt;
| | 9/87
&lt;/td&gt;
| | 124.138
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | <span style="font-size: 12.8px;">5/48</span>
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;114.286&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 125
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 1/9
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | <span style="font-size: 12.8px;">133.333</span>
        &lt;td&gt;11/114&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;115.7895&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129&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;span style="font-size: 12.8px;"&gt;7/72&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.667&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;span style="font-size: 12.8px;"&gt;5/51&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.647&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;118.274&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;span style="font-size: 12.8px;"&gt;8/81&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;118.5185&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;118.769&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/111&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;118.919&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/141&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.149&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;3/30&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;120&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;120.543&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;span style="font-size: 12.8px;"&gt;7/69&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;121.739&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;122.222&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;4/39&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123.138&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124.138&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;5/48&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8px;"&gt;133.333&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

This MOS is always proper because its period runs LLLs. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133.33). It represents, among other chromatic scales, that of the August temperament.

1/12 100
5/57 105.263
4/45 106.667
7/78 107.5385
10/111 108.108
3/33 109.111
109.992
8/87 110.345
110.557
5/54 111.111
111.815
7/75 112
9/96 112.5
11/117 112.8205
13/138 113.0435
2/21 114.286
11/114 115.7895
9/93 116.129
7/72 116.667
5/51 117.647
118.274
8/81 118.5185
118.769
11/111 118.919
14/141 119.149
3/30 120
120.543
7/69 121.739
11/108 122.222
4/39 123.138
9/87 124.138
5/48 125
1/9 133.333
Retrieved from "https://en.xen.wiki/index.php?title=9L_3s&oldid=1138"