1L 11s: 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>
{{MOS intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2014-12-01 19:58:19 UTC</tt>.<br>
: The original revision id was <tt>533423550</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, with its diatonic minor second generator, is the dodecatonic scale of Ripple (9:8=+2 generators) and Passion (6:5=+3 generators) temperaments. However, it feels markedly more hendecatonic to listeners used to the equally divided chromatic scale because of its unbroken chain of eleven equal steps–never mind that the 12th degree is actually less than the octave. This hendecatonic feel is especially pronounced above 2/23edo, where the octave feels like a comma shift of the 12th degree rather than an independent note.
||||~ Generator ||~ Cents ||~ 2g ||~ 3g ||
|| 1/12 ||  || 100 || 200 || 300 ||
|| 5/59 ||  || 101 41/59 || 203 23/59 || 305 5/59 ||
||  || 9/106 || 101 47/53 || 203 41/53 || 305 35/53 ||
||  || 13/153 || 101 49/51 || 203 47/51 || 305 15/17 ||
||  || 17/200 || 102 || 204 || 306 ||
|| 4/47 ||  || 102 6/47 || 204 12/47 || 306 18/47 ||
||  || 7/82 || 102 18/41 || 204 36/41 || 307 13/41 ||
||  || 10/117 || 102 22/39 || 205 5/39 || 307 9/13 ||
||  || 13/152 || 102 12/19 || 205 5/19 || 307 17/19 ||
||  || 16/187 || 102 126/187 || 205 65/187 || 308 4/187 ||
||  || 19/222 || 102 31/37 || 205 25/37 || 308 19/37 ||
|| 3/35 ||  || 102 6/7 || 205 5/7 || 308 4/7 ||
||  || 20/233 || 103 1/233 || 206 2/233 || 309 3/233 ||
||  || 17/198 || 103 1/33 || 206 2/33 || 309 1/11 ||
||  || 14/163 || 103 11/163 || 206 22/163 || 309 33/163 ||
||  || 11/128 || 103.125 || 206.25 || 309.375 ||
||  || 8/93 || 103 7/31 || 206 14/31 || 309 21/31 ||
||  || 5/58 || 103 13/29 || 206 26/29 || 310 10/29 ||
||  || 7/81 || 103 19/27 || 206 11/27 || 311 1/9 ||
||  || 9/104 || 103 11/13 || 207 9/13 || 311 7/13 ||
||  || 11/127 || 103 119/127 || 207 111/127 || 311 123/127 ||
||  || 13/150 || 104 || 208 || 312 ||
|| 2/23 ||  || 104 8/23 || 208 16/23 || 313 1/23 ||
||  || 11/126 || 104 16/21 || 209 11/21 || 314 2/7 ||
||  || 9/103 || 104 88/103 || 209 73/103 || 314 58/103 ||
||  || 7/80 || 105 || 210 || 315 ||
||  || 5/57 || 105 5/19 || 210 10/19 || 315 15/19 ||
||  || 8/91 || 105 45/91 || 210 90/91 || 316 44/91 ||
||  || 11/125 || 105.6 || 211.2 || 316.8 ||
|| 3/34 ||  || 105 15/17 || 211 13/17 || 317 11/17 ||
||  || 28/317 || 105 315/317 || 211 313/317 || 317 311/317 ||
||  || 25/283 || 106 2/283 || 212 4/283 || 318 6/283 ||
||  || 22/249 || 106 2/83 || 212 4/83 || 318 6/83 ||
||  || 19/215 || 106 2/43 || 212 4/43 || 318 6/43 ||
||  || 16/181 || 106 14/181 || 212 28/181 || 318 42/181 ||
||  || 13/147 || 106 6&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;/49&lt;/span&gt; || 212 12/49 || 318 18/49 ||
||  || 10/113 || 106 22/113 || 212 44/113 || 318 66/113 ||
||  || 7/79 || 106 26/79 || 212 52/79 || 318 78/79 ||
||  || 11/124 || 106 14/31 || 212 28/31 || 319 11/31 ||
|| 4/45 ||  || 106 2/3 || 213 1/3 || 320 ||
|| 5/56 ||  || 107 1/7 || 214 2/7 || 321 3/7 ||
|| 1/11 ||  || 109 1/11 || 218 2/11 || 327 3/11 ||</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 11s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, with its diatonic minor second generator, is the dodecatonic scale of Ripple (9:8=+2 generators) and Passion (6:5=+3 generators) temperaments. However, it feels markedly more hendecatonic to listeners used to the equally divided chromatic scale because of its unbroken chain of eleven equal steps–never mind that the 12th degree is actually less than the octave. This hendecatonic feel is especially pronounced above 2/23edo, where the octave feels like a comma shift of the 12th degree rather than an independent note.&lt;br /&gt;


The simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, or [[passion]] (5;4 = +3 generators), and even there it implies a val with warts for 3 and (for the most part) 5.


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &lt;th colspan="2"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;2g&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;3g&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;101 41/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203 23/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;305 5/59&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/106&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;101 47/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203 41/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;305 35/53&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/153&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;101 49/51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203 47/51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;305 15/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;204&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;306&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 6/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;204 12/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;306 18/47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/82&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 18/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;204 36/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;307 13/41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 22/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;205 5/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;307 9/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/152&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 12/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;205 5/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;307 17/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/187&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 126/187&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;205 65/187&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;308 4/187&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/222&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 31/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;205 25/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;308 19/37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102 6/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;205 5/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;308 4/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 1/233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206 2/233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309 3/233&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/198&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 1/33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206 2/33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309 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;14/163&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 11/163&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206 22/163&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309 33/163&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103.125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309.375&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 7/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206 14/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;309 21/31&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 13/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206 26/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;310 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;7/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 19/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;206 11/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311 1/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 11/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;207 9/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311 7/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103 119/127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;207 111/127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311 123/127&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/150&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;208&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;312&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104 8/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;208 16/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;313 1/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/126&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104 16/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;209 11/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;314 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;9/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104 88/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;209 73/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;314 58/103&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;210&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105 5/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;210 10/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315 15/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105 45/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;210 90/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316 44/91&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;211.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316.8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105 15/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;211 13/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;317 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;28/317&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105 315/317&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;211 313/317&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;317 311/317&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/283&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 2/283&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 4/283&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 6/283&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/249&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 2/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 4/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 6/83&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/215&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 2/43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 4/43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 6/43&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/181&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 14/181&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 28/181&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 42/181&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/147&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 6&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;/49&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 12/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 18/49&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 22/113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 44/113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 66/113&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 26/79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 52/79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;318 78/79&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/124&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 14/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212 28/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;319 11/31&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 2/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;213 1/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;107 1/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;214 2/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;321 3/7&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;1/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 1/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218 2/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;327 3/11&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
| 6/5 = ↑ [[Passionate]]
| 5/4 = [[Passion]]
| 13/8 = Unnamed golden tuning
| 12/5 = [[Slithy]]
| 13/5 = Golden [[octacot]] (88.118¢)
| 10/3 = [[Marvolo]]
| 7/2 = [[Nautilus]]
| 4/1 = [[Nuke]]
| 9/2 = [[Valentine]]
| 6/1 = [[Slurpee]], ↓ [[unicorn]]
}}
 
{{Todo| expand }}

Latest revision as of 18:49, 3 March 2025

↑ 1L 10s 2L 10s ↗
1L 11s 2L 11s →
↓ 1L 12s 2L 12s ↘ 
┌╥┬┬┬┬┬┬┬┬┬┬┬┐
│║││││││││││││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lsssssssssss
sssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\12 to 1\1 (1100.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 1L 10s
Sister 11L 1s
Daughters 12L 1s, 1L 12s
Neutralized 2L 10s
2-Flought 13L 11s, 1L 23s
Equal tunings
Equalized (L:s = 1:1) 11\12 (1100.0 ¢)
Supersoft (L:s = 4:3) 34\37 (1102.7 ¢)
Soft (L:s = 3:2) 23\25 (1104.0 ¢)
Semisoft (L:s = 5:3) 35\38 (1105.3 ¢)
Basic (L:s = 2:1) 12\13 (1107.7 ¢)
Semihard (L:s = 5:2) 25\27 (1111.1 ¢)
Hard (L:s = 3:1) 13\14 (1114.3 ¢)
Superhard (L:s = 4:1) 14\15 (1120.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 11 small steps, repeating every octave. 1L 11s is a grandchild scale of 1L 9s, expanding it by 2 tones. Generators that produce this scale range from 1100 ¢ to 1200 ¢, or from 0 ¢ to 100 ¢.

The simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, or passion (5;4 = +3 generators), and even there it implies a val with warts for 3 and (for the most part) 5.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 1L 11s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 100.0 ¢
Augmented 1-mosstep A1ms L 100.0 ¢ to 1200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 200.0 ¢
Major 2-mosstep M2ms L + s 200.0 ¢ to 1200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 300.0 ¢
Major 3-mosstep M3ms L + 2s 300.0 ¢ to 1200.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 400.0 ¢
Major 4-mosstep M4ms L + 3s 400.0 ¢ to 1200.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 500.0 ¢
Major 5-mosstep M5ms L + 4s 500.0 ¢ to 1200.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 600.0 ¢
Major 6-mosstep M6ms L + 5s 600.0 ¢ to 1200.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 700.0 ¢
Major 7-mosstep M7ms L + 6s 700.0 ¢ to 1200.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 800.0 ¢
Major 8-mosstep M8ms L + 7s 800.0 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 900.0 ¢
Major 9-mosstep M9ms L + 8s 900.0 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms 10s 0.0 ¢ to 1000.0 ¢
Major 10-mosstep M10ms L + 9s 1000.0 ¢ to 1200.0 ¢
11-mosstep Diminished 11-mosstep d11ms 11s 0.0 ¢ to 1100.0 ¢
Perfect 11-mosstep P11ms L + 10s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms L + 11s 1200.0 ¢

Generator chain

Generator chain of 1L 11s
Bright gens Scale degree Abbrev.
12 Augmented 0-mosdegree A0md
11 Augmented 1-mosdegree A1md
10 Major 2-mosdegree M2md
9 Major 3-mosdegree M3md
8 Major 4-mosdegree M4md
7 Major 5-mosdegree M5md
6 Major 6-mosdegree M6md
5 Major 7-mosdegree M7md
4 Major 8-mosdegree M8md
3 Major 9-mosdegree M9md
2 Major 10-mosdegree M10md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 12-mosdegree		 P0md
P12md
−1 Perfect 1-mosdegree P1md
−2 Minor 2-mosdegree m2md
−3 Minor 3-mosdegree m3md
−4 Minor 4-mosdegree m4md
−5 Minor 5-mosdegree m5md
−6 Minor 6-mosdegree m6md
−7 Minor 7-mosdegree m7md
−8 Minor 8-mosdegree m8md
−9 Minor 9-mosdegree m9md
−10 Minor 10-mosdegree m10md
−11 Diminished 11-mosdegree d11md
−12 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 1L 11s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
11|0 1 Lsssssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
10|1 12 sLssssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
9|2 11 ssLsssssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
8|3 10 sssLssssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|4 9 ssssLsssssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|5 8 sssssLssssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|6 7 ssssssLsssss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|7 6 sssssssLssss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|8 5 ssssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|9 4 sssssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|10 3 ssssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|11 2 sssssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 1L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\12 1100.000 100.000 1:1 1.000 Equalized 1L 11s
56\61 1101.639 98.361 6:5 1.200 ↑ Passionate
45\49 1102.041 97.959 5:4 1.250 Passion
79\86 1102.326 97.674 9:7 1.286
34\37 1102.703 97.297 4:3 1.333 Supersoft 1L 11s
91\99 1103.030 96.970 11:8 1.375
57\62 1103.226 96.774 7:5 1.400
80\87 1103.448 96.552 10:7 1.429
23\25 1104.000 96.000 3:2 1.500 Soft 1L 11s
81\88 1104.545 95.455 11:7 1.571
58\63 1104.762 95.238 8:5 1.600
93\101 1104.950 95.050 13:8 1.625 Unnamed golden tuning
35\38 1105.263 94.737 5:3 1.667 Semisoft 1L 11s
82\89 1105.618 94.382 12:7 1.714
47\51 1105.882 94.118 7:4 1.750
59\64 1106.250 93.750 9:5 1.800
12\13 1107.692 92.308 2:1 2.000 Basic 1L 11s
Scales with tunings softer than this are proper
49\53 1109.434 90.566 9:4 2.250
37\40 1110.000 90.000 7:3 2.333
62\67 1110.448 89.552 12:5 2.400 Slithy
25\27 1111.111 88.889 5:2 2.500 Semihard 1L 11s
63\68 1111.765 88.235 13:5 2.600 Golden octacot (88.118¢)
38\41 1112.195 87.805 8:3 2.667
51\55 1112.727 87.273 11:4 2.750
13\14 1114.286 85.714 3:1 3.000 Hard 1L 11s
40\43 1116.279 83.721 10:3 3.333 Marvolo
27\29 1117.241 82.759 7:2 3.500 Nautilus
41\44 1118.182 81.818 11:3 3.667
14\15 1120.000 80.000 4:1 4.000 Superhard 1L 11s
Nuke
29\31 1122.581 77.419 9:2 4.500 Valentine
15\16 1125.000 75.000 5:1 5.000
16\17 1129.412 70.588 6:1 6.000 Slurpee, ↓ unicorn
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 11s
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