12L 17s: Difference between revisions

Wikispaces>JosephRuhf
**Imported revision 566535471 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is the MOS which splits the small steps 1-2-1-2-1-2-1-1-2-1-1-2 between the large steps. Its generator is a near-perfect fourth of no less than 5/12edo (500 cents), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.
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>2015-11-15 17:06:32 UTC</tt>.<br>
: The original revision id was <tt>566535471</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 is the MOS which splits the small steps 1-2-1-2-1-2-1-1-2-1-1-2 between the large steps. Its generator is a near-perfect fourth of no less than 5/12edo (500 cents), and 53edo falls near the beginning of its boundary of "practicality" and its harmonic entropy minimum of exactly 4/3.
|| 12/29 ||  ||  ||  ||  || 496.552 ||
||  ||  ||  ||  || 53/128 || 496.875 ||
||  ||  ||  || 41/99 ||  || 496.97 ||
||  ||  ||  ||  || 70/169 || 497.041 ||
||  ||  || 29/70 ||  ||  || 497.143 ||
||  ||  ||  ||  ||  || 497.211 ||
||  ||  ||  ||  || 75/181 || 497.238 ||
||  ||  ||  ||  ||  || 497.254 ||
||  ||  ||  || 46/111 ||  || 497.297 ||
||  ||  ||  ||  ||  || 497.353 ||
||  ||  ||  ||  || 63/152 || 497.368 ||
||  || 17/41 ||  ||  ||  || 497.561 ||
||  ||  ||  ||  || 56/135 || 497.778 ||
||  ||  ||  || 39/94 ||  || 497.842 ||
||  ||  ||  ||  ||  || 497.935 ||
||  ||  ||  ||  || 61/147 || 497.959 ||
||  ||  ||  ||  ||  || 497.985 ||
||  ||  || 22/53 ||  ||  || 498.113 ||
||  ||  ||  ||  ||  || 498.178 ||
||  ||  ||  ||  || 49/118 || 498.305 ||
||  ||  ||  || 27/65 ||  || 498.4615 ||
||  ||  ||  ||  || 32/77 || 498.701 ||
|| 5/12 ||  ||  ||  ||  || 500 ||</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;12L 17s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS which splits the small steps 1-2-1-2-1-2-1-1-2-1-1-2 between the large steps. Its generator is a near-perfect fourth of no less than 5/12edo (500 cents), and 53edo falls near the beginning of its boundary of &amp;quot;practicality&amp;quot; and its harmonic entropy minimum of exactly 4/3.&lt;br /&gt;


 
{| class="wikitable"
&lt;table class="wiki_table"&gt;
|-
    &lt;tr&gt;
| | 12/29
        &lt;td&gt;12/29&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 496.552
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;496.552&lt;br /&gt;
| | 53/128
&lt;/td&gt;
| | 496.875
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 41/99
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 496.97
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;53/128&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;496.875&lt;br /&gt;
| | 70/169
&lt;/td&gt;
| | 497.041
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 29/70
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 497.143
&lt;/td&gt;
|-
        &lt;td&gt;41/99&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;496.97&lt;br /&gt;
| |
&lt;/td&gt;
| | 497.211
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 75/181
        &lt;td&gt;&lt;br /&gt;
| | 497.238
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;70/169&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;497.041&lt;br /&gt;
| |
&lt;/td&gt;
| | 497.254
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 46/111
&lt;/td&gt;
| |
        &lt;td&gt;29/70&lt;br /&gt;
| | 497.297
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;497.143&lt;br /&gt;
| |
&lt;/td&gt;
| | 497.353
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 63/152
        &lt;td&gt;&lt;br /&gt;
| | 497.368
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 17/41
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;497.211&lt;br /&gt;
| |
&lt;/td&gt;
| | 497.561
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 56/135
        &lt;td&gt;&lt;br /&gt;
| | 497.778
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;75/181&lt;br /&gt;
| |
&lt;/td&gt;
| | 39/94
        &lt;td&gt;497.238&lt;br /&gt;
| |
&lt;/td&gt;
| | 497.842
    &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;&lt;br /&gt;
| | 497.935
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;497.254&lt;br /&gt;
| | 61/147
&lt;/td&gt;
| | 497.959
    &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;&lt;br /&gt;
| | 497.985
&lt;/td&gt;
|-
        &lt;td&gt;46/111&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 22/53
&lt;/td&gt;
| |
        &lt;td&gt;497.297&lt;br /&gt;
| |
&lt;/td&gt;
| | 498.113
    &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;&lt;br /&gt;
| | 498.178
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;497.353&lt;br /&gt;
| | 49/118
&lt;/td&gt;
| | 498.305
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 27/65
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 498.4615
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;63/152&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;497.368&lt;br /&gt;
| | 32/77
&lt;/td&gt;
| | 498.701
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 5/12
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;17/41&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 500
&lt;/td&gt;
|}
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497.561&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;56/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497.778&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;39/94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497.842&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497.935&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;61/147&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497.959&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497.985&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;22/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.113&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.178&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;49/118&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.305&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.4615&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;32/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.701&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;500&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>