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**Imported revision 514562090 - Original comment: **
Wikispaces>Gedankenwelt
**Imported revision 538626006 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-20 21:10:12 UTC</tt>.<br>
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-01-26 18:07:35 UTC</tt>.<br>
: The original revision id was <tt>514562090</tt>.<br>
: The original revision id was <tt>538626006</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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According to [[http://untwelve.org/interviews/golden.html|this interview]], Monroe Golden's //Incongruity// uses just-intonation chord progressions that exploit this comma.
According to [[http://untwelve.org/interviews/golden.html|this interview]], Monroe Golden's //Incongruity// uses just-intonation chord progressions that exploit this comma.


=Relations to other Superparticular Ratios=
Superparticular ratios, like 81/80, can be expressed as products or quotients of other superparticular ratios. Following is a list of such representations r1 * r2 or r2 / r1 of 81/80, where r1 and r2 are other superparticular ratios.
Names in brackets refer to 7-limit [[Meantone family|meantone]] extensions, or 11-limit rank three temperaments from the [[Didymus rank three family|Didymus family]] that temper out the respective ratios as commas.
||~ Limit ||~ r1 * r2 ||~ r2 / r1 ||
|| 5 || - || 9/8 * 9/10 ||
|| 7 || 126/125 * 225/224 (septimal meantone) || 21/20 * 27/28 (sharptone), 36/35 * 63/64 (dominant) ||
|| 11 || 99/98 * 441/440 (euterpe), 121/120 * 243/242 (urania) || 33/32 * 54/55 (thalia), 45/44 * 99/100 (calliope) ||
|| 13 || 91/90 * 729/728, 105/104 * 351/350 || 27/26 * 39/40, 65/64 * 324/325, 66/65 * 351/352, 78/77 * 2079/2080 ||
|| 17 || 85/84 * 1701/1700 || 51/50 * 135/136 ||
|| 19 || 96/95 * 513/512, 153/152 * 171/170 || 57/56 * 189/190, 76/75 * 1215/1216, 77/76 * 1539/1540 ||
|| 23 || 161/160 * 162/161 || 69/68 * 459/460 ||
|| 29 || 117/116 * 261/260 || - ||
|| 31 || 93/92 * 621/620 || 63/62 * 279/280 ||
|| 37 || 111/110 * 297/296 || 75/74 * 999/1000 ||
|| 41 || 82/81 * 6561/6560 || 41/40 * 81/82 ||
|| 43 || 86/85 * 1377/1376, 87/86 * 1161/1160, 129/128 * 216/215 || - ||
|| 47 || 141/140 * 189/188 || - ||
|| 53 || - || 54/53 * 159/160 ||
|| 59 || - || - ||
|| 61 || - || 61/60 * 243/244 ||
|| 67 || 135/134 * 201/200 || - ||
|| 71 || - || 71/70 * 567/568, 72/71 * 639/640 ||
|| 73 || - || 73/72 * 729/730 ||
|| 79 || - || 79/78 * 3159/3160, 80/79 * 6399/6400 ||
|| 83 || 83/82 * 3321/3320, 84/83 * 2241/2240 || - ||
|| 89 || 89/88 * 891/890, 90/89 * 801/800 || - ||
|| 97 || 97/96 * 486/485 || - ||
|| 101 || 101/100 * 405/404 || - ||
|| 103 || - || - ||
|| 107 || 108/107 * 321/320 || - ||
==External Links==
[[http://en.wikipedia.org/wiki/Syntonic_comma]]</pre></div>
[[http://en.wikipedia.org/wiki/Syntonic_comma]]</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
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According to &lt;a class="wiki_link_ext" href="http://untwelve.org/interviews/golden.html" rel="nofollow"&gt;this interview&lt;/a&gt;, Monroe Golden's &lt;em&gt;Incongruity&lt;/em&gt; uses just-intonation chord progressions that exploit this comma.&lt;br /&gt;
According to &lt;a class="wiki_link_ext" href="http://untwelve.org/interviews/golden.html" rel="nofollow"&gt;this interview&lt;/a&gt;, Monroe Golden's &lt;em&gt;Incongruity&lt;/em&gt; uses just-intonation chord progressions that exploit this comma.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Syntonic_comma&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Relations to other Superparticular Ratios"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Relations to other Superparticular Ratios&lt;/h1&gt;
Superparticular ratios, like 81/80, can be expressed as products or quotients of other superparticular ratios. Following is a list of such representations r1 * r2 or r2 / r1 of 81/80, where r1 and r2 are other superparticular ratios.&lt;br /&gt;
Names in brackets refer to 7-limit &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone&lt;/a&gt; extensions, or 11-limit rank three temperaments from the &lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Didymus family&lt;/a&gt; that temper out the respective ratios as commas.&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Limit&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;r1 * r2&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;r2 / r1&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8 * 9/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;126/125 * 225/224 (septimal meantone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/20 * 27/28 (sharptone), 36/35 * 63/64 (dominant)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;99/98 * 441/440 (euterpe), 121/120 * 243/242 (urania)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;33/32 * 54/55 (thalia), 45/44 * 99/100 (calliope)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;91/90 * 729/728, 105/104 * 351/350&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/26 * 39/40, 65/64 * 324/325, 66/65 * 351/352, 78/77 * 2079/2080&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;85/84 * 1701/1700&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;51/50 * 135/136&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;96/95 * 513/512, 153/152 * 171/170&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;57/56 * 189/190, 76/75 * 1215/1216, 77/76 * 1539/1540&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;161/160 * 162/161&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;69/68 * 459/460&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117/116 * 261/260&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;93/92 * 621/620&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;63/62 * 279/280&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111/110 * 297/296&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;75/74 * 999/1000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;82/81 * 6561/6560&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41/40 * 81/82&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;86/85 * 1377/1376, 87/86 * 1161/1160, 129/128 * 216/215&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;141/140 * 189/188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;54/53 * 159/160&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;59&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;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;61/60 * 243/244&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;135/134 * 201/200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;71/70 * 567/568, 72/71 * 639/640&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;73/72 * 729/730&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;79/78 * 3159/3160, 80/79 * 6399/6400&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;83/82 * 3321/3320, 84/83 * 2241/2240&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89/88 * 891/890, 90/89 * 801/800&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;97&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;97/96 * 486/485&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;101/100 * 405/404&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;103&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;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;107&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;108/107 * 321/320&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Relations to other Superparticular Ratios-External Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;External Links&lt;/h2&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Syntonic_comma&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/81/80"