7-limit: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>

Relative to their size, the equal divisions [[12edo]], [[19edo]], [[31edo]], [[99edo]] and [[171edo]] provide good approximations to the 7-limit, with [[15edo]], [[22edo]], [[27edo]], [[41edo]], [[46edo]], [[53edo]], [[58edo]], [[68edo]], [[72edo]], [[118edo]], [[130edo]], [[140edo]] and [[152edo]] among the others worthy of notice.

=Music=  

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3|Prelude #1 in 7-limit JI]] by [[Ivor Darreg]] &lt;-- are there any notations for it?

[[http://www.archive.org/details/ClintonVariations|Clinton Variations]] [[http://www.archive.org/download/ClintonVariations/clinton.mp3|play]] by [[Gene Ward Smith]]

<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;7-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;7-limit&lt;/em&gt; or &amp;quot;7 prime-limit&amp;quot; refers to a constraint on rational intervals such that 7 is the highest allowable &lt;a class="wiki_link" href="/prime%20number"&gt;prime number&lt;/a&gt;, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 7. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;, &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, &lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_15"&gt;28/15&lt;/a&gt;, &lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;, &lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt;, &lt;a class="wiki_link" href="/25_14"&gt;25/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_25"&gt;28/25&lt;/a&gt;, &lt;a class="wiki_link" href="/25_21"&gt;25/21&lt;/a&gt;, &lt;a class="wiki_link" href="/42_25"&gt;42/25&lt;/a&gt;, &lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;, &lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;, &lt;a class="wiki_link" href="/35_28"&gt;35/28&lt;/a&gt;, &lt;a class="wiki_link" href="/56_35"&gt;56/35&lt;/a&gt;, 45/28, 56/45, 49/32, 64/49, 49/36, 72/49, 49/30, 60/49, 49/25, 50/49, 49/27, 54/49, 49/35, 70/49, 49/45, 90/49.&lt;br /&gt;

&lt;br /&gt;

Relative to their size, the equal divisions &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; and &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; provide good approximations to the 7-limit, with &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt; and &lt;a class="wiki_link" href="/152edo"&gt;152edo&lt;/a&gt; among the others worthy of notice.&lt;br /&gt;

&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;

&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3" rel="nofollow"&gt;Prelude #1 in 7-limit JI&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &amp;lt;-- are there any notations for it?&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://www.archive.org/details/ClintonVariations" rel="nofollow"&gt;Clinton Variations&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/ClintonVariations/clinton.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;