Consistency: Difference between revisions
Wikispaces>xenwolf **Imported revision 238915015 - Original comment: ** |
Wikispaces>hstraub **Imported revision 238923473 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-27 07:18:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238923473</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> | ||
| Line 8: | Line 8: | ||
<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">[[http://www.tonalsoft.com/enc/c/consistent.aspx|consistent (TonalSoft encyclopedia)]] | <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">[[http://www.tonalsoft.com/enc/c/consistent.aspx|consistent (TonalSoft encyclopedia)]] | ||
//see (add) also [[Odd-limit]]//</pre></div> | //see (add) also [[Odd-limit]]// | ||
An example for a system that is not consistent is [[25edo]]: | |||
The best approximation for the interval of [[7_6|7/6]] (the septimal subminor third) in 25edo is 6 steps, the best approximation for the [[3_2|perfect fifth 3/2]] is 15 steps. | |||
Adding the two just intervals gives 3/2 * 7/6 = [[7_4|7/4]], the harmonic seventh, for which the best approximation in 25edo is 20 steps. Adding the two approximated intervals, however, gives 21 steps. This means that 25edo is not consistent in [[7-limit]].</pre></div> | |||
<h4>Original HTML content:</h4> | <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"><html><head><title>consistent</title></head><body><a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/c/consistent.aspx" rel="nofollow">consistent (TonalSoft encyclopedia)</a><br /> | <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"><html><head><title>consistent</title></head><body><a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/c/consistent.aspx" rel="nofollow">consistent (TonalSoft encyclopedia)</a><br /> | ||
<br /> | <br /> | ||
<em>see (add) also <a class="wiki_link" href="/Odd-limit">Odd-limit</a></em></body></html></pre></div> | <em>see (add) also <a class="wiki_link" href="/Odd-limit">Odd-limit</a></em><br /> | ||
<br /> | |||
An example for a system that is not consistent is <a class="wiki_link" href="/25edo">25edo</a>:<br /> | |||
<br /> | |||
The best approximation for the interval of <a class="wiki_link" href="/7_6">7/6</a> (the septimal subminor third) in 25edo is 6 steps, the best approximation for the <a class="wiki_link" href="/3_2">perfect fifth 3/2</a> is 15 steps.<br /> | |||
Adding the two just intervals gives 3/2 * 7/6 = <a class="wiki_link" href="/7_4">7/4</a>, the harmonic seventh, for which the best approximation in 25edo is 20 steps. Adding the two approximated intervals, however, gives 21 steps. This means that 25edo is not consistent in <a class="wiki_link" href="/7-limit">7-limit</a>.</body></html></pre></div> | |||