Consistency
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- This revision was by author hstraub and made on 2011-06-27 07:18:21 UTC.
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Original Wikitext content:
[[http://www.tonalsoft.com/enc/c/consistent.aspx|consistent (TonalSoft encyclopedia)]] //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]].
Original HTML content:
<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 /> <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>