Superparticular ratio
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Superparticular numbers are ratios of the form (n+1)/n, or 1+1/n. In ancient Greece they were known as Epimoric (επιμοριοσ) ratios, which is literally translated as "above a part." These ratios have some peculiar properties: * The difference tone of the dyad is also the virtual fundamental. * The first 7 such ratios ([[Octave|2/1]], [[3_2|3/2]], [[4_3|4/3]], [[5_4|5/4]], [[6_5|6/5]], [[7_6|7/6]], [[8_7|8/7]]) are notable [[harmonic entropy]] minima. * The difference between two successive epimoric ratios is always an epimoric ratio. * The sum of two successive epimoric ratios is either an epimoric ratio or an epimeric ratio. Curiously enough, the ancient Greeks considered 2/1 a superparticular number even though 1 was not considered to be a true number. <span style="background-color: initial;">[[http://en.wikipedia.org/wiki/Superparticular_number]]</span>
Original HTML content:
<html><head><title>superparticular</title></head><body>Superparticular numbers are ratios of the form (n+1)/n, or 1+1/n. In ancient Greece they were known as Epimoric (επιμοριοσ) ratios, which is literally translated as "above a part."<br /> <br /> These ratios have some peculiar properties:<br /> <ul><li>The difference tone of the dyad is also the virtual fundamental.</li><li>The first 7 such ratios (<a class="wiki_link" href="/Octave">2/1</a>, <a class="wiki_link" href="/3_2">3/2</a>, <a class="wiki_link" href="/4_3">4/3</a>, <a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/8_7">8/7</a>) are notable <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> minima.</li><li>The difference between two successive epimoric ratios is always an epimoric ratio.</li><li>The sum of two successive epimoric ratios is either an epimoric ratio or an epimeric ratio.</li></ul><br /> Curiously enough, the ancient Greeks considered 2/1 a superparticular number even though 1 was not considered to be a true number.<br /> <br /> <br /> <span style="background-color: initial;"><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Superparticular_number" rel="nofollow">http://en.wikipedia.org/wiki/Superparticular_number</a></span></body></html>