Goldonic series
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- This revision was by author MasonGreen1 and made on 2015-11-30 23:31:11 UTC.
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Original Wikitext content:
A **goldonic series** or **golden series** is a series of frequencies that form a [[https://en.wikipedia.org/wiki/Geometric_progression|geometric progression]] whose generating interval is the golden ratio (1.61803....). ==Unique properties== The goldonic series is unique among geometric sequencies because only //<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">φ</span>// satisfies the equation //x//<span style="vertical-align: super;">n-1</span> //+ x//<span style="vertical-align: super;">n</span> //= x//<span style="vertical-align: super;">n+1</span>. From an acoustic standpoint, the goldonic series contains some "harmonic-like" characteristics despite being inharmonic. Because each term is equal the difference between the next highest and next lowest terms, a phenomenon similar to modelocking can occur (in which each oscillator becomes entrained to the difference tone generated by its nearest-neighbors)..
Original HTML content:
<html><head><title>Goldonic series</title></head><body>A <strong>goldonic series</strong> or <strong>golden series</strong> is a series of frequencies that form a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Geometric_progression" rel="nofollow">geometric progression</a> whose generating interval is the golden ratio (1.61803....).<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Unique properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Unique properties</h2> <br /> The goldonic series is unique among geometric sequencies because only <em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">φ</span></em> satisfies the equation <em>x</em><span style="vertical-align: super;">n-1</span> <em>+ x</em><span style="vertical-align: super;">n</span> <em>= x</em><span style="vertical-align: super;">n+1</span>.<br /> <br /> From an acoustic standpoint, the goldonic series contains some "harmonic-like" characteristics despite being inharmonic. Because each term is equal the difference between the next highest and next lowest terms, a phenomenon similar to modelocking can occur (in which each oscillator becomes entrained to the difference tone generated by its nearest-neighbors)..</body></html>