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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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 [https://en.wikipedia.org/wiki/Golden_ratio golden ratio] (1.61803....). |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2015-12-01 03:28:17 UTC</tt>.<br>
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| : The original revision id was <tt>568386057</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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">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 [[https://en.wikipedia.org/wiki/Golden_ratio|golden ratio]] (1.61803....).
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| ==Unique properties== | | ==Unique properties== |
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| 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>. | | 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>. |
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| 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). | | 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). |
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| Also, unlike the harmonic series, the goldonic series can be in theory extended infinitely in //both// directions and contains no fundamental.</pre></div> | | Also, unlike the harmonic series, the goldonic series can be in theory extended infinitely in ''both'' directions and contains no fundamental. |
| <h4>Original HTML content:</h4>
| | [[Category:golden]] |
| <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>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 <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Golden_ratio" rel="nofollow">golden ratio</a> (1.61803....).<br />
| | [[Category:golden_ratio]] |
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Unique properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Unique properties</h2>
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| 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 />
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| From an acoustic standpoint, the goldonic series contains some &quot;harmonic-like&quot; 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).<br />
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| Also, unlike the harmonic series, the goldonic series can be in theory extended infinitely in <em>both</em> directions and contains no fundamental.</body></html></pre></div>
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