Goldonic series: Difference between revisions
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Wikispaces>MasonGreen1 **Imported revision 568375387 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 568386057 - Original comment: ** |
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<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:xenwolf|xenwolf]] and made on <tt>2015-12-01 03:28:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>568386057</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;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 golden ratio (1.61803....). | <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....). | ||
==Unique properties== | ==Unique properties== | ||
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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.</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>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 /> | <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 /> | ||
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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> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Unique properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Unique properties</h2> | ||
Revision as of 03:28, 1 December 2015
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2015-12-01 03:28:17 UTC.
- The original revision id was 568386057.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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 [[https://en.wikipedia.org/wiki/Golden_ratio|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). Also, unlike the harmonic series, the goldonic series can be in theory extended infinitely in //both// directions and contains no fundamental.
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 <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Golden_ratio" rel="nofollow">golden ratio</a> (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).<br /> <br /> 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>