Prime harmonic series: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:danterosati|danterosati]] and made on <tt>2010-11-06 00:07:05 UTC</tt>.<br>

: This revision was by author [[User:danterosati|danterosati]] and made on <tt>2010-11-06 12:07:31 UTC</tt>.<br>

: The original revision id was <tt>~~176990617~~</tt>.<br>

: The original revision id was <tt>177041277</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>

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|| 104.96 || 146.39 || 46.17 || 88.8 || 165 || 76.96 || 73.68 || 138.57 || 128.3 || 60.75 || 115.46 || 54.97 ||</pre></div>

|| 104.96 || 146.39 || 46.17 || 88.8 || 165 || 76.96 || 73.68 || 138.57 || 128.3 || 60.75 || 115.46 || 54.97 ||

----

Any segment of the prime harmonic series can be used "as is" as musical material.

The step sizes of the series itself exhibit an interesting variety, including the phenomena of [[http://en.wikipedia.org/wiki/Twin_prime|twin primes]] which provide for small steps which contrast with the wider steps elsewhere in the series:

[[image:20101106025758.jpg]]

One example of using the prime harmonic series as a "found object" is Dante Rosati's "prime guitar".

Dante writes:

"The Prime Guitar is designed to play prime partials 17-199. The lowest string is tuned to the 17th partial of a series, and the successive strings are then tuned to partials 23, 37, 47, 67, and 89 to preserve the basic tonal spread of a standard set of guitar strings. Since every single note is a unique prime limit pitch, it was not practical to color code the frets in the same way as the previous guitars. On the other hand, it is very difficult to orient one's self on a neck with such irregular fret spacing without any color coding, so I settled on a simple alternating three color scheme that allows for easy visual spotting of where the frets are located.

<span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [[http://users.rcn.com/dante.interport//justguitar.html|(original page source)]]</span>

<span style="font-size: 90%;">[[http://www.youtube.com/watch?v=tP9iafbjlOw|"Tarkovsky's Mirror" for prime guitar by Dante Rosati]]</span></pre></div>

<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>The Prime Harmonic Series</title></head><body>The <strong>acoustic prime harmonic series</strong> is similar to the set of prime numbers, except that it begins with 1, and skips 2 because of octave equivalence : 1,3,5,7,11,13…etc.<br />

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</table>

</body></html></pre></div>

<br />

<hr />

<br />

Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material. <br />

<br />

The step sizes of the series itself exhibit an interesting variety, including the phenomena of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Twin_prime" rel="nofollow">twin primes</a> which provide for small steps which contrast with the wider steps elsewhere in the series:<br />

<br />

<img src="/file/view/20101106025758.jpg/177040355/20101106025758.jpg" alt="20101106025758.jpg" title="20101106025758.jpg" /><br />

<br />

One example of using the prime harmonic series as a &quot;found object&quot; is Dante Rosati's &quot;prime guitar&quot;.<br />

<br />

Dante writes:<br />

<br />

&quot;The Prime Guitar is designed to play prime partials 17-199. The lowest string is tuned to the 17th partial of a series, and the successive strings are then tuned to partials 23, 37, 47, 67, and 89 to preserve the basic tonal spread of a standard set of guitar strings. Since every single note is a unique prime limit pitch, it was not practical to color code the frets in the same way as the previous guitars. On the other hand, it is very difficult to orient one's self on a neck with such irregular fret spacing without any color coding, so I settled on a simple alternating three color scheme that allows for easy visual spotting of where the frets are located.<br />

<span style="font-size: 90%;">Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly.&quot; <a class="wiki_link_ext" href="http://users.rcn.com/dante.interport//justguitar.html" rel="nofollow">(original page source)</a></span><br />

<br />

<span style="font-size: 90%;"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=tP9iafbjlOw" rel="nofollow">&quot;Tarkovsky's Mirror&quot; for prime guitar by Dante Rosati</a></span></body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:danterosati|danterosati]] and made on <tt>2010-11-06 00:07:05 UTC</tt>.<br>
+: This revision was by author [[User:danterosati|danterosati]] and made on <tt>2010-11-06 12:07:31 UTC</tt>.<br>
-: The original revision id was <tt>176990617</tt>.<br>
+: The original revision id was <tt>177041277</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>
@@ Line 63: / Line 63: @@
 (31/29) || 64/62
 (32/31) ||
-|| 104.96 || 146.39 || 46.17 || 88.8 || 165 || 76.96 || 73.68 || 138.57 || 128.3 || 60.75 || 115.46 || 54.97 ||</pre></div>
+|| 104.96 || 146.39 || 46.17 || 88.8 || 165 || 76.96 || 73.68 || 138.57 || 128.3 || 60.75 || 115.46 || 54.97 ||
+----
+Any segment of the prime harmonic series can be used "as is" as musical material.
+The step sizes of the series itself exhibit an interesting variety, including the phenomena of [[http://en.wikipedia.org/wiki/Twin_prime|twin primes]] which provide for small steps which contrast with the wider steps elsewhere in the series:
+[[image:20101106025758.jpg]]
+One example of using the prime harmonic series as a "found object" is Dante Rosati's "prime guitar".
+Dante writes:
+"The Prime Guitar is designed to play prime partials 17-199. The lowest string is tuned to the 17th partial of a series, and the successive strings are then tuned to partials 23, 37, 47, 67, and 89 to preserve the basic tonal spread of a standard set of guitar strings. Since every single note is a unique prime limit pitch, it was not practical to color code the frets in the same way as the previous guitars. On the other hand, it is very difficult to orient one's self on a neck with such irregular fret spacing without any color coding, so I settled on a simple alternating three color scheme that allows for easy visual spotting of where the frets are located.
+&lt;span style="font-size: 90%;"&gt;Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly." [[http://users.rcn.com/dante.interport//justguitar.html|(original page source)]]&lt;/span&gt;
+&lt;span style="font-size: 90%;"&gt;[[http://www.youtube.com/watch?v=tP9iafbjlOw|"Tarkovsky's Mirror" for prime guitar by Dante Rosati]]&lt;/span&gt;</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;The Prime Harmonic Series&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;acoustic prime harmonic series&lt;/strong&gt; is similar to the set of prime numbers, except that it begins with 1, and skips 2 because of octave equivalence : 1,3,5,7,11,13…etc.&lt;br /&gt;
@@ Line 283: / Line 300: @@
 &lt;/table&gt;
-&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;br /&gt;
+&lt;hr /&gt;
+&lt;br /&gt;
+Any segment of the prime harmonic series can be used &amp;quot;as is&amp;quot; as musical material. &lt;br /&gt;
+&lt;br /&gt;
+The step sizes of the series itself exhibit an interesting variety, including the phenomena of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Twin_prime" rel="nofollow"&gt;twin primes&lt;/a&gt; which provide for small steps which contrast with the wider steps elsewhere in the series:&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:170:&amp;lt;img src=&amp;quot;/file/view/20101106025758.jpg/177040355/20101106025758.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/20101106025758.jpg/177040355/20101106025758.jpg" alt="20101106025758.jpg" title="20101106025758.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:170 --&gt;&lt;br /&gt;
+&lt;br /&gt;
+One example of using the prime harmonic series as a &amp;quot;found object&amp;quot; is Dante Rosati's &amp;quot;prime guitar&amp;quot;.&lt;br /&gt;
+&lt;br /&gt;
+Dante writes:&lt;br /&gt;
+&lt;br /&gt;
+&amp;quot;The Prime Guitar is designed to play prime partials 17-199. The lowest string is tuned to the 17th partial of a series, and the successive strings are then tuned to partials 23, 37, 47, 67, and 89 to preserve the basic tonal spread of a standard set of guitar strings. Since every single note is a unique prime limit pitch, it was not practical to color code the frets in the same way as the previous guitars. On the other hand, it is very difficult to orient one's self on a neck with such irregular fret spacing without any color coding, so I settled on a simple alternating three color scheme that allows for easy visual spotting of where the frets are located.&lt;br /&gt;
+&lt;span style="font-size: 90%;"&gt;Because the lowest partial is 17, there are no familiar lower prime limit intervals like octaves (2/1), fifths (3/2), thirds (5/4), etc. Nevertheless, some intervals between higher primes approximate the lower prime limit intervals (e.g. 61/31 is very close to an octave), without of course reproducing them exactly.&amp;quot; &lt;a class="wiki_link_ext" href="http://users.rcn.com/dante.interport//justguitar.html" rel="nofollow"&gt;(original page source)&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;span style="font-size: 90%;"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=tP9iafbjlOw" rel="nofollow"&gt;&amp;quot;Tarkovsky's Mirror&amp;quot; for prime guitar by Dante Rosati&lt;/a&gt;&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>