Prime harmonic series: Difference between revisions
Wikispaces>guest **Imported revision 411572484 - Original comment: ** |
Wikispaces>kentpollard **Imported revision 411572958 - Original comment: Reverted to Jun 29, 2011 5:34 am: Reverted to remove spam** |
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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:kentpollard|kentpollard]] and made on <tt>2013-03-03 14:26:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>411572958</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Reverted to Jun 29, 2011 5:34 am: Reverted to remove spam</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> | ||
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giving these step sizes: | giving these step sizes: | ||
|| 34/32 | || 34/32 | ||
(17/16) || 37/34 || 38/37 || 40/38 | (17/16) || 37/34 || 38/37 || 40/38 | ||
(20/19) || 44/40 | (20/19) || 44/40 | ||
(11/10) || 46/44 | (11/10) || 46/44 | ||
(23/22) || 48/46 | (23/22) || 48/46 | ||
(24/23) || 52/48 | (24/23) || 52/48 | ||
(13/12) || 56/52 | (13/12) || 56/52 | ||
(14/13) || 58/56 | (14/13) || 58/56 | ||
(29/28) || 62/58 | (29/28) || 62/58 | ||
(31/29) || 64/62 | (31/29) || 64/62 | ||
(32/31) || | (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 || | || 104.96 || 146.39 || 46.17 || 88.8 || 165 || 76.96 || 73.68 || 138.57 || 128.3 || 60.75 || 115.46 || 54.97 || | ||
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---- | ---- | ||
Any segment of the prime harmonic series can be used "as is" as musical material. | 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: | 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: | ||
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<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%;">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%;"> | <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> | <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 <a class="wiki_link" href="/prime%20numbers">prime numbers</a>, except that it begins with 1, and skips 2 because of <a class="wiki_link" href="/octave%20equivalence">octave equivalence</a> : 1, 3, 5, 7, 11, 13 etc.<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>The Prime Harmonic Series</title></head><body>The <strong>acoustic prime harmonic series</strong> is similar to the set of <a class="wiki_link" href="/prime%20numbers">prime numbers</a>, except that it begins with 1, and skips 2 because of <a class="wiki_link" href="/octave%20equivalence">octave equivalence</a> : 1, 3, 5, 7, 11, 13 etc.<br /> | ||
| Line 240: | Line 240: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>34/32<br /> | <td>34/32 <br /> | ||
(17/16)<br /> | (17/16)<br /> | ||
</td> | </td> | ||
| Line 250: | Line 250: | ||
(20/19)<br /> | (20/19)<br /> | ||
</td> | </td> | ||
<td>44/40<br /> | <td>44/40 <br /> | ||
(11/10)<br /> | (11/10)<br /> | ||
</td> | </td> | ||
<td>46/44<br /> | <td>46/44 <br /> | ||
(23/22)<br /> | (23/22)<br /> | ||
</td> | </td> | ||
<td>48/46<br /> | <td>48/46 <br /> | ||
(24/23)<br /> | (24/23)<br /> | ||
</td> | </td> | ||
<td>52/48<br /> | <td>52/48 <br /> | ||
(13/12)<br /> | (13/12)<br /> | ||
</td> | </td> | ||
<td>56/52<br /> | <td>56/52 <br /> | ||
(14/13)<br /> | (14/13)<br /> | ||
</td> | </td> | ||
<td>58/56<br /> | <td>58/56 <br /> | ||
(29/28)<br /> | (29/28)<br /> | ||
</td> | </td> | ||
<td>62/58<br /> | <td>62/58 <br /> | ||
(31/29)<br /> | (31/29)<br /> | ||
</td> | </td> | ||
<td>64/62<br /> | <td>64/62 <br /> | ||
(32/31)<br /> | (32/31)<br /> | ||
</td> | </td> | ||
| Line 306: | Line 306: | ||
<hr /> | <hr /> | ||
<br /> | <br /> | ||
Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material.<br /> | Any segment of the prime harmonic series can be used &quot;as is&quot; as musical material. <br /> | ||
<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 /> | 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 /> | ||