Prime harmonic series: Difference between revisions
Wikispaces>danterosati **Imported revision 176981401 - Original comment: ** |
Wikispaces>danterosati **Imported revision 176983675 - 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:danterosati|danterosati]] and made on <tt>2010-11-05 22: | : This revision was by author [[User:danterosati|danterosati]] and made on <tt>2010-11-05 22:47:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>176983675</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> | ||
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|| 12 (1,3,5,7,11,13,17,19,23,29,31,37) || 1/1, 17/16, 37/32, 19/16, 5/4, 11/8, 23/16, 3/2, 13/8, 7/4, 29/16, 31/16 (dodecatonic) || | || 12 (1,3,5,7,11,13,17,19,23,29,31,37) || 1/1, 17/16, 37/32, 19/16, 5/4, 11/8, 23/16, 3/2, 13/8, 7/4, 29/16, 31/16 (dodecatonic) || | ||
Of course, as in scales derived from the full series, there is nothing that says one must start at the beginning of the series or include consecutive members only. The possibilities are endless.</pre></div> | Of course, as in scales derived from the full series, there is nothing that says one must start at the beginning of the series or include consecutive members only. The possibilities are endless. | ||
<span style="color: #aaaaaa;"> | |||
</span> | |||
---- | |||
Let’s look more closely at the prime dodecatonic scale. It can also be notated thusly: | |||
32:34:37:38:40:44:46:48:52:56:58:62:(64) | |||
This way, it is easy to compute the step sizes: | |||
|| 34/32 | |||
(17/16) || 37/34 || 38/37 || 40/38 | |||
(20/19) || 44/40 | |||
(11/10) || 46/44 | |||
(23/22) || 48/46 | |||
(24/23) || 52/48 | |||
(13/12) || 56/52 | |||
(14/13) || 58/56 | |||
(29/28) || 62/58 | |||
(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> | |||
<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 prime numbers, except that it begins with 1, and skips 2 because of octave equivalence : 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 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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<br /> | <br /> | ||
Of course, as in scales derived from the full series, there is nothing that says one must start at the beginning of the series or include consecutive members only. The possibilities are endless.</body></html></pre></div> | Of course, as in scales derived from the full series, there is nothing that says one must start at the beginning of the series or include consecutive members only. The possibilities are endless.<br /> | ||
<span style="color: #aaaaaa;"><br /> | |||
</span><br /> | |||
<hr /> | |||
<br /> | |||
<br /> | |||
Let’s look more closely at the prime dodecatonic scale. It can also be notated thusly:<br /> | |||
<br /> | |||
32:34:37:38:40:44:46:48:52:56:58:62:(64)<br /> | |||
<br /> | |||
This way, it is easy to compute the step sizes:<br /> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>34/32 <br /> | |||
(17/16)<br /> | |||
</td> | |||
<td>37/34<br /> | |||
</td> | |||
<td>38/37<br /> | |||
</td> | |||
<td>40/38<br /> | |||
(20/19)<br /> | |||
</td> | |||
<td>44/40 <br /> | |||
(11/10)<br /> | |||
</td> | |||
<td>46/44 <br /> | |||
(23/22)<br /> | |||
</td> | |||
<td>48/46 <br /> | |||
(24/23)<br /> | |||
</td> | |||
<td>52/48 <br /> | |||
(13/12)<br /> | |||
</td> | |||
<td>56/52 <br /> | |||
(14/13)<br /> | |||
</td> | |||
<td>58/56 <br /> | |||
(29/28)<br /> | |||
</td> | |||
<td>62/58 <br /> | |||
(31/29)<br /> | |||
</td> | |||
<td>64/62 <br /> | |||
(32/31)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>104.96<br /> | |||
</td> | |||
<td>146.39<br /> | |||
</td> | |||
<td>46.17<br /> | |||
</td> | |||
<td>88.8<br /> | |||
</td> | |||
<td>165<br /> | |||
</td> | |||
<td>76.96<br /> | |||
</td> | |||
<td>73.68<br /> | |||
</td> | |||
<td>138.57<br /> | |||
</td> | |||
<td>128.3<br /> | |||
</td> | |||
<td>60.75<br /> | |||
</td> | |||
<td>115.46<br /> | |||
</td> | |||
<td>54.97<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||