Overtone scale: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 265540364 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 570440875 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2015-12-17 21:09:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>570440875</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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Mode 26 -- 26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:50:51:52 -- 39/26 is a 3/2 perfect fifth. Root-3rd-P5 chords include the tridecimal inframinor 26:30:39; a 31-limit minor triad at 26:31:39 (oddly normal-sounding on its own); a tridecimal neutral triad at 26:32:39; and a wide tridecimal major at 26:33:39. As odd harmonics go up to 51, a great variety is possible here. | Mode 26 -- 26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:50:51:52 -- 39/26 is a 3/2 perfect fifth. Root-3rd-P5 chords include the tridecimal inframinor 26:30:39; a 31-limit minor triad at 26:31:39 (oddly normal-sounding on its own); a tridecimal neutral triad at 26:32:39; and a wide tridecimal major at 26:33:39. As odd harmonics go up to 51, a great variety is possible here. | ||
== == | |||
===**Over-15 Scales**=== | |||
Mode 15 -- 15:16:17:18:19:20:21:22:23:24:25:26:27:28:29:30 | |||
Mode 30 -- 30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:50:51:52:53:54:55:56:57:58:59:60 | |||
Mode 30 in particular is interesting because 30 is the product of the first three primes, so it's a fairly good choice if we want a tonic that isn't a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60. | |||
==A Solfege System== | ==A Solfege System== | ||
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<br /> | <br /> | ||
Mode 26 -- 26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:50:51:52 -- 39/26 is a 3/2 perfect fifth. Root-3rd-P5 chords include the tridecimal inframinor 26:30:39; a 31-limit minor triad at 26:31:39 (oddly normal-sounding on its own); a tridecimal neutral triad at 26:32:39; and a wide tridecimal major at 26:33:39. As odd harmonics go up to 51, a great variety is possible here.<br /> | Mode 26 -- 26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:50:51:52 -- 39/26 is a 3/2 perfect fifth. Root-3rd-P5 chords include the tridecimal inframinor 26:30:39; a 31-limit minor triad at 26:31:39 (oddly normal-sounding on its own); a tridecimal neutral triad at 26:32:39; and a wide tridecimal major at 26:33:39. As odd harmonics go up to 51, a great variety is possible here.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><!-- ws:end:WikiTextHeadingRule:20 --> </h2> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="x-Over-n Scales-Over-15 Scales"></a><!-- ws:end:WikiTextHeadingRule:22 --><strong>Over-15 Scales</strong></h3> | |||
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Mode 15 -- 15:16:17:18:19:20:21:22:23:24:25:26:27:28:29:30<br /> | |||
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Mode 30 -- 30:31:32:33:34:35:36:37:38:39:40:41:42:43:44:45:46:47:48:49:50:51:52:53:54:55:56:57:58:59:60<br /> | |||
<br /> | |||
Mode 30 in particular is interesting because 30 is the product of the first three primes, so it's a fairly good choice if we want a tonic that isn't a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="x-A Solfege System"></a><!-- ws:end:WikiTextHeadingRule:24 -->A Solfege System</h2> | ||
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<a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> proposes a solfege system for overtones 16-32 (Mode 16):<br /> | <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> proposes a solfege system for overtones 16-32 (Mode 16):<br /> | ||
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Thus, the pentatonic scale in the example at the top (Mode 5) could be sung: <strong>mi sol ta do re mi</strong><br /> | Thus, the pentatonic scale in the example at the top (Mode 5) could be sung: <strong>mi sol ta do re mi</strong><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="x-Twelve Scales"></a><!-- ws:end:WikiTextHeadingRule:26 -->Twelve Scales</h2> | ||
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For those interested in learning to sing and hear just intervals, here are twelve of the simplest otonal scales to try. I leave it up to the curious learner to decide the value, beauty, or usefulness of these particular scales for their compositional purposes.<br /> | For those interested in learning to sing and hear just intervals, here are twelve of the simplest otonal scales to try. I leave it up to the curious learner to decide the value, beauty, or usefulness of these particular scales for their compositional purposes.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Next Steps"></a><!-- ws:end:WikiTextHeadingRule:28 -->Next Steps</h2> | ||
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Here are some next steps:<br /> | Here are some next steps:<br /> | ||
<ul><li>Go beyond the 24th overtone (eg. overtones 16-32 or higher).</li><li>Experiment with using different pitches as the &quot;tonic&quot; of the scale (eg. <strong>sol lu ta do re mi fu sol</strong>, which could be taken as the 7-note scale starting on <strong>sol</strong>).</li><li>Take subsets of larger scales, which are not strict adjacent overtone scales (eg. <strong>do re fe sol ta do</strong>).</li><li>Learn the inversions of these scales, which would be <strong>undertone</strong> scales. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)</li><li>Borrow overtones &amp; undertones from the overtones &amp; undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. Harry Partch's &quot;Monophonic Fabric,&quot; which consists of 43 unequal tones per octave, is one famous example.</li></ul></body></html></pre></div> | <ul><li>Go beyond the 24th overtone (eg. overtones 16-32 or higher).</li><li>Experiment with using different pitches as the &quot;tonic&quot; of the scale (eg. <strong>sol lu ta do re mi fu sol</strong>, which could be taken as the 7-note scale starting on <strong>sol</strong>).</li><li>Take subsets of larger scales, which are not strict adjacent overtone scales (eg. <strong>do re fe sol ta do</strong>).</li><li>Learn the inversions of these scales, which would be <strong>undertone</strong> scales. (Undertone scales would have smaller steps at the bottom of the scale, which would get larger as one ascends.)</li><li>Borrow overtones &amp; undertones from the overtones &amp; undertones of the fundamental -- this process can produce rich fields of interlocking harmonic series, and is often the sort of thing that composers do when they're composing in just intonation. Harry Partch's &quot;Monophonic Fabric,&quot; which consists of 43 unequal tones per octave, is one famous example.</li></ul></body></html></pre></div> | ||