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Easy Scales by Interpolating between Harmonic Series: Difference between revisions

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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>
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: This revision was by author [[User:mikesheiman|mikesheiman]] and made on <tt>2016-05-20 13:34:45 UTC</tt>.<br>
: This revision was by author [[User:mikesheiman|mikesheiman]] and made on <tt>2016-05-20 13:46:21 UTC</tt>.<br>
: The original revision id was <tt>583686711</tt>.<br>
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A very easy way to construct a scale that's instantly recognizable, even without repeated listening/priming in the absence of listening the music in 12EDO, is to interpolate between harmonic series.
A very easy way to construct a scale that's instantly recognizable, even without repeated listening/priming in the absence of listening the music in 12EDO, is to interpolate between harmonic series.


Some of the most prominent scales in existence can be very quickly derived from harmonic series. Take, for example, the diatonic major scale in 12EDO, where notes are approximately equal to  
Some of the most prominent scales in existence can be very quickly derived from harmonic series. Take, for example, the diatonic major scale in 12EDO, where notes are approximately equal to
|| C || D || E || F || G || A || B ||
|| C || D || E || F || G || A || B ||
|| 1/1 || 9/8 or 10/9 || 5/4 || 4/3 || 3/2 || 5/3 or 27/16 || 15/8 ||</pre></div>
|| 1/1 || 9/8 or 10/9 || 5/4 || 4/3 || 3/2 || 5/3 or 27/16 || 15/8 or 17/9 ||
This can be derived from the following harmonic series
 
**(x/9)** - 1/1, 10/9, 12/9 (4/3), 15/9 (5/3), 17/9
which is the same as the notes C D F A B and contains the **subdominant major chord F A C**
**(x/8)** - 1/1,9/8,10/8 (5/4), 12/8 (3/2), 15/8
which is the same as the notes C D E G B and contains the **tonic major chord C E G** along with the **dominant major chord G B D**</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Easy Scales by Interpolating between Harmonic Series&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Easy Scales by Interpolating between Harmonic Series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Easy Scales by Interpolating between Harmonic Series&lt;/h1&gt;
<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;Easy Scales by Interpolating between Harmonic Series&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Easy Scales by Interpolating between Harmonic Series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Easy Scales by Interpolating between Harmonic Series&lt;/h1&gt;
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A very easy way to construct a scale that's instantly recognizable, even without repeated listening/priming in the absence of listening the music in 12EDO, is to interpolate between harmonic series.&lt;br /&gt;
A very easy way to construct a scale that's instantly recognizable, even without repeated listening/priming in the absence of listening the music in 12EDO, is to interpolate between harmonic series.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Some of the most prominent scales in existence can be very quickly derived from harmonic series. Take, for example, the diatonic major scale in 12EDO, where notes are approximately equal to &lt;br /&gt;
Some of the most prominent scales in existence can be very quickly derived from harmonic series. Take, for example, the diatonic major scale in 12EDO, where notes are approximately equal to&lt;br /&gt;




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         &lt;td&gt;5/3 or 27/16&lt;br /&gt;
         &lt;td&gt;5/3 or 27/16&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15/8&lt;br /&gt;
         &lt;td&gt;15/8 or 17/9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
&lt;/table&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
This can be derived from the following harmonic series&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;(x/9)&lt;/strong&gt; - 1/1, 10/9, 12/9 (4/3), 15/9 (5/3), 17/9&lt;br /&gt;
which is the same as the notes C D F A B and contains the &lt;strong&gt;subdominant major chord F A C&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;(x/8)&lt;/strong&gt; - 1/1,9/8,10/8 (5/4), 12/8 (3/2), 15/8 &lt;br /&gt;
which is the same as the notes C D E G B and contains the &lt;strong&gt;tonic major chord C E G&lt;/strong&gt; along with the &lt;strong&gt;dominant major chord G B D&lt;/strong&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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