Easy Scales by Interpolating between Harmonic Series: Difference between revisions

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=Easy Scales by Interpolating 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
|| 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 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**
**(x/12) -** 1/1 5/4 4/3 3/2 5/3
the same as the notes C E F G A. 

The **x/12 and x/9** harmonic series become particularly stressed in the (Maqam) Rast scale of

Original HTML content:

<html><head><title>Easy Scales by Interpolating between Harmonic Series</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Easy Scales by Interpolating between Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:0 -->Easy Scales by Interpolating between Harmonic Series</h1>
 <br />
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.<br />
<br />
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<br />


<table class="wiki_table">
    <tr>
        <td>C<br />
</td>
        <td>D<br />
</td>
        <td>E<br />
</td>
        <td>F<br />
</td>
        <td>G<br />
</td>
        <td>A<br />
</td>
        <td>B<br />
</td>
    </tr>
    <tr>
        <td>1/1<br />
</td>
        <td>9/8 or 10/9<br />
</td>
        <td>5/4<br />
</td>
        <td>4/3<br />
</td>
        <td>3/2<br />
</td>
        <td>5/3 or 27/16<br />
</td>
        <td>15/8 or 17/9<br />
</td>
    </tr>
</table>

This can be derived from the following harmonic series<br />
<br />
<strong>(x/9)</strong> - 1/1, 10/9, 12/9 (4/3), 15/9 (5/3), 17/9<br />
which is the same as the notes C D F A B and contains the <strong>subdominant major chord F A C</strong><br />
<strong>(x/8)</strong> - 1/1,9/8,10/8 (5/4), 12/8 (3/2), 15/8<br />
which is the same as the notes C D E G B and contains the <strong>tonic major chord C E G</strong> along with the <strong>dominant major chord G B D</strong><br />
<strong>(x/12) -</strong> 1/1 5/4 4/3 3/2 5/3<br />
the same as the notes C E F G A. <br />
<br />
The <strong>x/12 and x/9</strong> harmonic series become particularly stressed in the (Maqam) Rast scale of</body></html>

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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:mikesheiman|mikesheiman]] and made on <tt>2016-05-20 13:46:21 UTC</tt>.<br>
+: This revision was by author [[User:mikesheiman|mikesheiman]] and made on <tt>2016-05-20 13:56:50 UTC</tt>.<br>
-: The original revision id was <tt>583687769</tt>.<br>
+: The original revision id was <tt>583688859</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 17: / Line 17: @@
 **(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>
+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**
+**(x/12) -** 1/1 5/4 4/3 3/2 5/3
+the same as the notes C E F G A.
+The **x/12 and x/9** harmonic series become particularly stressed in the (Maqam) Rast scale of</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;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;
@@ Line 66: / Line 70: @@
 &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;
+&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>
+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;br /&gt;
+&lt;strong&gt;(x/12) -&lt;/strong&gt; 1/1 5/4 4/3 3/2 5/3&lt;br /&gt;
+the same as the notes C E F G A. &lt;br /&gt;
+&lt;br /&gt;
+The &lt;strong&gt;x/12 and x/9&lt;/strong&gt; harmonic series become particularly stressed in the (Maqam) Rast scale of&lt;/body&gt;&lt;/html&gt;</pre></div>

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