Harmonic series: Difference between revisions

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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:~~hstraub~~|~~hstraub~~]] and made on <tt>2009-10-~~15 03~~:32~~:25~~ UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-10-17 12:20:32 UTC</tt>.<br>

: The original revision id was <tt>~~95321062~~</tt>.<br>

: The original revision id was <tt>95820656</tt>.<br>

: The revision comment was: <tt>~~Link to overtone music network fixed~~</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>

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=Music based on the overtone series=

The overtone series can be mathematically generated by frequency ratios 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1... ad infinitum.

The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.

Steps between adjacent members of either series are called "superparticular," & they appear in the form a/(a-1), eg. 4/3, 28/27, 33/32...

In just intonation theory, the overtone series is often treated as the foundation of consonance.

One might compose with the overtone series by, for instance:

* Tuning to the first several overtones over one fundamental.

* Tuning to an octave-repeating slice of the overtone series for use as a scale (for instance overtones 8 though 16 or 12 through 24).

* Tuning to the overtones of the overtones.

* Tuning to the overtones of the overtones & the undertones of the undertones. (This can produce complex scales such as [[Harry Partch]]'s 43-tone Monophonic; this kind of thing is more often called "[[just intonation]]" than "overtone music".)

== ==

==External links==

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<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>OverToneSeries</title></head><body><h1 id="toc0"><a name="Music based on the overtone series"></a>Music based on the overtone series</h1>

<h2 id="toc1"> </h2>

<br />

The overtone series can be mathematically generated by frequency ratios 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1... ad infinitum.<br />

The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.<br />

Steps between adjacent members of either series are called &quot;superparticular,&quot; &amp; they appear in the form a/(a-1), eg. 4/3, 28/27, 33/32...<br />

<br />

In just intonation theory, the overtone series is often treated as the foundation of consonance.<br />

<br />

One might compose with the overtone series by, for instance:<br />

<ul><li>Tuning to the first several overtones over one fundamental.</li><li>Tuning to an octave-repeating slice of the overtone series for use as a scale (for instance overtones 8 though 16 or 12 through 24).</li><li>Tuning to the overtones of the overtones.</li><li>Tuning to the overtones of the overtones &amp; the undertones of the undertones. (This can produce complex scales such as <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>'s 43-tone Monophonic; this kind of thing is more often called &quot;<a class="wiki_link" href="/just%20intonation">just intonation</a>&quot; than &quot;overtone music&quot;.)</li></ul><br />

<h2 id="toc1"> </h2>

<h2 id="toc2"><a name="Music based on the overtone series-External links"></a>External links</h2>

<br />

@@ Line 1: / Line 1: @@
 <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:hstraub|hstraub]] and made on <tt>2009-10-15 03:32:25 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-10-17 12:20:32 UTC</tt>.<br>
-: The original revision id was <tt>95321062</tt>.<br>
+: The original revision id was <tt>95820656</tt>.<br>
-: The revision comment was: <tt>Link to overtone music network fixed</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=Music based on the overtone series=
+The overtone series can be mathematically generated by frequency ratios 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1... ad infinitum.
+The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.
+Steps between adjacent members of either series are called "superparticular," &amp; they appear in the form a/(a-1), eg. 4/3, 28/27, 33/32...
+In just intonation theory, the overtone series is often treated as the foundation of consonance.
+One might compose with the overtone series by, for instance:
+* Tuning to the first several overtones over one fundamental.
+* Tuning to an octave-repeating slice of the overtone series for use as a scale (for instance overtones 8 though 16 or 12 through 24).
+* Tuning to the overtones of the overtones.
+* Tuning to the overtones of the overtones &amp; the undertones of the undertones. (This can produce complex scales such as [[Harry Partch]]'s 43-tone Monophonic; this kind of thing is more often called "[[just intonation]]" than "overtone music".)
 == ==
 ==External links==
@@ Line 31: / Line 44: @@
 <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;OverToneSeries&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="Music based on the overtone series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music based on the overtone series&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h2&gt;
+  &lt;br /&gt;
+The overtone series can be mathematically generated by frequency ratios 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1... ad infinitum.&lt;br /&gt;
+The undertone series is its inversion: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum.&lt;br /&gt;
+Steps between adjacent members of either series are called &amp;quot;superparticular,&amp;quot; &amp;amp; they appear in the form a/(a-1), eg. 4/3, 28/27, 33/32...&lt;br /&gt;
+&lt;br /&gt;
+In just intonation theory, the overtone series is often treated as the foundation of consonance.&lt;br /&gt;
+&lt;br /&gt;
+One might compose with the overtone series by, for instance:&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Tuning to the first several overtones over one fundamental.&lt;/li&gt;&lt;li&gt;Tuning to an octave-repeating slice of the overtone series for use as a scale (for instance overtones 8 though 16 or 12 through 24).&lt;/li&gt;&lt;li&gt;Tuning to the overtones of the overtones.&lt;/li&gt;&lt;li&gt;Tuning to the overtones of the overtones &amp;amp; the undertones of the undertones. (This can produce complex scales such as &lt;a class="wiki_link" href="/Harry%20Partch"&gt;Harry Partch&lt;/a&gt;'s 43-tone Monophonic; this kind of thing is more often called &amp;quot;&lt;a class="wiki_link" href="/just%20intonation"&gt;just intonation&lt;/a&gt;&amp;quot; than &amp;quot;overtone music&amp;quot;.)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h2&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Music based on the overtone series-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;External links&lt;/h2&gt;
   &lt;br /&gt;