Overtone scale: 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-17 10:57:01 UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-17 11:16:04 UTC</tt>.<br>

: The original revision id was <tt>~~265532000~~</tt>.<br>

: The original revision id was <tt>265540364</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">This page was originally developed by [[Andrew Heathwaite]], but others are welcome to add to it. For another take on the subject, see **[[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]**.

<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">This page was originally developed by [[Andrew Heathwaite]], but others are welcome to add to it. For another take on the subject, see **[[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]**. This article focuses on a systematic approach to building modes of the harmonic series and taking subsets of it, with attention paid to the different kinds of relationships available depending on the starting pitch, or tonic notes. It is not concerned with "purity", "consonance", "naturalness" or avoidance of "dissonance." Here, what might be called dissonant is intead called complex, and the reader is encouraged to explore the sounds of harmonic ratios ranging from the simplest to the most complex. This does not mean that the more complex intervals can be treated exactly the same way as the simpler ones, but that different levels of complexity can be valuable to explore in a tuning system. The usefulness of all this is left to each composer to determine through experimentation.

== ==

==Introduction - Modes of the Harmonic Series==

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* Borrow overtones & undertones from the overtones & 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 "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.</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"><html><head><title>overtone scales</title></head><body>This page was originally developed by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, but others are welcome to add to it. For another take on the subject, see <strong><a class="wiki_link" href="/Mike%20Sheiman%27s%20Very%20Easy%20Scale%20Building%20From%20The%20Harmonic%20Series%20Page">Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page</a></strong>.<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>overtone scales</title></head><body>This page was originally developed by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, but others are welcome to add to it. For another take on the subject, see <strong><a class="wiki_link" href="/Mike%20Sheiman%27s%20Very%20Easy%20Scale%20Building%20From%20The%20Harmonic%20Series%20Page">Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page</a></strong>. This article focuses on a systematic approach to building modes of the harmonic series and taking subsets of it, with attention paid to the different kinds of relationships available depending on the starting pitch, or tonic notes. It is not concerned with &quot;purity&quot;, &quot;consonance&quot;, &quot;naturalness&quot; or avoidance of &quot;dissonance.&quot; Here, what might be called dissonant is intead called complex, and the reader is encouraged to explore the sounds of harmonic ratios ranging from the simplest to the most complex. This does not mean that the more complex intervals can be treated exactly the same way as the simpler ones, but that different levels of complexity can be valuable to explore in a tuning system. The usefulness of all this is left to each composer to determine through experimentation.<br />

<h2 id="toc0"> </h2>

<h2 id="toc1"><a name="x-Introduction - Modes of the Harmonic Series"></a>Introduction - Modes of the Harmonic Series</h2>

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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-17 10:57:01 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-17 11:16:04 UTC</tt>.<br>
-: The original revision id was <tt>265532000</tt>.<br>
+: The original revision id was <tt>265540364</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">This page was originally developed by [[Andrew Heathwaite]], but others are welcome to add to it. For another take on the subject, see **[[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]**.
+<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">This page was originally developed by [[Andrew Heathwaite]], but others are welcome to add to it. For another take on the subject, see **[[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]**. This article focuses on a systematic approach to building modes of the harmonic series and taking subsets of it, with attention paid to the different kinds of relationships available depending on the starting pitch, or tonic notes. It is not concerned with "purity", "consonance", "naturalness" or avoidance of "dissonance." Here, what might be called dissonant is intead called complex, and the reader is encouraged to explore the sounds of harmonic ratios ranging from the simplest to the most complex. This does not mean that the more complex intervals can be treated exactly the same way as the simpler ones, but that different levels of complexity can be valuable to explore in a tuning system. The usefulness of all this is left to each composer to determine through experimentation.
 == ==
 ==Introduction - Modes of the Harmonic Series==
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 * 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 "Monophonic Fabric," which consists of 43 unequal tones per octave, is one famous example.</pre></div>
 <h4>Original HTML content:</h4>
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+<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;overtone scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This page was originally developed by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;, but others are welcome to add to it. For another take on the subject, see &lt;strong&gt;&lt;a class="wiki_link" href="/Mike%20Sheiman%27s%20Very%20Easy%20Scale%20Building%20From%20The%20Harmonic%20Series%20Page"&gt;Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page&lt;/a&gt;&lt;/strong&gt;. This article focuses on a systematic approach to building modes of the harmonic series and taking subsets of it, with attention paid to the different kinds of relationships available depending on the starting pitch, or tonic notes. It is not concerned with &amp;quot;purity&amp;quot;, &amp;quot;consonance&amp;quot;, &amp;quot;naturalness&amp;quot; or avoidance of &amp;quot;dissonance.&amp;quot; Here, what might be called dissonant is intead called complex, and the reader is encouraged to explore the sounds of harmonic ratios ranging from the simplest to the most complex. This does not mean that the more complex intervals can be treated exactly the same way as the simpler ones, but that different levels of complexity can be valuable to explore in a tuning system. The usefulness of all this is left to each composer to determine through experimentation.&lt;br /&gt;
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