Muddle: 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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2012-01-20 00:52:37 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-01-20 15:36:26 UTC</tt>.<br>

: The original revision id was <tt>~~293773328~~</tt>.<br>

: The original revision id was <tt>293983704</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">//Muddling// refers to a process of mapping one [[periodic scale]] onto another one; the scale thus produced is a //muddle//. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a **parent scale** and a **target ~~scale~~**, or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or //shape// of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[EDO]].

<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">//Muddling// refers to a process of mapping one [[periodic scale]] onto another one; the scale thus produced is a //muddle//. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a **parent scale** and a **target shape**, or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or //shape// of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[EDO]].

The simplest sort of muddle is a MOS Muddle, which is a sort of second-order [[MOSScales|MOS Scale]] and is useful for generating usable subsets of larger MOS scales and for navigating [[Regular Temperaments]]. This article will mostly deal with MOS muddles, but it should be remembered that this process can be generalized to other structures.

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<span class="commentBody">As one example of a muddle with a non-MOS parent</span><span class="text_exposed_show">, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span></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>Muddle</title></head><body><em>Muddling</em> refers to a process of mapping one <a class="wiki_link" href="/periodic%20scale">periodic scale</a> onto another one; the scale thus produced is a <em>muddle</em>. By periodic scale is meant a scale that repeats &quot;at the something&quot; (octave, tritave, something else). There are two necessary components: a <strong>parent scale</strong> and a <strong>target ~~scale~~</strong>, or simply &quot;parent&quot; and &quot;target&quot;. The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or <em>shape</em> of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an <a class="wiki_link" href="/EDO">EDO</a>.<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>Muddle</title></head><body><em>Muddling</em> refers to a process of mapping one <a class="wiki_link" href="/periodic%20scale">periodic scale</a> onto another one; the scale thus produced is a <em>muddle</em>. By periodic scale is meant a scale that repeats &quot;at the something&quot; (octave, tritave, something else). There are two necessary components: a <strong>parent scale</strong> and a <strong>target shape</strong>, or simply &quot;parent&quot; and &quot;target&quot;. The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or <em>shape</em> of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an <a class="wiki_link" href="/EDO">EDO</a>.<br />

<br />

The simplest sort of muddle is a MOS Muddle, which is a sort of second-order <a class="wiki_link" href="/MOSScales">MOS Scale</a> and is useful for generating usable subsets of larger MOS scales and for navigating <a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a>. This article will mostly deal with MOS muddles, but it should be remembered that this process can be generalized to other structures.<br />

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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:genewardsmith|genewardsmith]] and made on <tt>2012-01-20 00:52:37 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-01-20 15:36:26 UTC</tt>.<br>
-: The original revision id was <tt>293773328</tt>.<br>
+: The original revision id was <tt>293983704</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">//Muddling// refers to a process of mapping one [[periodic scale]] onto another one; the scale thus produced is a //muddle//. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a **parent scale** and a **target scale**, or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or //shape// of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[EDO]].
+<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">//Muddling// refers to a process of mapping one [[periodic scale]] onto another one; the scale thus produced is a //muddle//. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a **parent scale** and a **target shape**, or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or //shape// of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[EDO]].
 The simplest sort of muddle is a MOS Muddle, which is a sort of second-order [[MOSScales|MOS Scale]] and is useful for generating usable subsets of larger MOS scales and for navigating [[Regular Temperaments]]. This article will mostly deal with MOS muddles, but it should be remembered that this process can be generalized to other structures.
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 &lt;span class="commentBody"&gt;As one example of a muddle with a non-MOS parent&lt;/span&gt;&lt;span class="text_exposed_show"&gt;, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.&lt;/span&gt;</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;Muddle&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Muddling&lt;/em&gt; refers to a process of mapping one &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt; onto another one; the scale thus produced is a &lt;em&gt;muddle&lt;/em&gt;. By periodic scale is meant a scale that repeats &amp;quot;at the something&amp;quot; (octave, tritave, something else). There are two necessary components: a &lt;strong&gt;parent scale&lt;/strong&gt; and a &lt;strong&gt;target scale&lt;/strong&gt;, or simply &amp;quot;parent&amp;quot; and &amp;quot;target&amp;quot;. The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or &lt;em&gt;shape&lt;/em&gt; of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;.&lt;br /&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;Muddle&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;Muddling&lt;/em&gt; refers to a process of mapping one &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt; onto another one; the scale thus produced is a &lt;em&gt;muddle&lt;/em&gt;. By periodic scale is meant a scale that repeats &amp;quot;at the something&amp;quot; (octave, tritave, something else). There are two necessary components: a &lt;strong&gt;parent scale&lt;/strong&gt; and a &lt;strong&gt;target shape&lt;/strong&gt;, or simply &amp;quot;parent&amp;quot; and &amp;quot;target&amp;quot;. The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or &lt;em&gt;shape&lt;/em&gt; of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 The simplest sort of muddle is a MOS Muddle, which is a sort of second-order &lt;a class="wiki_link" href="/MOSScales"&gt;MOS Scale&lt;/a&gt; and is useful for generating usable subsets of larger MOS scales and for navigating &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt;. This article will mostly deal with MOS muddles, but it should be remembered that this process can be generalized to other structures.&lt;br /&gt;