Bohlen–Pierce 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:guest|guest]] and made on <tt>2010-02-19 05:03:57 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 05:17:49 UTC</tt>.<br>

: The original revision id was <tt>~~121492871~~</tt>.<br>

: The original revision id was <tt>121493955</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">=The Bohlen-Pierce scale=

The Bohlen-Pierce scale is a [[nonoctave]] scale, a 13-part equal division of the perfect-twelfth (3/1). Each step is about 146 ¢, making it a [[macrotonal]] scale.

It was discovered independently by Heinz Bohlen, John Pierce, Kees van Prooijen, and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.

~~[[image:http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG width="270" height="133"]]Cutaway Bohlen-Pierce Classical Guitar~~

~~[[image:http://ronsword.com/bpguitar.JPG width="212" height="290"]]~~

~~Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: "//the Bohlen-Box//")~~

[[image:http://ronsword.com/images/bpwhite.jpg width="166" height="120"]][[image:http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG width="261" height="132"]]

Cutaway Bohlen-Pierce Classical Guitar

[[image:http://ronsword.com/bpguitar.JPG width="171" height="224"]]Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: "//the Bohlen-Box//")

**Triple Bohlen-Pierce**

Proposed by Paul Erlich, is the Triple Bohlen-Pierce Scale, or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.

[[image:http://www.ronsword.com/images/3BP3.JPG width="545" height="263"]]

**Theory**

[[http://www.huygens-fokker.org/bpsite/|Bohlen Pierce website]]

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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"><html><head><title>Bohlen-Pierce</title></head><body><h1 id="toc0"><a name="The Bohlen-Pierce scale"></a>The Bohlen-Pierce scale</h1>

<br />

The Bohlen-Pierce scale is a <a class="wiki_link" href="/nonoctave">nonoctave</a> scale, a 13-part equal division of the perfect-twelfth (3/1). Each step is about 146 ¢, making it a <a class="wiki_link" href="/macrotonal">macrotonal</a> scale.<br />

<br />

It was discovered independently by Heinz Bohlen, John Pierce, Kees van Prooijen, and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.<br />

<img src="http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG" alt="external image Sword_Bohlen_Pierce_acoustic.JPG" title="external image Sword_Bohlen_Pierce_acoustic.JPG" style="height: 133px; width: 270px;" />Cutaway Bohlen-Pierce Classical Guitar<br />

<br />

<img src="http://ronsword.com/bpguitar.JPG" alt="external image bpguitar.JPG" title="external image bpguitar.JPG" style="height: 290px; width: 212px;" /><br />

~~Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: &quot;<em>the Bohlen-Box</em>&quot;)<br />~~

<br />

<img src="http://ronsword.com/images/bpwhite.jpg" alt="external image bpwhite.jpg" title="external image bpwhite.jpg" style="height: 120px; width: 166px;" /><img src="http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG" alt="external image Sword_Bohlen_Pierce_acoustic.JPG" title="external image Sword_Bohlen_Pierce_acoustic.JPG" style="height: 132px; width: 261px;" /><br />

Cutaway Bohlen-Pierce Classical Guitar<br />

<br />

<img src="http://ronsword.com/bpguitar.JPG" alt="external image bpguitar.JPG" title="external image bpguitar.JPG" style="height: 224px; width: 171px;" />Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: &quot;<em>the Bohlen-Box</em>&quot;)<br />

<br />

<strong>Triple Bohlen-Pierce</strong><br />

<br />

Proposed by Paul Erlich, is the Triple Bohlen-Pierce Scale, or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.<br />

<br />

<img src="http://www.ronsword.com/images/3BP3.JPG" alt="external image 3BP3.JPG" title="external image 3BP3.JPG" style="height: 263px; width: 545px;" /><br />

<strong>Theory</strong><br />

<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">Bohlen Pierce website</a><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:guest|guest]] and made on <tt>2010-02-19 05:03:57 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-02-19 05:17:49 UTC</tt>.<br>
-: The original revision id was <tt>121492871</tt>.<br>
+: The original revision id was <tt>121493955</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">=The Bohlen-Pierce scale=
 The Bohlen-Pierce scale is a [[nonoctave]] scale, a 13-part equal division of the perfect-twelfth (3/1). Each step is about 146 ¢, making it a [[macrotonal]] scale.
 It was discovered independently by Heinz Bohlen, John Pierce, Kees van Prooijen, and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.
-[[image:http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG width="270" height="133"]]Cutaway Bohlen-Pierce Classical Guitar
-[[image:http://ronsword.com/bpguitar.JPG width="212" height="290"]]
-Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: "//the Bohlen-Box//")
+[[image:http://ronsword.com/images/bpwhite.jpg width="166" height="120"]][[image:http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG width="261" height="132"]]
+Cutaway Bohlen-Pierce Classical Guitar
+[[image:http://ronsword.com/bpguitar.JPG width="171" height="224"]]Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: "//the Bohlen-Box//")
+**Triple Bohlen-Pierce**
+Proposed by Paul Erlich, is the Triple Bohlen-Pierce Scale, or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.
+[[image:http://www.ronsword.com/images/3BP3.JPG width="545" height="263"]]
 **Theory**
 [[http://www.huygens-fokker.org/bpsite/|Bohlen Pierce website]]
@@ Line 36: / Line 44: @@
 <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;Bohlen-Pierce&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="The Bohlen-Pierce scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;The Bohlen-Pierce scale&lt;/h1&gt;
   &lt;br /&gt;
+&lt;br /&gt;
 The Bohlen-Pierce scale is a &lt;a class="wiki_link" href="/nonoctave"&gt;nonoctave&lt;/a&gt; scale, a 13-part equal division of the perfect-twelfth (3/1). Each step is about 146 ¢, making it a &lt;a class="wiki_link" href="/macrotonal"&gt;macrotonal&lt;/a&gt; scale.&lt;br /&gt;
 &lt;br /&gt;
 It was discovered independently by Heinz Bohlen, John Pierce, Kees van Prooijen, and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:6:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 133px; width: 270px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG" alt="external image Sword_Bohlen_Pierce_acoustic.JPG" title="external image Sword_Bohlen_Pierce_acoustic.JPG" style="height: 133px; width: 270px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:6 --&gt;Cutaway Bohlen-Pierce Classical Guitar&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:7:&amp;lt;img src=&amp;quot;http://ronsword.com/bpguitar.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 290px; width: 212px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/bpguitar.JPG" alt="external image bpguitar.JPG" title="external image bpguitar.JPG" style="height: 290px; width: 212px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:7 --&gt;&lt;br /&gt;
-Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: &amp;quot;&lt;em&gt;the Bohlen-Box&lt;/em&gt;&amp;quot;)&lt;br /&gt;
 &lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:6:&amp;lt;img src=&amp;quot;http://ronsword.com/images/bpwhite.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 120px; width: 166px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/bpwhite.jpg" alt="external image bpwhite.jpg" title="external image bpwhite.jpg" style="height: 120px; width: 166px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:6 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:7:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 132px; width: 261px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG" alt="external image Sword_Bohlen_Pierce_acoustic.JPG" title="external image Sword_Bohlen_Pierce_acoustic.JPG" style="height: 132px; width: 261px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:7 --&gt;&lt;br /&gt;
+Cutaway Bohlen-Pierce Classical Guitar&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:8:&amp;lt;img src=&amp;quot;http://ronsword.com/bpguitar.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 224px; width: 171px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/bpguitar.JPG" alt="external image bpguitar.JPG" title="external image bpguitar.JPG" style="height: 224px; width: 171px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:8 --&gt;Ron Sword and his hand-built 9-string Bohlen-Pierce Touchstick/Guitar crossover (aka: &amp;quot;&lt;em&gt;the Bohlen-Box&lt;/em&gt;&amp;quot;)&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Triple Bohlen-Pierce&lt;/strong&gt;&lt;br /&gt;
+&lt;br /&gt;
+Proposed by Paul Erlich, is the Triple Bohlen-Pierce Scale, or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:9:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/3BP3.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 263px; width: 545px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/3BP3.JPG" alt="external image 3BP3.JPG" title="external image 3BP3.JPG" style="height: 263px; width: 545px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:9 --&gt;&lt;br /&gt;
 &lt;strong&gt;Theory&lt;/strong&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow"&gt;Bohlen Pierce website&lt;/a&gt;&lt;br /&gt;