Bohlen–Pierce scale

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=The Bohlen-Pierce scale= 


The **Bohlen-Pierce** (**BP**) scale is a [[nonoctave]] scale, a 13-part equal division of the perfect-twelfth ([[3_1|3/1]]) or [[Tritave]] (**13edt**). Each step is about 146 ¢, making it a [[macrotonal]] scale. It is closely related to the rank two temperament [[Sensamagic clan#Bohpier|bohpier]]. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroups|subgroup]]. However, it (or at least 3.5.7-limit [[edt|13edt]]) can be extended to the 3.5.7.11/4 subgroup. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page [[chords of bohpier]]. Bohlen-Pierce 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. but not necessarily 4:11.



[[image:http://www.ronsword.com/images/Sword_BP_guitars.jpg width="543" height="422"]]

[[image:http://ronsword.com/bpguitar.JPG width="171" height="224"]]
[[Ron Sword]] and his 9-string 13-tone BP Touchstick/Guitar crossover instrument (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="672" height="340"]](triple bohlen-pierce <span class="UIStory_Message">39√3 Classical Guitar by Ron Sword</span>)
**Theory**
[[http://www.huygens-fokker.org/bpsite/|Bohlen Pierce website]]
[[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale|Wikipedia Bohlen-Pierce scale]]
[[http://ziaspace.com/_microtonality/BP/|Bohlen-Pierce Scale Research]] by Elaine Walker
Sword, Ronald. "Bohlen Pierce Scales for Guitar" IAAA Press, UK-USA. First Ed: May 2009.
[[Intervals of BP]]
==Physical instruments tuned to the BP scale== 
[[@http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG|Bohlen Pierce guitar]]
[[microtonal clarinet#BPClarinets|Clarinets]]
Metallophone
Electronic Organ
Stredici
==Compositions== 
Links to available music written in BP at [[http://www.huygens-fokker.org/bpsite/references2.html#anchor81501|above website]].
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3|Bohl-en Roll]]</span></span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/004e4fe53f09c06fd5e709a08d53d0d5-4.html|blog entry]])
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[@http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3|Bohlen-Pierce electric guitar improvisation]]</span></span> by [[@Jean-Pierre Poulin]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[@http://www.ronsword.com/sounds/BP_stretched_chroma.mp3|Bohlen-Pierce "Stretched Chroma" Acoustic Improvisation]]</span></span> by [[Ron Sword]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.kunstmusik.com/mp3/reminiscences.mp3|Reminiscences]]</span> by [[@http://www.kunstmusik.com/2010/03/08/reminiscences/|Steven Yi]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.jeanpierrepoulin.com/mp3/Roll%27n%27Peace.mp3|Roll'n'Peace]]</span></span> by Jean-Pierre Poulin[[media type="custom" key="11371948"]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/01%20-%201.%20Bohlen-Pierce.mp3|Comets Over Flatland 1]]</span></span> by [[Randy Winchester]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/02%20-%202.%20Bohlen-Pierce.mp3|Comets Over Flatland 2]]</span></span> by [[Randy Winchester]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/03%20-%203.%20Bohlen-Pierce.mp3|Comets Over Flatland 3]]</span></span> by [[Randy Winchester]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/04%20-%204.%20Bohlen-Pierce.mp3|Comets Over Flatland 4]]</span></span> by [[Randy Winchester]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/bohlen-pierce/daily20110915_BP_strings-Bohlen-Pierce-Island.mp3|Bohlen-Pierce Island audio]]</span></span> by [[Chris Vaisvil]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/bohlen-pierce/mesonic_atom_13th_root_of_3_BP_apx_X1.mp3|Mesonic Atom]]</span></span> by [[Chris Vaisvil]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/MOTU/Vaisvil-MOTU-8a-bending-the-rules-in-bohlen-pierce.mp3|Bending the Rules]]</span></span> by [[Chris Vaisvil]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Hansen/Bohlen-Pierce%20Canon.mp3|Bohlen-Pierce Canon]]</span> by <span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">[[http://www.youtube.com/watch?v=sd1b9Lh8iFA|Kjell Hansen]]</span>.

Original HTML content:

<html><head><title>Bohlen-Pierce</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="The Bohlen-Pierce scale"></a><!-- ws:end:WikiTextHeadingRule:1 -->The Bohlen-Pierce scale</h1>
 <br />
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The <strong>Bohlen-Pierce</strong> (<strong>BP</strong>) scale is a <a class="wiki_link" href="/nonoctave">nonoctave</a> scale, a 13-part equal division of the perfect-twelfth (<a class="wiki_link" href="/3_1">3/1</a>) or <a class="wiki_link" href="/Tritave">Tritave</a> (<strong>13edt</strong>). Each step is about 146 ¢, making it a <a class="wiki_link" href="/macrotonal">macrotonal</a> scale. It is closely related to the rank two temperament <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier</a>. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a>. However, it (or at least 3.5.7-limit <a class="wiki_link" href="/edt">13edt</a>) can be extended to the 3.5.7.11/4 subgroup. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page <a class="wiki_link" href="/chords%20of%20bohpier">chords of bohpier</a>. Bohlen-Pierce was discovered independently by <a class="wiki_link" href="/Heinz%20Bohlen">Heinz Bohlen</a>, <a class="wiki_link" href="/John%20Pierce">John Pierce</a>, <a class="wiki_link" href="/Kees%20van%20Prooijen">Kees van Prooijen</a>, and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc. but not necessarily 4:11.<br />
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<!-- ws:start:WikiTextRemoteImageRule:7:&lt;img src=&quot;http://www.ronsword.com/images/Sword_BP_guitars.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 422px; width: 543px;&quot; /&gt; --><img src="http://www.ronsword.com/images/Sword_BP_guitars.jpg" alt="external image Sword_BP_guitars.jpg" title="external image Sword_BP_guitars.jpg" style="height: 422px; width: 543px;" /><!-- ws:end:WikiTextRemoteImageRule:7 --><br />
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<!-- ws:start:WikiTextRemoteImageRule:8:&lt;img src=&quot;http://ronsword.com/bpguitar.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 224px; width: 171px;&quot; /&gt; --><img src="http://ronsword.com/bpguitar.JPG" alt="external image bpguitar.JPG" title="external image bpguitar.JPG" style="height: 224px; width: 171px;" /><!-- ws:end:WikiTextRemoteImageRule:8 --><br />
<a class="wiki_link" href="/Ron%20Sword">Ron Sword</a> and his 9-string 13-tone BP Touchstick/Guitar crossover instrument (aka: &quot;<em>the Bohlen-Box</em>&quot;)<br />
<br />
<strong>Triple Bohlen-Pierce</strong><br />
<br />
Proposed by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>, 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 />
<!-- ws:start:WikiTextRemoteImageRule:9:&lt;img src=&quot;http://www.ronsword.com/images/3BP3.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 340px; width: 672px;&quot; /&gt; --><img src="http://www.ronsword.com/images/3BP3.JPG" alt="external image 3BP3.JPG" title="external image 3BP3.JPG" style="height: 340px; width: 672px;" /><!-- ws:end:WikiTextRemoteImageRule:9 -->(triple bohlen-pierce <span class="UIStory_Message">39√3 Classical Guitar by Ron Sword</span>)<br />
<strong>Theory</strong><br />
<a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow">Bohlen Pierce website</a><br />
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bohlen-Pierce_scale" rel="nofollow">Wikipedia Bohlen-Pierce scale</a><br />
<a class="wiki_link_ext" href="http://ziaspace.com/_microtonality/BP/" rel="nofollow">Bohlen-Pierce Scale Research</a> by Elaine Walker<br />
Sword, Ronald. &quot;Bohlen Pierce Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: May 2009.<br />
<a class="wiki_link" href="/Intervals%20of%20BP">Intervals of BP</a><br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="The Bohlen-Pierce scale-Physical instruments tuned to the BP scale"></a><!-- ws:end:WikiTextHeadingRule:3 -->Physical instruments tuned to the BP scale</h2>
 <a class="wiki_link_ext" href="http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG" rel="nofollow" target="_blank">Bohlen Pierce guitar</a><br />
<a class="wiki_link" href="/microtonal%20clarinet#BPClarinets">Clarinets</a><br />
Metallophone<br />
Electronic Organ<br />
Stredici<br />
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="The Bohlen-Pierce scale-Compositions"></a><!-- ws:end:WikiTextHeadingRule:5 -->Compositions</h2>
 Links to available music written in BP at <a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/references2.html#anchor81501" rel="nofollow">above website</a>.<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3" rel="nofollow">Bohl-en Roll</a></span></span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/004e4fe53f09c06fd5e709a08d53d0d5-4.html" rel="nofollow">blog entry</a>)<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3" rel="nofollow" target="_blank">Bohlen-Pierce electric guitar improvisation</a></span></span> by <a class="wiki_link" href="/Jean-Pierre%20Poulin" target="_blank">Jean-Pierre Poulin</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.ronsword.com/sounds/BP_stretched_chroma.mp3" rel="nofollow" target="_blank">Bohlen-Pierce &quot;Stretched Chroma&quot; Acoustic Improvisation</a></span></span> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.kunstmusik.com/mp3/reminiscences.mp3" rel="nofollow">Reminiscences</a></span> by <a class="wiki_link_ext" href="http://www.kunstmusik.com/2010/03/08/reminiscences/" rel="nofollow" target="_blank">Steven Yi</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/mp3/Roll%27n%27Peace.mp3" rel="nofollow">Roll'n'Peace</a></span></span> by Jean-Pierre Poulin<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/11371948?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;11371948&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js">
</script><!-- ws:end:WikiTextMediaRule:0 --><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/01%20-%201.%20Bohlen-Pierce.mp3" rel="nofollow">Comets Over Flatland 1</a></span></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/02%20-%202.%20Bohlen-Pierce.mp3" rel="nofollow">Comets Over Flatland 2</a></span></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/03%20-%203.%20Bohlen-Pierce.mp3" rel="nofollow">Comets Over Flatland 3</a></span></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/04%20-%204.%20Bohlen-Pierce.mp3" rel="nofollow">Comets Over Flatland 4</a></span></span> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/bohlen-pierce/daily20110915_BP_strings-Bohlen-Pierce-Island.mp3" rel="nofollow">Bohlen-Pierce Island audio</a></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/bohlen-pierce/mesonic_atom_13th_root_of_3_BP_apx_X1.mp3" rel="nofollow">Mesonic Atom</a></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/MOTU/Vaisvil-MOTU-8a-bending-the-rules-in-bohlen-pierce.mp3" rel="nofollow">Bending the Rules</a></span></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Hansen/Bohlen-Pierce%20Canon.mp3" rel="nofollow">Bohlen-Pierce Canon</a></span> by <span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=sd1b9Lh8iFA" rel="nofollow">Kjell Hansen</a></span>.</body></html>