Bohlen–Pierce scale: Difference between revisions
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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2016-01-21 10: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2016-01-21 10:29:35 UTC</tt>.<br> | ||
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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;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">[[xenharmonie/Bohlen-Pierce|Deutsch]] | <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"><span style="display: block; text-align: right;">[[xenharmonie/Bohlen-Pierce|Deutsch]] | ||
</span> | </span> | ||
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. | 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. | ||
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[[Ron Sword]] and his 9-string 13-tone BP Touchstick/Guitar crossover instrument (aka: "//the Bohlen-Box//") | [[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. | 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>) | [[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://www.huygens-fokker.org/bpsite/|Bohlen Pierce website]] | ||
[[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale|Wikipedia Bohlen-Pierce scale]] | [[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale|Wikipedia Bohlen-Pierce scale]] | ||
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Sword, Ronald. "Bohlen Pierce Scales for Guitar" IAAA Press, UK-USA. First Ed: May 2009. | Sword, Ronald. "Bohlen Pierce Scales for Guitar" IAAA Press, UK-USA. First Ed: May 2009. | ||
[[Intervals of BP]] | [[Intervals of BP]] | ||
=Physical instruments tuned to the BP scale= | |||
[[@http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG|Bohlen Pierce guitar]] | [[@http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG|Bohlen Pierce guitar]] | ||
[[microtonal clarinet#BPClarinets|Clarinets]] | [[microtonal clarinet#BPClarinets|Clarinets]] | ||
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Electronic Organ | Electronic Organ | ||
Stredici | Stredici | ||
=Compositions= | |||
Links to available music written in BP at [[http://www.huygens-fokker.org/bpsite/references2.html#anchor81501|above website]]. | 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.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]]) | ||
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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><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Bohlen-Pierce">Deutsch</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>Bohlen-Pierce</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Bohlen-Pierce">Deutsch</a><br /> | ||
</span><br /> | </span><br /> | ||
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 /> | 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: | <!-- ws:start:WikiTextRemoteImageRule:10:&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:10 --><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 /> | <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 /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Triple Bohlen-Pierce"></a><!-- ws:end:WikiTextHeadingRule:1 -->Triple Bohlen-Pierce</h1> | ||
<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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:11:&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:11 -->(triple bohlen-pierce <span class="UIStory_Message">39√3 Classical Guitar by Ron Sword</span>)<br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:3 -->Theory</h1> | ||
<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://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://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 /> | <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 /> | 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 /> | <a class="wiki_link" href="/Intervals%20of%20BP">Intervals of BP</a><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Physical instruments tuned to the BP scale"></a><!-- ws:end:WikiTextHeadingRule:5 -->Physical instruments tuned to the BP scale</h1> | ||
<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_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 /> | <a class="wiki_link" href="/microtonal%20clarinet#BPClarinets">Clarinets</a><br /> | ||
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Electronic Organ<br /> | Electronic Organ<br /> | ||
Stredici<br /> | Stredici<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:7 -->Compositions</h1> | ||
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 /> | 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.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 /> | ||