Bohlen–Pierce scale: Difference between revisions
Wikispaces>vaisvil **Imported revision 580997649 - Original comment: ** |
Wikispaces>vaisvil **Imported revision 583902781 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:vaisvil|vaisvil]] and made on <tt>2016- | : This revision was by author [[User:vaisvil|vaisvil]] and made on <tt>2016-05-23 22:52:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>583902781</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 10: | Line 10: | ||
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. | ||
Chris Vaisvil's BP electric => [[http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/|Music from this guitar]] | |||
[[image:http://chrisvaisvil.com/wp-content/uploads/2016/05/052-crop.jpg]] | |||
[[image:http://www.ronsword.com/images/Sword_BP_guitars.jpg width="543"]] | [[image:http://www.ronsword.com/images/Sword_BP_guitars.jpg width="543"]] | ||
| Line 57: | Line 58: | ||
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 /> | ||
<br /> | <br /> | ||
Chris Vaisvil's BP electric =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/" rel="nofollow">Music from this guitar</a><br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:9:&lt;img src=&quot;http://chrisvaisvil.com/wp-content/uploads/2016/05/052-crop.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://chrisvaisvil.com/wp-content/uploads/2016/05/052-crop.jpg" alt="external image 052-crop.jpg" title="external image 052-crop.jpg" /><!-- ws:end:WikiTextRemoteImageRule:9 --><br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:10:&lt;img src=&quot;http://www.ronsword.com/images/Sword_BP_guitars.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;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="width: 543px;" /><!-- ws:end:WikiTextRemoteImageRule:10 --><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:11:&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:11 --><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 /> | ||
| Line 67: | Line 69: | ||
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:12:&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:12 -->(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> | <!-- 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 /> | ||