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:

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-05 19:43:35 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-05 19:44:22 UTC</tt>.

: The original revision id was <tt>~~289924615~~</tt>.

: The original revision id was <tt>289924719</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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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. ~~The chords 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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The Bohlen-Pierce (BP) 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> (13edt). 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. ~~The chords 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.

The Bohlen-Pierce (BP) 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> (13edt). 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.

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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>2012-01-05 19:43:35 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-05 19:44:22 UTC</tt>.<br>
-: The original revision id was <tt>289924615</tt>.<br>
+: The original revision id was <tt>289924719</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>
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-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. The chords 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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 &lt;br /&gt;
-The &lt;strong&gt;Bohlen-Pierce&lt;/strong&gt; (&lt;strong&gt;BP&lt;/strong&gt;) 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 (&lt;a class="wiki_link" href="/3_1"&gt;3/1&lt;/a&gt;) or &lt;a class="wiki_link" href="/Tritave"&gt;Tritave&lt;/a&gt; (&lt;strong&gt;13edt&lt;/strong&gt;). Each step is about 146 ¢, making it a &lt;a class="wiki_link" href="/macrotonal"&gt;macrotonal&lt;/a&gt; scale. It is closely related to the rank two temperament &lt;a class="wiki_link" href="/Sensamagic%20clan#Bohpier"&gt;bohpier&lt;/a&gt;. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt;. However, it (or at least 3.5.7-limit &lt;a class="wiki_link" href="/edt"&gt;13edt&lt;/a&gt;) 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. The chords chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page &lt;a class="wiki_link" href="/chords%20of%20bohpier"&gt;chords of bohpier&lt;/a&gt;. Bohlen-Pierce was discovered independently by &lt;a class="wiki_link" href="/Heinz%20Bohlen"&gt;Heinz Bohlen&lt;/a&gt;, &lt;a class="wiki_link" href="/John%20Pierce"&gt;John Pierce&lt;/a&gt;, &lt;a class="wiki_link" href="/Kees%20van%20Prooijen"&gt;Kees van Prooijen&lt;/a&gt;, 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.&lt;br /&gt;
+The &lt;strong&gt;Bohlen-Pierce&lt;/strong&gt; (&lt;strong&gt;BP&lt;/strong&gt;) 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 (&lt;a class="wiki_link" href="/3_1"&gt;3/1&lt;/a&gt;) or &lt;a class="wiki_link" href="/Tritave"&gt;Tritave&lt;/a&gt; (&lt;strong&gt;13edt&lt;/strong&gt;). Each step is about 146 ¢, making it a &lt;a class="wiki_link" href="/macrotonal"&gt;macrotonal&lt;/a&gt; scale. It is closely related to the rank two temperament &lt;a class="wiki_link" href="/Sensamagic%20clan#Bohpier"&gt;bohpier&lt;/a&gt;. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt;. However, it (or at least 3.5.7-limit &lt;a class="wiki_link" href="/edt"&gt;13edt&lt;/a&gt;) 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 &lt;a class="wiki_link" href="/chords%20of%20bohpier"&gt;chords of bohpier&lt;/a&gt;. Bohlen-Pierce was discovered independently by &lt;a class="wiki_link" href="/Heinz%20Bohlen"&gt;Heinz Bohlen&lt;/a&gt;, &lt;a class="wiki_link" href="/John%20Pierce"&gt;John Pierce&lt;/a&gt;, &lt;a class="wiki_link" href="/Kees%20van%20Prooijen"&gt;Kees van Prooijen&lt;/a&gt;, 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.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;