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Bohlen–Pierce scale: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
|en = Bohlen-Pierce
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-12-20 08:03:18 UTC</tt>.<br>
|de = Bohlen-Pierce
: The original revision id was <tt>13753501</tt>.<br>
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: The revision comment was: <tt>Wikipedia link (page "BP" and "BohlenPierce" integrated)</tt><br>
{{Wikipedia}}
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
[[File:vaisvil-BP-guitar-052-crop.jpg|thumb|x00px|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]]]
<h4>Original Wikitext content:</h4>
[[File:Sword_BP_guitars.jpg|thumb|300px]]
<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.
The '''Bohlen–Pierce scale''' ('''BP''') is a 13-tone [[macrotonal]] [[nonoctave]] [[scale]] designed to emphasize odd-number intervals and chords, such as the 3:5:7:9 tetrad. It was first described as a 7-limit [[just intonation]] scale and as an [[equal-step tuning|equal temperament]], [[13edt|13 equal divisions of the tritave]]. The [[tritave]] (3/1) usually replaces the [[octave]] in the role of the [[equave]], such that intervals a tritave apart are considered [[equivalent]].


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.
It is closely related to the rank two temperament [[Sensamagic clan #Bohpier|bohpier]]. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroup|subgroup]]. However, it can be extended to the 3.5.7.11/4 subgroup, especially when considering 13edt instead of the JI version. 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]].  


[[http://members.aol.com/bpsite/|Bohlen Pierce website]]
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, 5:6, 6:7, etc.


Links to avaliable music written in BP at [[http://members.aol.com/bpsite/references2.html#anchor81501|above website]].
== Theory ==
* [[Relationship between Bohlen–Pierce and octave-ful temperaments]]


[[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale|Wikipedia Bohlen-Pierce scale]]
=== Lambda scale ===
{{Main|4L 5s (3/1-equivalent)}}


Physical instruments tuned to the BP scale
== Intervals ==
Guitar
{{Main|Intervals of BP}}
Clarinets
 
Metallophone
== Variations ==
Electronic Organ</pre></div>
=== Triple Bohlen–Pierce ===
<h4>Original HTML content:</h4>
Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) 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.
<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;
== Regular temperament properties ==
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;
{{Main| 13edt#Regular temperament properties }}
&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;
== Instruments ==
&lt;br /&gt;
* [http://www.huygens-fokker.org/bpsite/instruments.html#anchor39641 Bohlen Pierce guitar]
&lt;a class="wiki_link_ext" href="http://members.aol.com/bpsite/" rel="nofollow"&gt;Bohlen Pierce website&lt;/a&gt;&lt;br /&gt;
* [[Clarinet#Bohlen-Pierce clarinets|Clarinets]]
&lt;br /&gt;
* Metallophone
Links to avaliable music written in BP at &lt;a class="wiki_link_ext" href="http://members.aol.com/bpsite/references2.html#anchor81501" rel="nofollow"&gt;above website&lt;/a&gt;.&lt;br /&gt;
* Electronic Organ
&lt;br /&gt;
* Stredici
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bohlen-Pierce_scale" rel="nofollow"&gt;Wikipedia Bohlen-Pierce scale&lt;/a&gt;&lt;br /&gt;
* [http://bp.b0b.com/2016/01/tuning-a-kalimba-to-bp/ Kalimba] (Mbira)
&lt;br /&gt;
* [http://bp.b0b.com/2012/11/sierra-pedal-steel/ Pedal Steel Guitar]
Physical instruments tuned to the BP scale&lt;br /&gt;
 
Guitar&lt;br /&gt;
== Music ==
Clarinets&lt;br /&gt;
{{Main| Bohlen–Pierce scale/Music }}
Metallophone&lt;br /&gt;
{{Catrel|Bohlen-Pierce tracks}}
Electronic Organ&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== See also ==
* [[Catalog of 3.5.7 subgroup rank two temperaments]]
* [[Lumatone mapping for Bohlen–Pierce]]
 
== Further reading ==
* [[Sword, Ron]]. [https://ronsword.bigcartel.com/product/creative-applications-for-polyscales-and-scale-sequences ''Bohlen-Pierce Scales for Guitar: Includes Paul Erlich's Triple BP Scales. Notation methods, Chord-Scales, Melody Chords, Polyscales, and new Scales for the Bohlen-Pierce tuning'']. 2009. ([http://www.metatonalmusic.com/books.html Metatonal Music link])
 
== External links ==
* [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site]
* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]
 
[[Category:Bohlen–Pierce| ]] <!-- main article -->
[[Category:13-tone scales]]
[[Category:Guitar]]
[[Category:Macrotonal]]
Retrieved from "https://en.xen.wiki/w/Bohlen–Pierce_scale"