Xenharmonic Wiki

Bohlen–Pierce scale: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>xenwolf
**Imported revision 126123733 - Original comment: composition by Steven Yi added**
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,474 edits
m Categories
 
(108 intermediate revisions by 28 users not shown)
Line 1: Line 1:
<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:xenwolf|xenwolf]] and made on <tt>2010-03-09 08:19:43 UTC</tt>.<br>
|de = Bohlen-Pierce
: The original revision id was <tt>126123733</tt>.<br>
}}
: The revision comment was: <tt>composition by Steven Yi added</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''' ('''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]].


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.
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]].  


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.
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.


== Theory ==
* [[Relationship between Bohlen–Pierce and octave-ful temperaments]]


=== Lambda scale ===
{{Main|4L 5s (3/1-equivalent)}}


[[image:http://www.ronsword.com/images/Sword_BP_guitars.jpg width="543" height="422"]]
== Intervals ==
{{Main|Intervals of BP}}


[[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//")
== Variations ==
=== Triple Bohlen–Pierce ===
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.


**Triple Bohlen-Pierce**
== Regular temperament properties ==
{{Main| 13edt#Regular temperament properties }}


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.
== Instruments ==
* [http://www.huygens-fokker.org/bpsite/instruments.html#anchor39641 Bohlen Pierce guitar]
* [[Clarinet#Bohlen-Pierce clarinets|Clarinets]]
* Metallophone
* Electronic Organ
* Stredici
* [http://bp.b0b.com/2016/01/tuning-a-kalimba-to-bp/ Kalimba] (Mbira)
* [http://bp.b0b.com/2012/11/sierra-pedal-steel/ Pedal Steel Guitar]


[[image:http://www.ronsword.com/images/3BP3.JPG width="672" height="340"]](triple bohlen-pierce &lt;span class="UIStory_Message"&gt;39√3 Classical Guitar by Ron Sword&lt;/span&gt;)
== Music ==
**Theory**
{{Main| Bohlen–Pierce scale/Music }}
[[http://www.huygens-fokker.org/bpsite/|Bohlen Pierce website]]
{{Catrel|Bohlen-Pierce tracks}}
[[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale|Wikipedia Bohlen-Pierce scale]]
 
[[http://www.ziaspace.com/elaine/BP/The%20Bohlen-Pierce%20Scale.html|Bohlen-Pierce Scale Research]] by Elaine Walker
== See also ==
Sword, Ronald. "Bohlen Pierce Scales for Guitar" IAAA Press, UK-USA. First Ed: May 2009.
* [[Catalog of 3.5.7 subgroup rank two temperaments]]
[[Intervals of BP]]
* [[Lumatone mapping for Bohlen–Pierce]]
==Physical instruments tuned to the BP scale==  
 
[[@http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG|Bohlen Pierce guitar]]
== Further reading ==
[[microtonal clarinet#BPClarinets|Clarinets]]
* [[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])
Metallophone
 
Electronic Organ
== External links ==
Stredici
* [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site]
==Compositions==  
* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]
Links to available music written in BP at [[http://www.huygens-fokker.org/bpsite/references2.html#anchor81501|above website]].
 
[[http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3|Bohl-en Roll]] by Carlo Serafini
[[Category:Bohlen–Pierce| ]] <!-- main article -->
[[@http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3|Bohlen-Pierce electric guitar improvisation]] by [[@http://www.jeanpierrepoulin.com/|Jean-Pierre Poulin]]
[[Category:13-tone scales]]
[[@http://www.ronsword.com/sounds/BP_stretched_chroma.mp3|Bohlen-Pierce "Stretched Chroma" Acoustic Improvisation]] by Ron Sword
[[Category:Guitar]]
[[@http://www.kunstmusik.com/2010/03/08/reminiscences/|Reminiscences]] [[Steven Yi]]</pre></div>
[[Category:Macrotonal]]
<h4>Original HTML content:</h4>
<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;
&lt;br /&gt;
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;
&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;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:6:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/Sword_BP_guitars.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 422px; width: 543px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:6 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:7:&amp;lt;img src=&amp;quot;http://ronsword.com/bpguitar.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 224px; width: 171px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/bpguitar.JPG" alt="external image bpguitar.JPG" title="external image bpguitar.JPG" style="height: 224px; width: 171px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:7 --&gt;Ron Sword and his 9-string 13-tone BP Touchstick/Guitar crossover instrument (aka: &amp;quot;&lt;em&gt;the Bohlen-Box&lt;/em&gt;&amp;quot;)&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Triple Bohlen-Pierce&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:8:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/3BP3.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 340px; width: 672px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/3BP3.JPG" alt="external image 3BP3.JPG" title="external image 3BP3.JPG" style="height: 340px; width: 672px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:8 --&gt;(triple bohlen-pierce &lt;span class="UIStory_Message"&gt;39√3 Classical Guitar by Ron Sword&lt;/span&gt;)&lt;br /&gt;
&lt;strong&gt;Theory&lt;/strong&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/" rel="nofollow"&gt;Bohlen Pierce website&lt;/a&gt;&lt;br /&gt;
&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;
&lt;a class="wiki_link_ext" href="http://www.ziaspace.com/elaine/BP/The%20Bohlen-Pierce%20Scale.html" rel="nofollow"&gt;Bohlen-Pierce Scale Research&lt;/a&gt; by Elaine Walker&lt;br /&gt;
Sword, Ronald. &amp;quot;Bohlen Pierce Scales for Guitar&amp;quot; IAAA Press, UK-USA. First Ed: May 2009.&lt;br /&gt;
&lt;a class="wiki_link" href="/Intervals%20of%20BP"&gt;Intervals of BP&lt;/a&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="The Bohlen-Pierce scale-Physical instruments tuned to the BP scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Physical instruments tuned to the BP scale&lt;/h2&gt;
&lt;a class="wiki_link_ext" href="http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG" rel="nofollow" target="_blank"&gt;Bohlen Pierce guitar&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/microtonal%20clarinet#BPClarinets"&gt;Clarinets&lt;/a&gt;&lt;br /&gt;
Metallophone&lt;br /&gt;
Electronic Organ&lt;br /&gt;
Stredici&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="The Bohlen-Pierce scale-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Compositions&lt;/h2&gt;
Links to available music written in BP at &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/bpsite/references2.html#anchor81501" rel="nofollow"&gt;above website&lt;/a&gt;.&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3" rel="nofollow"&gt;Bohl-en Roll&lt;/a&gt; by Carlo Serafini&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3" rel="nofollow" target="_blank"&gt;Bohlen-Pierce electric guitar improvisation&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/" rel="nofollow" target="_blank"&gt;Jean-Pierre Poulin&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/BP_stretched_chroma.mp3" rel="nofollow" target="_blank"&gt;Bohlen-Pierce &amp;quot;Stretched Chroma&amp;quot; Acoustic Improvisation&lt;/a&gt; by Ron Sword&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.kunstmusik.com/2010/03/08/reminiscences/" rel="nofollow" target="_blank"&gt;Reminiscences&lt;/a&gt; &lt;a class="wiki_link" href="/Steven%20Yi"&gt;Steven Yi&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Bohlen–Pierce_scale"