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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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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.]]]
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]]
[[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//")
== Intervals ==
{{Main|Intervals of BP}}
**Triple Bohlen-Pierce**
== 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.
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.
== Regular temperament properties ==
{{Main| 13edt#Regular temperament properties }}
[[image:http://www.ronsword.com/images/3BP3.JPG width="545" height="263"]](triple bohlen-pierce <span class="UIStory_Message">39√3 Classical Guitar by Ron Sword</span>)
Links to available music written in BP at [[http://www.huygens-fokker.org/bpsite/references2.html#anchor81501|above website]].
* [[Catalog of 3.5.7 subgroup rank two temperaments]]
[[http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3|Bohl-en Roll]] by Carlo Serafini
* [[Lumatone mapping for Bohlen–Pierce]]
[[@http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3|Bohlen-Pierce electric guitar improvisation]] by [[@http://www.jeanpierrepoulin.com/|Jean-Pierre Poulin]]
[[@http://www.ronsword.com/sounds/BP_stretched_chroma.mp3|Bohlen-Pierce "Stretched Chroma" Acoustic Improvisation]] by Ron Sword</pre></div>
== Further reading ==
<h4>Original HTML content:</h4>
* [[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])
* [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site]
The Bohlen-Pierce scale is a <a class="wiki_link" href="/nonoctave">nonoctave</a> scale, a 13-part equal division of the perfect-twelfth (3/1). Each step is about 146 ¢, making it a <a class="wiki_link" href="/macrotonal">macrotonal</a> scale.<br />
* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]
<br />
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.<br />
[[Category:Bohlen–Pierce| ]] <!-- main article -->
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.<br />
<a class="wiki_link_ext" href="http://www.ziaspace.com/elaine/BP/The%20Bohlen-Pierce%20Scale.html" 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 />
<a class="wiki_link" href="/Intervals%20of%20BP">Intervals of BP</a><br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="The Bohlen-Pierce scale-Physical instruments tuned to the BP scale"></a><!-- ws:end:WikiTextHeadingRule:2 -->Physical instruments tuned to the BP scale</h2>
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 />
<a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3" rel="nofollow">Bohl-en Roll</a> by Carlo Serafini<br />
<a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3" rel="nofollow" target="_blank">Bohlen-Pierce electric guitar improvisation</a> by <a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/" rel="nofollow" target="_blank">Jean-Pierre Poulin</a><br />
<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/BP_stretched_chroma.mp3" rel="nofollow" target="_blank">Bohlen-Pierce &quot;Stretched Chroma&quot; Acoustic Improvisation</a> by Ron Sword</body></html></pre></div>
It is closely related to the rank two temperament bohpier. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 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.
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.
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.
