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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| 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:guest|guest]] and made on <tt>2008-04-16 06:36:06 UTC</tt>.<br>
| | |de = Bohlen-Pierce |
| : The original revision id was <tt>21904703</tt>.<br>
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| : The revision comment was: <tt></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=
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| 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]]. |
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| 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]]. |
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| [[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. |
| [[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale|Wikipedia Bohlen-Pierce scale]] | |
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| ==Physical instruments tuned to the BP scale== | | == Theory == |
| | * [[Relationship between Bohlen–Pierce and octave-ful temperaments]] |
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| Guitar
| | === Lambda scale === |
| Clarinets
| | {{Main|4L 5s (3/1-equivalent)}} |
| Metallophone
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| Electronic Organ
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| ==Compositions== | | == Intervals == |
| | {{Main|Intervals of BP}} |
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| Links to avaliable music written in BP at [[http://members.aol.com/bpsite/references2.html#anchor81501|above website]].
| | == 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. |
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| [[http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3|Bohl-en Roll]] by Carlo Serafini</pre></div>
| | == Regular temperament properties == |
| <h4>Original HTML content:</h4>
| | {{Main| 13edt#Regular temperament properties }} |
| <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"><html><head><title>Bohlen-Pierce</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="The Bohlen-Pierce scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->The Bohlen-Pierce scale</h1>
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| | == Instruments == |
| 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://www.huygens-fokker.org/bpsite/instruments.html#anchor39641 Bohlen Pierce guitar] |
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| | * [[Clarinet#Bohlen-Pierce clarinets|Clarinets]] |
| 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 />
| | * Metallophone |
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| | * Electronic Organ |
| <a class="wiki_link_ext" href="http://members.aol.com/bpsite/" rel="nofollow">Bohlen Pierce website</a><br />
| | * Stredici |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bohlen-Pierce_scale" rel="nofollow">Wikipedia Bohlen-Pierce scale</a><br />
| | * [http://bp.b0b.com/2016/01/tuning-a-kalimba-to-bp/ Kalimba] (Mbira) |
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| | * [http://bp.b0b.com/2012/11/sierra-pedal-steel/ Pedal Steel Guitar] |
| <!-- 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>
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| | == Music == |
| Guitar<br />
| | {{Main| Bohlen–Pierce scale/Music }} |
| Clarinets<br />
| | {{Catrel|Bohlen-Pierce tracks}} |
| Metallophone<br />
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| Electronic Organ<br />
| | == See also == |
| <br />
| | * [[Catalog of 3.5.7 subgroup rank two temperaments]] |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="The Bohlen-Pierce scale-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h2>
| | * [[Lumatone mapping for Bohlen–Pierce]] |
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| Links to avaliable music written in BP at <a class="wiki_link_ext" href="http://members.aol.com/bpsite/references2.html#anchor81501" rel="nofollow">above website</a>.<br />
| | == Further reading == |
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| | * [[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]) |
| <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</body></html></pre></div>
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| | == External links == |
| | * [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site] |
| | * [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]] |
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| | [[Category:Bohlen–Pierce| ]] <!-- main article --> |
| | [[Category:13-tone scales]] |
| | [[Category:Guitar]] |
| | [[Category:Macrotonal]] |