Bohlen–Pierce scale: Difference between revisions
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The '''Bohlen-Pierce''' ('''BP''') scale is a [[nonoctave]] scale, a 13-part equal division of the perfect-twelfth ([[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, 5:6, 6:7, etc. | The '''Bohlen-Pierce''' ('''BP''') scale is a [[nonoctave]] scale, a 13-part equal division of the perfect-twelfth ([[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, 5:6, 6:7, etc. | ||
==Theory== | == Theory == | ||
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|+Approximation of prime intervals in 13-EDT | |+Approximation of prime intervals in 13-EDT | ||
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[[File:vaisvil-BP-guitar-052-crop.jpg|frame|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]] | |||
[[File:Sword_BP_guitars.jpg|thumb|500px]] | |||
* [http://www.huygens-fokker.org/bpsite/ Bohlen Pierce website] | * [http://www.huygens-fokker.org/bpsite/ Bohlen Pierce website] | ||
* [http://en.wikipedia.org/wiki/Bohlen-Pierce_scale Wikipedia Bohlen-Pierce scale] | * [http://en.wikipedia.org/wiki/Bohlen-Pierce_scale Wikipedia Bohlen-Pierce scale] | ||