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~~]].

[[File:vaisvil-BP-guitar-052-crop.jpg|thumb|400px|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]]]

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~~.

[[File:Sword_BP_guitars.jpg|thumb|400px]]

The '''Bohlen-Pierce''' ('''BP''') scale 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]].

[[~~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.~~]]

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]].

[[~~File~~:~~Sword_BP_guitars~~.~~jpg|thumb|500px]]~~

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 ==

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== Intervals ==

* [[Intervals of BP~~]] (equal version)~~

== Variations ==

=== Lambda scale ===

=== Triple Bohlen-Pierce ===

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* [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]

~~== Links ==~~

* [[Wikipedia: Bohlen-Pierce scale]]

* [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site]

* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]

== Compositions ==

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* [[Catalog of 3.5.7 subgroup rank two temperaments]]

* [[No-twos 31-limit]]

== External links ==

* [[Wikipedia: Bohlen-Pierce scale]]

* [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| ]]

[[Category:13-tone scales]]

[[Category:Edonoi]]

[[Category:Edt]]

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 |de = Bohlen-Pierce
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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]].
+[[File:vaisvil-BP-guitar-052-crop.jpg|thumb|400px|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]]]
-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.
+[[File:Sword_BP_guitars.jpg|thumb|400px]]
+The '''Bohlen-Pierce''' ('''BP''') scale 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]].
-[[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.]]
+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]].
-[[File:Sword_BP_guitars.jpg|thumb|500px]]
+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 ==
@@ Line 15: / Line 17: @@
 == Intervals ==
-* [[Intervals of BP]] (equal version)
+{{Main|Intervals of BP}}
 == Variations ==
 === Lambda scale ===
-{{main|4L 5s (tritave-equivalent)}}
+{{Main|4L 5s (tritave-equivalent)}}
 === Triple Bohlen-Pierce ===
@@ Line 94: / Line 96: @@
 * [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]
-== Links ==
-* [[Wikipedia: Bohlen-Pierce scale]]
-* [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site]
-* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]
 == Compositions ==
@@ Line 124: / Line 121: @@
 * [[Catalog of 3.5.7 subgroup rank two temperaments]]
 * [[No-twos 31-limit]]
+== External links ==
+* [[Wikipedia: Bohlen-Pierce scale]]
+* [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:Edonoi]]
 [[Category:Edt]]