Bohlen–Pierce scale: Difference between revisions

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[[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.]]]

[[File:Sword_BP_guitars.jpg|thumb|300px]]

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]].

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]].

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]]

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

== Intervals ==

{{Main|Intervals of BP}}

== Variations ==

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.

== Regular temperament properties ==

* [http://www.huygens-fokker.org/bpsite/instruments.html#anchor39641 Bohlen Pierce guitar]

* [[Clarinet#Bohlen-Pierce clarinets|Clarinets]]

* [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]

== Music ==

{{Main| Bohlen–Pierce scale/Music }}

{{Catrel|Bohlen-Pierce tracks}}

== See also ==

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

* [[Lumatone mapping for Bohlen–Pierce]]