Bohlen–Pierce scale: Difference between revisions
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[[File:Sword_BP_guitars.jpg|thumb|500px]] | [[File:Sword_BP_guitars.jpg|thumb|500px]] | ||
* [[Intervals of BP]] | * [[Intervals of BP]] | ||
* [[Relationship between Bohlen-Pierce and octave-ful temperaments]] | * [[Relationship between Bohlen-Pierce and octave-ful temperaments]] | ||
== Lambda scale == | == Variations == | ||
=== Lambda scale === | |||
{{main|4L 5s (tritave-equivalent)}} | {{main|4L 5s (tritave-equivalent)}} | ||
== Triple Bohlen-Pierce == | === Triple Bohlen-Pierce === | ||
Proposed by [[Paul Erlich]], is the [[Triple BP|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. | Proposed by [[Paul Erlich]], is the [[Triple BP|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. | ||
== | == Publications == | ||
[ | * [https://ronsword.bigcartel.com/product/creative-applications-for-polyscales-and-scale-sequences ''Bohlen Pierce Scales for Guitar''] by [[Ron Sword]], IAAA Press, UK-USA. First Ed: May 2009. | ||
[[Microtonal clarinet #BPClarinets|Clarinets]] | == Instruments == | ||
* [http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG Bohlen Pierce guitar] | |||
* [[Microtonal clarinet #BPClarinets|Clarinets]] | |||
* Metallophone | |||
* Electronic Organ | |||
* Stredici | |||
* [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/ Bohlen Pierce website] | |||
* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]] | |||
[http:// | |||
[http:// | |||
== Compositions == | == Compositions == | ||
Revision as of 07:13, 15 July 2021
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 bohpier. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 subgroup. However, it (or at least 3.5.7-limit 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
| Prime interval | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -29.6 | 0.0 | -6.5 | -3.8 | -54.8 | -51.4 | +69.4 | +23.1 |
| relative (%) | -20 | 0 | -4 | -3 | -37 | -35 | +47 | +16 | |
| Patent val | 8 | 13 | 19 | 23 | 28 | 30 | 34 | 35 | |
| Fifthspan | -1 | 0 | -4 | +2 | +3 | +6 | -1 | +7 | |
Variations
Lambda scale
Triple Bohlen-Pierce
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.
Publications
- Bohlen Pierce Scales for Guitar by Ron Sword, IAAA Press, UK-USA. First Ed: May 2009.
Instruments
- Bohlen Pierce guitar
- Clarinets
- Metallophone
- Electronic Organ
- Stredici
- Kalimba (Mbira)
- Pedal Steel Guitar
Links
Compositions
- A Mean Little Voice by Stephen Weigel
- Ask For It by Chris Vaisvil
- Links to available music written in BP at above website.
- Bohl-en Roll by Carlo Serafini (blog entry)
- Bohlen-Pierce electric guitar improvisation by Jean-Pierre Poulin
- Bohlen-Pierce "Stretched Chroma" Acoustic Improvisation by Ron Sword
- Reminiscences by Steven Yi
- Roll'n'Peace by Jean-Pierre Poulin
- Comets Over Flatland 1 by Randy Winchester
- Comets Over Flatland 2 by Randy Winchester
- Comets Over Flatland 3 by Randy Winchester
- Comets Over Flatland 4 by Randy Winchester
- Bohlen-Pierce Island audio by Chris Vaisvil
- Mesonic Atom by Chris Vaisvil
- Bending the Rules by Chris Vaisvil
- Bohlen-Pierce Canon by Kjell Hansen.
- Bohlen's Pierced Waltz by Chris Vaisvil
- The Complex Plane by Chris Vaisvil
- 120420 by Ralph Jarzombek