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 == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+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] | ||
Revision as of 07:03, 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 | |
- Bohlen Pierce website
- Wikipedia Bohlen-Pierce scale
- Bohlen-Pierce Scale Research by Elaine Walker
- Sword, Ronald. "Bohlen Pierce Scales for Guitar" IAAA Press, UK-USA. First Ed: May 2009.
- Intervals of BP
- Relationship between Bohlen-Pierce and octave-ful temperaments
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.
Physical instruments tuned to the BP scale
Metallophone
Electronic Organ
Stredici
Kalimba (Mbira)
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