On this
page:
The early history
of BP
"I think
he was investigating other things"
A collection of BP-related
literature
Early BP compositions
The first live BP
concerts
The early history of BP (Not really important; just reported here for those who like to know when and why.)
BP was born of plain curiosity. In the early 1970s Heinz Bohlen¹, a microwave electronics and communications engineer lacking any serious musical education, happened to meet a group of talented, ambitious students of the Hamburger Musikhochschule (among them Christian Brunnert, Helmut W. Erdmann, Clemens Kühn and Peter W. Schatt) and their composition professor, Diether de la Motte. They found him useful, despite his musical handicap, because he was prepared to make free-of-charge recordings of their concerts. These concerts embraced the whole spectrum of Western music, from Gregorian chants to musical happenings, a frequent feature in those days. Listening to this music during rehearsals and recordings, the engineer became curious: The material used to create all this wealth seemed to be comprised in a single scale that consisted of 12 tone steps, sometimes equal, sometimes not, filling the framework of an octave. Why 12 exponentially growing steps, and why the octave compass?
At first Bohlen thought that it would be easy for him to get profound answers to his questions: he had just to ask his professional friends, hadn't he? But he soon found out that most musicians are much more interested in the use of their material than in its origin, and the answers he got didn't satisfy him. His questions turned into a quest that finally was given a direction by Helga de la Motte-Haber, who pointed him at Paul Hindemith's book "Unterweisung im Tonsatz" ("The Craft of Musical Composition"). Reading this book he gained a first understanding of tonality, but he also soon understood that the great composer and teacher was not a physicist, and that his conclusions regarding consonance and harmony were certainly correct, however, for all the wrong reasons. At this point he became quite obsessed with his investigation. He started raiding music libraries, reading through almost everything that was available on his subject. Finally, in early 1972, he found the answer he had been looking for, at least as far as he was concerned. Combination tones, it seemed to him, gave the major triad (4:5:6) an almost unique "gestalt" appearance. This and the octave as a framework was all that was needed; the 12-tone scale (in just tuning) and its diatonic modes rose from this foundation inevitably and as the only possible solution. He toyed a little around with his find and, replacing the traditional triad by a novel 3:5:7 alternative, stumbled over something stunning: There appeared a just scale of thirteen almost equal steps within the compass of the perfect twelfth. It didn't contain the octave, but it was certainly harmonic. Conversion into an equal-tempered scale with again thirteen tone steps was possible with a minimal defect. It seemed to him that this scale, and especially its diatonic modes, shared a certain duality with the traditional Western scale, that it might be useful for an alternative kind of harmonic and even tonal music...and thus he got hooked again.
Rather to explain to himself what he had found than wishing to share it with others at this stage, he jotted down a few notes (see [1] ) and began to think about realization of what he had started to call the "13-Step Scale" [2]. He then set out to find something that would let him hear his novel sounds. Synthesizers were still rare at that time and out of his financial reach. Thus he resorted to building an electronic organ. It turned out that he had to solve a number of technical problems, but he was lucky enough to get considerable assistance from fellow engineers. It nevertheless took him the better part of a year to finish the instrument. In between, he wrote an abstract that he sent out to a selected circle of cognizant people [3]. The organ turned out to be worth the effort. Despite primitive sound generation, the acoustic results made him confident that he had found something valuable enough to share it with practicing musicians. The organist Andreas Rondthaler, on the occasion of a visit in 1974, had little difficulties in finding attractive chords on this unusual instrument, and on this memorable day became the first ever person to play real music in the novel scale. Encouraged, Bohlen sent out a second version of his 1972 abstract (1974, [3]), and in 1975 he finally wrote a comprehensive paper on the subject, published 1978 in a renowned German acoustics magazine [5] (English version: [19]).
The resulting echo from the musical establishment to Bohlen's publications varied between cautious acceptance and outright objection. A dialogue, discussing the merits or otherwise of the scale, developed over the years. Jürgen Meyer (PTB Braunschweig), in May 1973, happened to be the first professional to comment on the 13-Step Scale. Correspondence continued until about 1978 with Rudolf Haase (Hans-Kayser-Institut, Vienna), Heinrich Kuttruff (RWTH Aachen), Fridemar Pache (Dortmund University), Hans-Peter Reinecke (Federal Institute for Music Research, Berlin), Martin Vogel (Bonn University), Rudolf Wille (TH Darmstadt), and especially Ernst Terhardt (TU Munich). But the response remained rather restricted to this circle, and to the German speaking zone of Europe. European microtonalists, scattered individuals at that time anyway, did not react. The microtonal community in the US did not become involved either, simply because German literature is scarcely read here; and vice versa, since the Internet was not invented yet, Bohlen was not even aware of the existence of that community. He was not discouraged, however. Due to an increasing workload in his professional life, he decided to mothball his new scale for a while, intending to deal with it again after his retirement.
A few months after Bohlen's 1978 article, a paper was published that contains the equal-tempered version of the BP scale, among several other possible equal-tempered scales, in a rather encoded form [6]. Its author, Kees van Prooijen², a Dutch software engineer and music theorist, had independently arrived at this result when searching for equal-tempered scales that satisfy consonance with higher harmonics, but he decided to keep it concealed until further investigation. Only many years later, then living in California, he finally lifted the veil [16].
Though published in a worldwide distributed acoustics magazine, the "13-Step Scale" gained little recognition until about six years later something amazing happened. Another microwave electronics and communications engineer, this time one with extensive musical, acoustical and psycho-acoustical background, discovered the same scale again: John Robinson Pierce³, "Father of the Communications Satellite", creator of the "Pierce (electron) Gun" and "Godfather of the Transistor", working as a professor of music at Stanford University in California after an engineering career that earned him fame. Together with Max V. Mathews and others, he published his discovery in 1984 [7]. Learning finally [8] about Bohlen's earlier publication, the authors dubbed the new scale the "Bohlen-Pierce scale" [9], [10]. That name stuck. (It was a reluctant acknowledgement, though. Pierce, understandably intrigued with his discovery, continued to refer to it in private conversations as the "Pierce scale" throughout the rest of his life.) Published this time in the United States (and in English, naturally) the find drew considerably more attention. The first compositions in "BP" appeared, and theorists started to include the scale in their investigations. In 1993 Bohlen, too, moved to California, but he would have remained ignorant regarding this development for quite a while still had not Enrique Ignacio Moreno [11] accidentally met him in 1995.
For almost a decade between Bohlen's arrival in California in 1993 and Pierce's death in 2002, and by sheer accident, the three discoverers of the novel scale lived within a few miles from each other in the San Francisco Bay Area. But only van Prooijen and Bohlen used this chance and shared their stories of the scale in a single, but very amicable meeting at a cafe in Los Altos in 1996(?). Pierce, probably already severely ill at the time Bohlen learned about his contribution to the scale, did not respond to repeated suggestions to chat about BP. Thus in hindsight it turns out that it was pure irony of fate that Bohlen and Pierce had a vivid phone discussion on a microwave issue in autumn of 1993, with obviously neither of them realizing that they shared something even more interesting than the subject of their conversation that day.
![]() |
![]() |
![]() |
in 2006 (Snapshot taken by Hannelore Bohlen) |
Japan 2006 (Photography stolen from Kees' web site) |
1910 -2002 (Picture courtesy of CCRMA, Stanford, CA) |
None of the three discoverers ever intended to earn a penny from the BP scale, and consequently they didn't. Their engineering profession had to take care of their financial needs, but even this face of the coin shows some funny similarities.
1) b. 1935,
Krefeld, Germany
2) b. 1952, The Hague, Netherlands
3) b. 1910, Des Moines, Iowa, d. 2002, Palo Alto, California,
U.S.A.
A collection of BP-related literature (sorted by dates)
There is a whole host of publications available on Bohlen-Pierce meanwhile. The list below is restricted to those written before 2010, and it is in no way considered comprehensive. (For a comprehensive list of literature on all aspects of microtonality see Manuel Op de Coul's bibliography.)
[1] Bohlen, Heinz: Manuscript, untitled,
undated, pencil, 24 pages (in German). Hamburg, early 1972.
Original archived at Huygens-Fokker Foundation (Stichting
Huygens-Fokker), Amsterdam.
The paper describes the derivation of the 13-step scale (later
BP) in both just and equal-tempered form, in conformance with
two basic, independent principles: consonance with combination
tones, and approximate equidistance of scale steps. The notes
comprise a 13-step chromatic and four 9-step diatonic versions.
[2] Bohlen, Heinz: Die Bildungsgesetze
des 12-stufigen Tonsystems und ihre Anwendung auf einen Sonderfall.
Manuscript, ink, 50 pages, Hamburg, July 1972.
Original archived at Huygens-Fokker Foundation (Stichting Huygens-Fokker),
Amsterdam.
Mainly an expanded and refined version of [1], containing also
first considerations of realization essentials (tone names, notation,
plans for an electronic organ).
[3] Bohlen, Heinz: Versuch
über den Aufbau eines tonalen Systems auf der Basis einer
13-stufigen Skala.
Manuscript, first version, typed, 7 pages, Hamburg,
Dec. 1972.
Manuscript, second version, typed, 9 pages, Hamburg, July 1974.
(Referenced in [4]).
Originals archived at Huygens-Fokker Foundation (Stichting Huygens-Fokker),
Amsterdam.
These are
mainly abstracts of [2], intended to inform a selected readership
about the 13-step scale.
[4] Wille, Rudolf: Mathematik und
Musiktheorie.
Preprint, Technische Hochschule Darmstadt, Aug. 1975.
Musik und Zahl, Verlag für systematische Musikwissenschaft
GmbH, Bonn-Bad Godesberg, 1976, pp. 233-264.
The paper
raises the question: What can today's mathematics do for music
theory? It refers to Bohlen's 13-step scale as to one of the open
issues in the theory of harmony.
[5] Bohlen, Heinz: 13 Tonstufen in der Duodezime.
Acustica, vol. 39 no. 2, S. Hirzel Verlag, Stuttgart, January
1978, pp. 76-86.
Manuscript December 1975, original archived at Huygens-Fokker
Foundation (Stichting Huygens-Fokker), Amsterdam.
In this
paper (submitted for publication in Sept. 1976) the author emphasizes
the influence of combination tones on the gestalt impression of
intervals and hence on scale generation, using the 13-step scale
as an example. (A translation into English is listed under [19].)
[6] Prooijen, Kees van: A
Theory of Equal-Tempered Scales.
Interface, vol. 7 no. 1, Swets & Zeitlinger B.V., Lisse, June
1978, pp. 50-51.
The paper
(submitted for publication in Febr. 1978) describes "an attempt
to construct equal-tempered scales proceeding from the harmonic
constitution of musical sounds". The possible division of
the third harmonic of the base tone (the twelfth) into 13 equal
steps appears two times in this mathematical treatise and marks
an independent discovery of the scale.
[7] Mathews, Max V., L. A. Roberts and
John R. Pierce: Four
New Scales Based on Nonsuccessive-Integer-Ratio Chords.
J. Acoust. Soc. Amer. 75 (1984), S10(A).
The paper
introduces, amongst others, a scale called P3579 which, though
the authors do not know this, is identical with one of Bohlen's
diatonic versions of his 13-step scale.
[8]
Mathews, Max V., John R. Pierce and L. A. Roberts: Harmony
and New Scales.
Harmony
and Tonality, Royal Swedish Academy of Music, Editor J.
Sundberg, No. 54 (1987), pp. 59-84.
This paper
marks the time that the authors became aware of Bohlen's earlier
publication (see page
66).
[8a]
Mathews, Max V. and John R. Pierce: The
Acquisition of Musical Percepts with a New Scale.
Report No. STAN-M-40, Department of Music, CCRMA, July 1987.
Text of
a proposal submitted to the National Science Foundation for research
to study long-term learning of high-level musical concepts using
the Bohlen-Pierce scale.
The new denomination appears in this publication for the first
time.
[9]
Mathews, Max V., John R. Pierce, A. Reeves and L. A. Roberts:
Theoretical and Experimental Explorations of the Bohlen-Pierce
Scale.
J. Acoust. Soc. Amer. 84 (1988), pp. 1214-1222.
Contains
the description of a critical-bandwidth dissonance model and of
consonance ratings of both "major" and "minor"
BP triads.
[10] Mathews, Max V. and John R. Pierce:
The
Bohlen-Pierce Scale.
Current Directions in Computer Music Research, The MIT Press,
Cambridge/MA-London, 1991, pp. 165-173.
This paper
deals with the acoustical impressions of a 9-step diatonic BP
version on both musicians and non-musicians and the subsequent
ratings of harmony and chord similarity.
[11] Moreno, Enrique Ignacio: Embedding
Equal Pitch Spaces and The Question of Expanded Chromas: An Experimental
Approach.
Dissertation, Stanford University, Dec. 1995, pp. 12-22.
In a critical
disputation of [5], [7] and [9] the author comes to the conclusion
that "despite the problems with the logic of Mathews' and
Pierce's articles describing the Bohlen-Pierce scale, we will
try to show why Bohlen's and Pierce's implied belief in the scale's
ultimate potential for cognitive coherence turns out to be a profound
and correct intuition".
[12] Sethares, William: Tuning, Timbre, Spectrum, Scale.
Springer-Verlag London, 1998, pp. 57, 102-104.
The special
suitability of instruments "which act like tubes open at
a single end" (for example pan flutes and clarinets) for
the BP scale is documented. "The Bohlen-Pierce scale really
is fundamentally different, and requires a fundamentally new music
theory....This theory is not trivial or obvious."
[13]
Reyes, Juan and Cynthia Lawson: Vientos de Los Santos Apóstoles.
Web
page, 2000.
[14]
Benson, David: Mathematics and Music.
Academic course published on the Web, © Dave Benson 1995-2000,
pp.140-145.
The course
contains, next to a general discussion of BP, the development
of a Pythagorean BP version.
[15]
Krantz R.J. and J. Douthett: Construction and Interpretation
of Equal-Tempered Scales Using Frequency Ratios, Maximally Even
Sets, and P-Cycles.
J Acoust Soc Am 2000 May; 107 (5 Pt 1): pp. 2725-2734.
Applies
a formalism, developed for the design of equal-tempered scales,
to BP.
[16] Prooijen, Kees van: 13 tones in the 3rd harmonic.
Web
page, 2000.
This website
introduces 7-step diatonic versions of BP, as opposed to the 9-step
diatonic BP versions of both Bohlen and Pierce.
[17]
Walker, Elaine: The Bohlen-Pierce Scale: Continuing Research.
Web Page, 2001.
Contains
four new 9-step diatonic BP scales and listening test experiments
on issues like harmonic movement, finality and key modulation
of BP chord progressions and compositions.
[18]
A
Non-Traditional Scale Option
Web Page,
2001.
Describes
the use of the BP scale in the therapy of patients with implants
in the cochlea.
[19]
Bohlen, Heinz: 13
Tone Steps in the Twelfth.
Acustica,
vol. 87 no. 5, S. Hirzel Verlag, Stuttgart, Sept./Oct. 2001, pp.617-624.
This is
a word-by-word translation of [5] into English. No attempt has
been made to correct any idiosyncrasies or errors.
[20]
Hajdu, Georg: Überlegungen
zu einer neuen Theorie der Harmonie
Mikrotöne und mehr, Hrsg. Manfred Stahnke. Schriftenreihe:
Musik und, Band 8, Weidler Verlag, Berlin, 2005, pp. 165-187
[21]
Hajdu, Georg: Research and Technology in the Opera Der Sprung
Nova Acta Leopoldina, 92 Nr. 341, 2005
[22]
Loui, Psyche, David Wessel and Carla Hudson Kam: Acquiring
New Musical Grammars: a Statistical Learning Approach
Proceedings of the 28th Conference of the Cognitive Science Society,
2006
Examines
the ability of humans to acquire knowledge via passive exposure
to a new musical system, in this case BP.
[23]
Benson, David: Musical
scales and the Baker's Dozen
Matilde,
Nyhedsbrev for Dansk Matematisk Forening, Nr. 28, September 2006,
pp.15-16
Investigates
what happens when abandoning the octave.
[24]
Loy, Gareth: Musimathics, volume 1
The MIT Press, Cambridge/MA-London, 2006, pp. 86-92
The book,
dedicated to the memory of John R. Pierce, presents a mathematics-based,
detailed description and discussion of the BP scale.
[25]
Loui, Psyche and David Wessel: Learning and Liking an Artificial
Musical System: Effects of Set Size and Repeated Exposure
Musicae Scientiae, vol. 12(2), 2008, pp. 207-230
[26]
Loui,Psyche, Elaine H. Wu, David L. Wessel and Robert T. Knight:
A
Generalized Mechanism for Perception of Pitch Patterns
The Journal of Neuroscience, vol. 29(2), 2009, pp. 454-459
Sometimes
the question is asked: "What does music using the Bohlen-Pierce
scale sound like?"
John Pierce said about BP: "You can write attractive music
in it, but a good composer can write attractive music with any
sounds...", and he is certainly right in so far as BP provides
just novel musical material. How it sounds depends on imagination,
inventiveness and skill of the composer. The samples listed below
in this and the following section bear witness to that, beyond
any theorizing.
A
composer attempting to write a piece using the BP scale faces
two additional challenges beyond those he/she would have to deal
with anyway:
· There is so far little theoretical support when being
confronted with harmonic and/or tonal considerations, and
· the available range of instruments, except synthesizers,
is growing but still small.
Of the early compositions ("early" is here defined as
composed by approximately the year 2000) the following, most probably
only a minority of the existing ones, have come to the attention
of the caretaker. They are listed here by composers in alphabetical
order.
Jon Appleton: Eros Ex Machina (1987)
Recorded
on a CD that contains 88 sound examples discussed in the book
Current Directions in Computer Music Research, Editors
Max V. Mathews and John R. Pierce (see Literature [6] ). The CD
and the annex of the book describing the sound examples are available
from Department GRLiterature,
The MIT Press
55 Hayward Street
Cambridge, MA 02142, USA
(The code for the CD is MATCCD 0-262-63121-0)
Richard
Boulanger: I Know of No Geometry (1988/89)
For Radio
Baton.
Richard
Boulanger: Solemn Song for Evening (1990)
For soprano
and Radio Baton. Lyrics after Herrmann Hesse, translated by Marjorie
Mathews. There exists a CD recording with Maureen Chowning, soprano,
and Richard Boulanger, Radio Baton. Lyrics.
Charles
Carpenter: Frog à la Pêche (1994) [44:31]
Charles Carpenter: Splat (1996) [46:00]
2 full-size CDs entirely dedicated to BP. Charles Carpenter, K2000
and K2500 synthesizers; Ben Simborski, MIDI drum controller. A
review that is very much in accord with the general attitude to
BP can be found here. The CDs are available
from amazon.com and from:
Charles
Carpenter
P.O. Box 205
Andover, NH 03216, USA
Georg
Hajdu: Ich kannte sie, Herr Kollege (1999) [4:00]
Wolfgang Tiemann, tenor, and Hans Hermann Jansen, tenor. The first
scene of Georg Hajdu's opera Der Sprung, describing a dialog
between two university professors who are the victims of a shooting,
is written in BP. The composer explains: "As this scale,
not having any octaves, is an intellectual achievement in itself,
it symbolizes the abstract, academic world of a university department."
A CD, containing the whole opera, is distributed by NRW Vertrieb.
Herman
Miller: The Bent Vortex [0:20]
Herman Miller, synthesizer. A
study, only available from the composer.
Herman
Miller: Warped Canon in BP (just and tempered) [4:56]
Herman Miller, synthesizer. This is part of Miller's exercise
to present Pachelbel's Canon in various tunings.
Mats
Öljare: Blue Rondo à la Thai (2001)
Mats Öljare,
synthesizer. Available as a MIDI
file.
Joseph
Pehrson: Beepy (2001) [6:19]
Joseph
Pehrson,
synthesizer.
Kees
van Prooijen: Odd Piano (2000)
Kees
van Prooijen,
synthesizer. Written on July 8, 2000 on the occasion of George
Antheil's
100th birth anniversary.
Ami
Radunskaya: A Wild and Reckless Place (1990) [8:33]
Composed for electronic cello and Radio Baton. Amy Radunskaya,
electronic cello, and Max Mathews, Radio Baton. Available on CD
(CRC 2190) from
Centaur
Records, Inc.
CDCM Computer Music Series
Volume 15 (The Virtuoso in the Computer Age - V)
Alyson
Reeves: Minuet
Alyson Reeves: Canon 4
Recorded
on a CD that contains 88 sound examples discussed in the book
Current Directions in Computer Music Research, Editors
Max V. Mathews and John R. Pierce (see Literature [6] ). The CD
and the annex of the book describing the sound examples are available
from
Department GRLiterature,
The MIT Press
55 Hayward Street
Cambridge, MA 02142, USA
(The code for the CD is MATCCD 0-262-63121-0)
Juan
Reyes, Cynthia Lawson: Vientos
de Los Santos Apóstoles
Juan
Reyes:
"It is more of a sound installation but I still consider
it a composition. The idea is having several phrases in CD indices
for every pitch class of the Bohlen-Pierce scale. When the listener
comes he starts combining the phrases and thus making the composition.
The aim is creating a virtual organ environment taking advantage
of the harmonics of the flute or pipe sound."
Juan
Reyes: ppP (1999-2000) [8:29]
Juan Reyes: "ppP, in its concert version, is an algorithmic
composition for traditional acoustic piano and modeling of the
piano. This piece uses a computer model of the piano (developed
by Scott Van Duyne at CCRMA) in an unusual tuning (Bohlen-Pierce)
as contrast and complement to the real instrument on stage."
Juan
Reyes: Chryseis [10:06]
for BP-pitched Scan Synthesis.
A CD containing ppP and Chryseis is available from
the composer.
Curtis
Roads: Purity (1994)
[7:13]
Track 4 on disc 2 of CCMIX
Paris
(New electroacoustic music from Paris), Mode Records 98/99
Elaine Walker: Stick Men (1992) [7:20]
Elaine Walker: 1 - rx^2 (1992)
Elaine Walker: Space Time (1994) (19tet and BP)
Elaine Walker: The Building (1994) (19tet and BP)
Elaine Walker: Big Bang (2000)
Elaine
Walker: Love Song
Elaine
Walker ,
soprano and synthesizer (Stick Men, 1 - rx^2, Space Time, The
Building), synthesizer (Big Bang). Stick Men, Space Time and The
Building can be found on Elaine Walker's CD "ZIA v 1.5",
Big Bang on "Space Elevator Music". Both CDs are available
from:
Elaine Walker
1051 West Paseo Way
Tempe, AZ 85283, USA
Randy
Winchester: Comets Over
Flatlands.
Randy
Winchester,
synthesizer.
For more microtonal recordings, see Manuel Op de Coul's discography.
Footnote
Actually,
the
first
ever BP composition
was attempted by Heinz Bohlen, and that certainly doesn't come
as a surprise. However, Bohlen never would have dared to consider
himself a composer. Thus his little exercise is mentioned here
out of competition.
The first live BP concerts
Early
on already single Bohlen-Pierce compositions have been presented
live here and there in concerts, predominantly by Elaine Walker
and Richard Boulanger and in Georg Hajdu's opera
"Der Sprung". But it took many years and the creation
of acoustic BP clarinets by Stephen Fox, as instigated by Georg
Hajdu, before events could happen that could justly be called
live BP concerts.
The
first one took place on March 20, 2008, at the University of Guelph
(near Toronto, Canada).
Tilly Kooyman and Stephen Fox (both playing Bohlen-Pierce
soprano clarinets) and Todd Harrop (percussion and electronics),
all founding members of the group tranSpectra, performed
among traditional pieces:
1. Wanderer (for two
BP clarinets) [4:10] by Owen Bloomfield
2. Calypso (for two
BP clarinets, percussion and electronics) [8:24] by Todd Harrop
Only a short time later, on June 13, 2008, the next live Bohlen-Pierce
concert followed, this time at the Hochschule für Musik und
Theater in Hamburg (Germany), as a presentation of STUDIO 21
für aktuelle Musik.
The performers were Anna Christina Bardeli and Nora-Louise
Müller (both BP soprano clarinet and traditional B clarinet),
Victoria Reich (percussion), Xiaorui Hao (viola)
and Andrej Koroliov (synthesizer), playing among traditional
pieces:
1. Die Umkehrung der Mitte (for two BP clarinets, viola, marimba
and vibraphone) [6:54] by Peter Michael Hamel
2. The "Bird People" of St. Kilda (for two BP clarinets)
[9:23] by Manfred Stahnke
3. Pas de deux (for one BP clarinet, one B clarinet and electronics)
[8:56] by Sascha Lino Lemke
4. Night Hawks - dark scene for two clarinets (for one BP clarinet
and one B clarinet) [6:18] by Fredrik Schwenk
5. Beyond the Horizon (for two BP clarinets and BP-tuned synthesizer)
[7:17] by Georg Hajdu