The early history of BP
"I think he was investigating other things"
A collection of BP-related literature
Early compositions in BP
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 1970's 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 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 twelve tone steps, sometimes equal, sometimes not, filling the framework of an octave. Why 12 steps, and why the octave frame?

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 the 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 framework 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 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 luckily he got 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]).

Heinz Bohlen in 1973, tinkering with the transcription of a Christmas carol into his "13-Step Scale" (now BP)

A few months later a paper was published that contains the equal-tempered version of the BP scale, next to numerous 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, now living in California, he finally lifted the veil [16].

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 in the following 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 shelve his new scale for a while, intending to deal with it again after his retirement.

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 and psycho-acoustical education, 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 later 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 had not Enrique Moreno [11] accidentally met him in 1995.

...................
Kees van Prooijen (Japan 2006)...........John Robinson Pierce, 1910 - 2002
(Photography stolen from Kees' web site)....(Picture courtesy of CCRMA, Stanford, CA)

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.

[1] Bohlen, Heinz: Manuscript, untitled, undated, pencil, 23 pages (in German).
Hamburg, early 1972.
The paper describes the derivation of the 13-step scale (later BP) in both a just and equal-tempered form, in conformance with two basic, independent principles: consonance with combination tones, and approximate equidistance of scale steps. The presentation comprises 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.
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]).
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.
In this paper (manuscript from Dec. 1975, submitted for publication in Sept. 1976) the author emphasizes the influence of combination tones 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).

[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 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 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.

(For a comprehensive list of literature on all aspects of microtonality see Manuel Op de Coul's bibliography.)

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 [part 1] / [part 2] (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)
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.

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 , 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

The reception of the concert is mirrored in an article of The Ontarion.

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

More details (in German) regarding this concert, including URLs for real-time-streaming listening to the pieces performed, may be found here.

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