Picture of Clarence Barlow by Harald Fronzeck (©1996)
Clarence Barlow. Detail of a photograph by Harald Fronzeck (©1996)

Blue by sound: the microtonal legacy of composer and theorist Clarence Barlow

By Georg Hajdu

Composer Clarence Barlow passed away in June 2023 at age 77. He was noted for his pioneering work in computer music and computational music theory. He also laid the ground for musical conceptionalism and his own direction of spectralism. His exceptional humor (which included countless variations of his own name) was deeply rooted in his heightened sense for language and semantic ambiguity. Born in Calcutta on December 27, 1945, into a Catholic and English-speaking enclave, he was educated in Western classical music, and didn’t have any exposure to Indian classical music traditions before age 18. Trained as a pianist, Barlow started composing at age 11, discovering contemporary music at age 15 through the offerings of the local Goethe institute. With a knack for mathematics and astrophysics, he obtained a bachelor’s degree in natural science but also taught music theory at the Calcutta Conservatory until, in 1968, he moved to Cologne, Germany to study with Bernd Alois Zimmermann and, after his teacher’s death in 1970, with Karlheinz Stockhausen.

Cologne was a hotspot for the musical avantgarde at the time and his compositional interests fell on fertile ground. After completing his studies at the Cologne music school in 1972, he immersed himself in computer programming using the infrastructure at the Cologne Institute of Phonetics during nighttime when their system was not being used by the regular members of the institute. With his unique background as well as his keen knowledge of contemporary music practices, he embarked in 1975 on an ambitious journey: the composition of a 30-minute tonal piano piece by use of a computer. While computers had been employed for music composition since the 1950s and 60s (most prominently by Iannis Xenakis), his approach differed from previous practices in that he was searching for a profound understanding of the “substance” that music was made of.

On a bus trip through Anatolia in May of 1975, he sketched out the ideas which later would culminate in his piece Çoǧluotobüsişletmesi, completed in late 1978 and produced at IRCAM in 1980. In his remarkable thesis Bus Journey to Parametron, Barlow gave an account of the creative process that began with his sketches and led to the creation of the final score. A major achievement consisted in the formalization of meter and scale as the basis for rhythm, melody and harmony: He understood that in Western music meter and scales follow interdependent hierarchical principles. Yet, his approach was to be style agnostic and sufficiently universal to work independently from cultural preferences—style being an emergent property of his system rather than the other way around. To achieve this, he resorted to mathematics and the fields of psychoacoustics and cognitive psychology, often relying on his friends as test subjects to validate or falsify his theories.

Barlow captured the hierarchical nature of scales through rationalizing their pitch content. This method consisted of finding “tuning alternatives” for arbitrary cent values, deriving a harmonic-distance values from them and calculating an optimal tuning for the scale by considering all possible combinations. For a suitable harmonic-distance function, he reviewed existing approaches from Euler to Hindemith but deemed none of them satisfying. Therefore, he developed his own formula which he derived from prime factorization of integer numbers and called the indigestibility of a number.

Harmonic-distance values (which he referred to as harmonicity) were to be calculated as the reciprocal of the sum of the indigestibilities for the numerator and denominator of the ratio. His function also considers its polarity, by deriving the sign (i.e. plus or minus) from the difference of the respective indigestibility values. Barlow defines polarity as the tendency of an interval to establish itself as a tonic or serve as a harmonic attractor, as in the case of the just fourth (4/3) and the minor third (6/5). In the stochastic process which he applied to the composing of Çoǧluotobüsişletmesi and few other pieces between 1980 and 2010, weak intervals with positive polarity are favored over strong “anti-tonal” intervals with negative polarity.

The advantage of Barlows approach is that it works for any microtonal scale and yields predictions about the nature of the scale which is central to a generative system. Barlow used it in Çoǧluotobüsişletmesi where he tuned four of the black keys a quarter tone flat as well as in Otodeblu, a piano piece using a subset of 17EDO and Pinball Play for four clarinets in the Bohlen-Pierce scale.

I first met Clarence in 1982 a few years before entering the Cologne music school, when I was still a student of biology. He made a lasting impression on me, and I am hard-pressed to name another person whose life and work, friendship and teaching are as intertwined as with Clarence. His deep and early involvement with computers, his concept of music both as substance and meaning resonated with me and showed me a path into the future of music. 

Much of my research and compositional work was and still is inspired by him.

In July of 1990, Clarence Barlow and James Tenney met at the Darmstadt Summer Course. Larry Polansky and I were present when these two exceptional composers whose works are entrenched in the exact sciences, boundless experimentation and conceptualism sat down at a table and talked for hours noticing how much in common they had. Barlow invited Tenney to the Ratio Symposium which took place in December of 1992 at the Royal College of Music in The Hague. Barlow subsequently published the presentations in his Ratio Book. It also features their respective formulae: Barlow’s indigestibility and harmonicity functions as well as Tenney’s harmonic distance function (Figure 1). They have in common that they are mathematically either based on logarithms (Tenney) or on a logarithm-like function (Barlow). Yet they differ in the results they produce; and their choice might also be the result of (aesthetic) bias and by the fact that perception and cognition of pitch, melody and harmony depends on the integration of several mechanisms, either top-down (i.e. depending on former exposure) or bottom-up (i.e. based on immediate sensations) and that trying to capture these mechanisms will ultimately lead to different results.

Barlow’s indigestibility and harmonicity functions (top and middle) Tenney’s harmonic distance function (bottom)
Figure 1. Barlow’s indigestibility and harmonicity functions (top and middle) Tenney’s harmonic distance function (bottom)

My experience is that Barlow’s approach works better for linear melodic motion and polyphony while Tenney’s approach lends itself slightly better for (just-intonation) harmony and spectral music. It should also be mentioned that Paul Erlich derives his notion of harmonic entropy from Tenney (Figure 3), whereas my harmonic energy function is rooted in Barlow’s work, yet they both attempt to formalize the continuum of (in)stability in interval space (Figure 2).

Harmonic energy profile according to Barlow and Hajdu.
Figure 2. Harmonic energy profile according to Barlow and Hajdu.
Harmonic Entropy - Tenney

In 1986, Clarence embarked on a new project: the creation of a real-time environment for the generative approach he used in the composition of Çoǧluotobüsişletmesi which he dubbed Autobusk (Figure 4). It was to use the MIDI capabilities of the Atari ST series computers and supported microtonal tunings via the tuning tables of the DX 7 II and other Yamaha synths.

Figure 4. The graphical user interface of Autobusk, Barlow’s real-time generative program

The first microtonal piece he composed with Autobusk was Otodeblu, a name that like many of his titles works in several languages (in Japanese it’s supposed to mean “turned into blues by sound”: 音でブルース). This piece was included in a collection of pieces for two pianos in 17EDO which I initiated and published in 1992, the pianos having the same white keys but differing black key so they can represent all 17 tones. Barlow was particularly interested in the blues scheme with its I-IV-I-V-IV-I progression and the neutral thirds that the first of the two pianos afforded. He composed a few more pieces with his system (e.g. Pandora, the amazing piano cadenza of his orchestra piece Orchideae ordinariae, for which he daisy-chained two Autobusk instances) and made improvements to his software until 2000, seven years after the last Atari ST 1040 computer was produced. This sealed Autobusk’s fate as it became increasingly dependent on Atari emulators for MacOS and Windows, and in 2008, Clarence helped me to take over the development in Max/MSP. I redesigned the software from scratch and renamed it DJster (as a nod to his notion of indigestibility, Figure 5). In its current real-time and non-real-time incarnations for Max and Ableton Live, it supports arbitrary tunings as well as meters and was used extensively in various projects by Hamburg-based composers.

The graphical user interface of DJster, a Max/MSP port (and further development) of Autobusk
Figure 5. The graphical user interface of DJster, a Max/MSP port (and further development) of Autobusk

In his piece Pinball Play for four Bohlen-Pierce clarinets which I had the good fortune to commission for the 2010 Bohlen-Pierce symposium in Boston, Clarence used his harmonicity formula to determine the stability for the tones in the BP scale, identifying the BP eighth (1170 cents or 49/25) as an out-of-tune octave (2/1). He then performed multi-dimensional scaling of the harmonic-distance profile obtaining a 2-dimensional arrangement of the scale of which he made the notes bounce off as they were balls in a pinball machine, hence the title (Figure 6 and 7). He wrote about the composition process: “As the main part of the compositional process, four straight lines are repeatedly projected into the square, each from a different side. If a line meets one of the notes of the scale, the note is sounded and the line is generally deflected to a spatially nearby note, which is also sounded. This process is repeated until a path is re-traversed or the line exits from the diagram.”

Figure 6. Multidimensional scaling of the rationalized Bohlen-Pierce pitch set used in Pinball Play.

Barlow’s treatment of the 1170ct interval as an octave is where I begged to differ in my own use of the scale: I solved the conundrum by eliminating prime 2 from the harmonic-distance calculations allowing me to treat the interval as a harmonically distant one.

The first eight measures of Pinball Play, a piece for four Bohlen-Pierce soprano clarinets in fingering notation. ©Barlow 2010
Figure 7. The first eight measures of Pinball Play, a piece for four Bohlen-Pierce soprano clarinets in fingering notation. ©Barlow 2010

Clarence Barlow become professor of composition at the University of California, Santa Barbara the same year (2006) James Tenney passed away—a mere 100 km from Cal Arts where the latter held the same position. He retired in 2019 and moved to Barcelona, Spain briefly working for the Catalonia College of Music (ESMUC). All but cut off from social life by the COVID-19 pandemic, he managed to keep in contact with his large circle of friends, former students and admirers via email. One of his last projects was a collaboration with Purva Gujar-Kale on the translation and transcription of Vishnu Narayan Bhatkhande’s collection of ragas into English language and Western notation.

Further reading

By Clarence Barlow:

Bus Journey To Parametron (all about ‘çoğluotobüsişletmesi’), Feedback Papers Vol.21-23, 135 pages, Feedback Studio Cologne, W. Germany, 1980

On Musiquantics – English translation of: Von der Musiquantenlehre (2008), 130 pages, Report No. 51 of the Musicological Institute / Musikinformatik & Medientechnik of the University of Mainz, ISSN 0941-0309.

Two Essays on Theory, pp. 44-60, Computer Music Journal Vol. 11 No. 1/MIT Press Cambridge MA, 1987.

THE RATIO BOOK, Editor C. Barlow 350 pages, Feedback Papers Vol. 43, Feedback Studio Cologne, Germany (incl. C.Barlow article On the Quantification of Harmony and Metre, pp.2-23)

AUTOBUSK Manual, Report No. 44 of the Musicological Institute/ Musikinformatik & Medientechnik of the University of Mainz, Germany, ISSN 0941-0309, 2001.

By Georg Hajdu

Low Energy and Equal Spacing – the Multifactorial Evolution of Tuning Systems. Interface, 22, 1993, pp. 319-333.

17 Töne. A collection of compositions in 17-tone equal temperament by C. Barlow, C.Bauckholt, G. Hajdu, C.J. Walter, and C. Wilkens. Georg Hajdu (editor), 1992.

Resurrecting a Dinosaur — the adaptation of Clarence Barlow’s legacy software AUTOBUSK, Proceedings of the TENOR conference. 2016.

Syntactic Considerations on the Transcription of and Modulation Between Microtonal Scales, in: Mikrotöne: Small is Beautiful (edited by Agustin Castilla-Águstin). Mackingerverlag, 2021.