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Petr Kotik: Explorations in the Geometry of Thinking 

From the album S.E.M. Ensemble

One of the most fascinating and idiosyncratic exponents of musical minimalism, the Czech composer Petr Kotik has lived in the United States since 1969, when he emigrated at the invitation of Lejaren Hiller. Kotik quickly integrated himself into the American new music scene. Working closely with composers such as Frederic Rzewski and John Cage, he relished the proverbially American spirit of experimentation. “In America, there is a tendency to welcome surprises and unusual ideas with much greater openness to it than in Europe,” he noted. “That could be one of the attributes that separates America from Europe.”

Kotik’s mature style is marked by the polyphonic layering of melodic lines, dissonant yet mellifluous, and characterized by a slow, processional rhythmic pulse. Although clearly influenced by American minimalism, Kotik’s music often has an angular and cerebral tone far removed from the modal sweetness of John Adams or Philip Glass. While those composers were driven by an urge for renewed emotional directness, in Kotik’s hands the stripped-down gestures becomes a vehicle of “dispassionate objectivity,” in the words of Petr Bakla. (In this respect, his work could be compared to that of American composer Tom Johnson.) In addition to composing, Kotik leads the S.E.M. Ensemble, an important contributor to contemporary music whose releases include a one-of-a-kind recording of the complete works of Marcel Duchamp.

The process of chance is an integral part of my method, not something that stands separately. Chance operations I use have a direction and are partially controlled. I then take the result and proceed to work on my own. The way I compose could be called a game. It’s a kind of a dialogue between the results of my method and my reaction to it, intuitively correcting, editing and introducing other elements in a quasi-improvised way. This result can be further processed by the method, which can set off a chain of more intuitive interventions. 


Much of Kotik’s music uses modernist prose as its basis, creating striking parallels between tonal and linguistic patterning. His major work in this vein is the six-hour-long Many Many Women (1976-1978), based on Gertrude Stein's book of the same name. The piece also integrates contrapuntal techniques typical of medieval composers such as Perotin and Machaut

Explorations in the Geometry of Thinking, composed shortly thereafter, sets the prose of Buckminster Fuller's magnum opus Synergetics. The oracular proclamations of Fuller’s writing match up perfectly with Kotik’s architectural approach to vocal polyphony. The composer dismisses the notion that music can express or illustrate words, instead arguing that the two are governed by independent forms of structural logic: “For me the text and the music are two different entities.”

Music is expressing itself—music, nothing more and nothing less, just as everything else ultimately expresses itself, whether it is a stone, or a human being or a tree. […] Music invokes a situation that can lead to meditation; a personal, poetic and intellectual meditation. It is a field of sound, which we perceive in a time space. Music is not universal, it is always specific, and the ability to “understand” or navigate in this sound field requires education. A real education, that comes through one’s own initiative. 

Played 177 time(s).

November 09, 2012, 3:11pm

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Tom Johnson: VI3

From the album Rational Melodies (1982)

Using a variety of compositional techniques based on mathematical and algorithmic manipulations, the American composer Tom Johnson has devoted his career to exploring musical analogs to fractal self-similarity, first described in the mid-1970s in the groundbreaking work of Benoit Mandelbrot. One simple example of this kind of technique is to define a set of rules for replacing individual elements with sets of other elements, and then applying these rules repeatedly to create nested self-similar structures. An excellent overview of Johnson’s compositional techniques can be found in his paper "Self-Similar Structures in My Music: An Inventory," presented at IRCAM in 2006. Johnson has also described his methods in greater depth in a nearly 300-page tome entitled Self-Similar Melodies.

Johnson was a student of Morton Feldman, whose own highly idiosyncratic form of minimalism I have described elsewhere. You might not guess the master’s influence: while Feldman’s music is typically spare and laconic, Johnson’s is often playful and garrulous. Moreover, Feldman was famously dismissive of formalist and mathematical techniques of composition, advocating intuition above all.  But both composers shared the desire to create music free from the dominant Romantic/expressionist paradigm— to create, in Johnson’s words, “something more objective, something that doesn’t express my emotions, something that doesn’t try to manipulate the emotions of the listener either, something outside myself.” 



Excerpts from Symmetries, a series of graphic scores begun in 1979 and created with a musical typewriter

The pieces comprising the collection Rational Melodies are fascinating miniatures of algorithmic composition. Johnson’s music as a whole, while characterized by a systematic and rationalist approach, is aesthetically quite diverse. Nine Bells (1979) is based on the ritualized movement of the performer in a 3 by 3 matrix of hanging bells. The maniacally systematic Chord Catalog (1986) presents “all 8178 chords possible in one octave.” In Music for 88, which features pieces such as “Pascal’s Triangle” and “Euler’s Harmonies,” various numerical phenomena are demonstrated at the piano, with the idea being that one can “hear” the otherwise abstract principal at work. Here the didactic slant of the music gets a bit heavy-handed for my taste. Still, Johnson’s work contains some of the most fascinating investigations of algorithmic and formulaic compositional strategies of the last 30 years.

Rationality, or more precisely, deductive logic, has seldom been the controlling factor in musical composition. Composers are usually more interested in inspiration, intuition, feelings, self-expression. Lately, however, there has been a tendency for composers to give up individual control over every note, and rely on factors outside themselves. Pieces have been controlled by the wind, by chance, by the idiosyncrasies of tape recorders, or by unpredictable variations in electronic circuity, for example, and it seems to me that composing by rigorous adherence to logical premises involves a similar way of thinking.

Alongside his work as a composer, from 1972 to 1982 Johnson was also an influential music critic for the New York paper The Village Voice. His collected writings were published in 1989 as The Voice of the New Music, now available as a free download.

Played 239 time(s).

April 17, 2012, 2:29pm

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Louis Andriessen: Excerpt from De Staat (1976)

From the album De Staat

While the musical style broadly known as American minimalism comes in many flavors, from the cinematic ear-candy of Philip Glass to the playful psychedelia of Terry Riley and the symphonic bombast of John Adams, these various manifestations have in common a modal-diatonic approach to pitch organization and a tendency to eschew abrupt transitions in favor of gradually unfolding tone-patterns. American minimalism was intended (and in large part received) as a corrective to the overly “difficult” music of the mid-century avant-garde.

When minimalism made its inevitable appearance on the European continent, it took on a very different tone, one conditioned by the generally darker tendencies of European music in the postwar period. The premiere of Dutch composer Louis Andriessen's De Staat in 1976 signaled a radically new take on the possibilities of musical minimalism.  Jagged, angular, and suffused with lush dissonances that betray the composer’s debt to Igor StravinskyDe Staat pummels the listener with the brusque juxtaposition of highly differentiated textural blocks (Stravinsky again) played at a consistently breakneck pace. 

De Staat is written for an unorthodox ensemble heavily weighted toward winds and brass, plus the distinctive addition of electric and bass guitars. (Beginning in the early 1970s, Andriessen refused to compose for the conventional orchestra, which he saw as a symbol of the conservative musical establishment.) Four female singers intone snippets from Plato’s Republic concerning (ironically) music’s potential to disrupt the social order.



Played 149 time(s).

January 15, 2012, 10:24pm

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Karel Goeyvaerts: Composition No. 4 with Dead Tones (1952)

From the album The Serial Works (#1-7)

In this second installment of a series of three posts exploring the early productions of the WDR Studio for Electronic Music in Cologne, we hear a remarkable and little-known work by the Belgian composer Karel Goeyvaerts (1923-1993).  

Composed in 1952, but realized in sound nearly three decades later, Composition No. 4 comprises a basic sound material of four tones, identical in pitch, timbre, and duration with each appearance. (Hence the “dead tones” of the title.) Technically, these tones are what were called Tongemische, or “tone mixtures”— that is, artificially generated tones consisting of sine waves in non-harmonic proportions to the fundamental frequency. The only variation in the piece is in the duration of the silences between each iteration of the tones, which is altered according to serial procedures. As the interjections of silence between each tone gradually increase and decrease over the course of the composition, the four sonic layers of the piece are brought out of phase and back into phase again. The result is a remarkable phenomenon of motion in stasis, a slowly shimmering stillness that musicologist Hermann Sabbe has anointed the first ever piece of “process music.” For Sabbe, “Composition No. 4” is also an early example of conceptual art, being based on a simple generative idea that could be realized in any number of ways. (Goeyvaerts did not specify the pitch of the tones, only their duration and timbral quality.)

In the early 1950s, Goeyvaerts and Karlheinz Stockhausen carried on an intense theoretical conversation concerning the principles of serial composition. Although the two shared a deep fascination with the technique, they diverged aesthetically: Goeyvaerts distinguished his approach from Stockhausen’s, calling the German’s music “baroque,” and claiming that he based his composition on a preconceived sonic image. Goeyvaerts, by contrast, envisioned music as (in the words of Mark Delaere) “the objectification of a spiritual idea in a structure of sound.” This distinctly modernist form of musical mysticism can be traced to such varied sources as the medieval concept of numerus sonorus—music as “sounding number,” essentially Pythagoreanism made into compositional doctrine—and the vision of a static, painterly “neoplastic music” outlined by Piet Mondrian in the 1920s. Delaere has called Goeyvaert’s early works “the most abstract compositions ever written.”

Goeyvaerts (middle) with Luigi Nono and Stockhausen (c. 1950)

Played 171 time(s).

December 22, 2011, 11:52pm

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Henryk GóreckiConcerto pour clavecin et cordes, op. 40 (excerpt; 1980)

From the album Rhythm Plus (1990)

Here’s a piece of “power minimalism” from Polish composer Henryk Górecki, an interesting figure best known for his hugely successful Symphony No. 3 (1977), a mournful but relatively accessible composition that was re-released in 1992 and became a surprise hit, selling over a million copies. This piece was by no means representative of Górecki’s music, however, and his larger body of work remained heterogeneous and largely unknown.

The Concerto pour clavecin et cordes (Concerto for Harpsichord and Strings) is based on pulsating harpsichord figures and underlying string tones, both outlining a stark minor scale. The effect is overpowering, though unavoidably cinematic in association (thank you, Phillipp Glass). In its rough, punchy texture, this piece recalls the minimalist music of the Dutch composer Louis Andriessen, and perhaps points toward a distinctive European spin on what is generally regarded as an American phenomenon.

Górecki’s piece, like most of the others on this disc, was written for Elisabeth Chojnacka, a brilliant Polish harpsichordist who through her virtuosic playing and advocacy for new music has positioned herself as a veritable court musician of the European avant-garde. In addition to Górecki, composers such as Xenakis, Ligeti, Halffter, Ohana, Donatoni, and Bussotti have written pieces dedicated to her.

Played 159 time(s).

March 30, 2011, 12:03pm

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Johannes Ockeghem (attributed): Deo gratias

From the album Utopia Triumphans: The Great Polyphony of the Renaissance

Attributed to the Franco-Flemish composer Johannes Ockeghem (c. 1410-1497), a master of the byzantine art of Renaissance polyphony, Deo gratias is an extreme example of a kind of composition called a canon.  The underlying principle is the strict imitation of the initial melody by a number of subsequently entering voices. The composer must in fact write only one melody, but this melody must be formed so as to harmonically “agree” with itself when it is layered with its own iterations at various time intervals.  Writing a successful canon is an extraordinary test of compositional prowess.  Although the sound of such a piece is usually smooth and fluid, the compositional labor required to make this music is nothing short of herculean.

In Deo gratias, the chorus is broken up into four groups of nine voices, each in a vocal range corresponding roughly to the modern designations soprano-alto-tenor-bass. Each group has its own canon, introduced by an initial voice and then followed by the other voices in a gently accumulating cascade of sound.  The technical marvel of this piece is that each of the four canons is combined will all the others in various contrapuntal configurations.  The result is a lush, hypnotic web of sound that is strikingly suggestive of the late 20th-century “holy minimalism” of composers such as Arvo Pärt.

Played 220 time(s).

January 03, 2011, 8:32am

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