Modern Music and After – Part 02
Regarding various techniques in the application of serialism, Boulez “obtained his duration series by applying numbers to the pitch series, and then translating all the other serial forms into number sequences by using the same pitch-number equivalences: thus the retrograde inversion B-F-C-Bb-A-…translates as 12-11-9-10-3-…Boulez also arranged the number sequences- twelve for the prime forms, twelve for the inverted forms (retrogrades can be simply read off backwards)- in two twelve-by-twelve squares, and obtained series of dynamic markings by reading the squares diagonally and interpreting the numbers on a scale from 1 = pppp to 12 = ffff. Structures Ia is quite simply a presentation of the forty-eight forms of the pitch series, each with a different form of the duration series (so that pitches do not always have the same durations, as happens in the Mode de valeurs and generally within each major section of Kreuzspiel), and each with a particular dynamic level and attack marking.
Stockhausen, the composer of Kreuzspiel, followed similar techniques as Boulez. “Both composers see a need to generalize the serial principle, but for Stockhausen this entailed deriving single, through-composed forms from the basic ideas…whereas Boulez was concerned to establish the foundations of a musical language, rules of musical grammar and vocabulary that composers could use to write scripts that would be their own.”
All of these ideas were somewhat philosophical, since the performances of these works by live musicians proved to be a challenging and somewhat subjective feat. What they really needed were the computer tools we have readily available today in order to accomplish the accuracy they were imagining. They didn’t have these available, so many of their early experiments were not as successful as they had hoped. “If rhythmic serialism was fraught with difficulties, then the serialization of timbre presented still more intractable problems…One had to be able to ‘tune’ timbre, to control it.” Stockhausen focused his attention on experimentation with such things as “the conversion of a complex event into a single sound, or the treatment of duration as a variable with the same capacity for complex relationships as pitch.” All of this is readily done on today’s computers and DAWs (Digital Audio Workstations). We teach students in our music school in Odessa, Texas how to use Digital Audio Workstations.
In fact Stockhausen was imagining and working towards what ultimately would become known as the Keyboard Synthesizer, common to all performers today. “A new musical architecture demanded new material, not refashionings of the old. The work of Helmholtz and Fourier had suggested that any sound could be analyzed as a collection of pure frequencies, of sine tones, and this was something that Stockhausen thought he had confirmed, in analyzing instrumental sounds in Paris. So it seemed reasonable to suppose that the process could be reversed, that timbres could be synthesized by playing together a chosen group of sine tones at chosen relative dynamic levels. One could thereby form a repertory of artificial timbres that were related in defined ways, and therefore suited to serial composition. This Stockhausen tried, working with a sine-wave generator at the postal headquarters in Paris, but the practical problems were insuperable. Instead, in December 1952, he turned to using initial moments from prepared piano sounds in his first electronic composition, the Etude.” The first digital synthesizers began to come out in the 1970s, a couple decades later. We explain to our students in our music school in Odessa, Texas various current forms of digital synthesis.
Elliot Carter was also experimenting with time and duration. “The three great forefathers of modern music still alive at the end of 1945 were all United States citizens: Ives, Schoenberg, and Stravinsky.” From these Elliot Carter emerged. Carter was born into a wealthy New York family and studied in France with Nadia Boulanger. “Carter’s polyphony, in the First Quartet as in his later music, is one proof against subjectivity: because the music is happening in several speeds simultaneously, it has no speed of its own, and therefore allows no presumption that it speeds or sings (or, given the abundant pulsed rhythms, dances) the thinking of one person at one time…liberation form psychological time…has an effect on the notion of what constitutes a musical movement.” Composition students in our music school in Odessa, Texas learn the value of macro-polyrythms.
Milton Babbitt, also in New York became very interested in total serialization. “Babbitt characteristically bases his pitch organization on bringing together fractions of serial forms to produce ‘aggregates’, a term he uses to mean collections that contain all twelve pitch classes, but that are not instances of a work’s series. (A pitch class- the term is again Babbitt’s- is a virtual pitch, not yet ascribed to any register. A twelve-note series is a series of pitch classes, because a C in a series can be any C. Babbitt’s nomenclature, more systematic than that of earlier serial composers, is required by music that is similarly more systematic.) Babbitt spent much time working with one of the earliest computers available (hired by RCA as consultant composer to work with their RCA Mark II Synthesizer at the Columbia-Princeton Electronic Music Center) providing him accuracy of all the parameters he was numerically controlling.
“Where Boulez and Messiaen…were producing music of great expressive force and dynamism, Babbitt and Cage were making their music as objective as possible. This difference at least balances the similarity between Boulez and Babbitt as serial composers, or that between Cage and Messiaen as anti-polyphonic musicians.”
Parenthetically, when I was at Juilliard, I saw the aged Babbitt and Carter regularly shuffling down the hallways to teach classes.
Nancarrow was another composer seeking to gain a higher degree of control of tempo by using the player piano. “It allowed him to create rhythmic canons (and most of his player-piano studies are canonic) in which the voices move at complex relative speeds: in Study No. 37, to take an extreme case, there are twelve voices, at tempos in the ratios 1:15/ 14:9/ 8:6/ 5:5 4:4/ 3:7/ 5:3; 2:8/ 5:5/ 3:7/ 4:15/ 8 (a rhythmic encoding of a chromatic scale in just intonation). Also, the studies exult in possibilities of keyboard sound beyond any keyboard player or combination of keyboard players: not only twelve-part canons, but colossal, precisely simultaneous chords and immense glissandos, all moving at speed with perfect accuracy.” This is an early version of what can now be accomplished with computer sequencing software. Nancarrow was working with these ideas about a decade or two before sequencers were available in their earliest beginnings, in the 1980s. Again, composers in our music school in Odessa, Texas learn how to apply complex polyrhythms by studying Nancarrow’s work.
Just after WWII, Avant-guard composers “who were beginning to assemble regularly at Darmstadt saw themselves as bringing in a revolution that would be more than musical…though Darmstadt in its infancy was also a U.S. intervention, sponsored by the military authorities in their sector of immediate postwar Germany, officials appear rapidly to have washed their hands of these disputatious musicians.”
In Darmstadt, Boulez and Stockhausen, along with others, were exploring the total serialization of music, endeavoring to create a new musical language. Boulez, in an essay, “speculates about the possibility of a composition existing as a set of ‘formants’, each linked to the organizational bases of the work as the formants of a timbre are linked to the fundamental, and yet each independent.” Boulez’ groundbreaking work, Le Marteau sans maître became the expression of these ideas, and “had been installed as a modern masterpiece- and hailed by Stravinsky, who attended a performance Boulez conducted in Los Angeles in 1957- long before anyone but its composer had any knowledge of its moment-to-moment compositional workings.”
Also in Darmstadt, Stockhausen was working on Studien, to prove “a practical demonstration of how pitch and duration- the two parameters whose parallel ordering had been such a problem to total serialism- are aspects of a single phenomenon, that of vibration. A vibration of, say, 32 Hz will be perceived as a pitched note, whereas one of 4 Hz will be heard as a regular rhythm, and somewhere in between the one will merge into the other. So for different reasons- to do with acoustics rather than mathematics- Stockhausen came to the same conclusion that Babbitt had reached a little earlier, that some deep coherence had to be sought between the principles applied to pitch and to rhythm in forming a work. The scale of chromatic durations was inadequate, in Stockhausen’s view, because it contradicted acoustical reality, being an additive series and not a logarithmic one, such as lay behind the chromatic scale of pitches; moreover, it led to absurdities and inconsistencies, such as the tendency towards regular pulsation when many lines are superimposed, or the undue weight of long durations. We teach students in our music school in Odessa, Texas new developments in the use of the overtone series.
I came to this conclusion within the past decade or so, in my own studies, independently of knowing about Stockhausen’s work. Reading this completely rocked my world. Up to this point, I had no idea anyone had put these ideas together. Everyone I talked with couldn’t seem to understand the concept when I would discuss it…even respected musicians I know. Stockhausen did not have the technological tools to fully pursue these ideas, and ended up going in a completely different direction, but the tools to explore this are sitting right in front of us, using digital sequencing and tuning logarithms.
We teach students in our music school in Odessa, Texas forefront techniques in how to integrate pitch, rhythm, serialism, and harmony based on the overtone series, using forefront technology.