As mentioned in the opening remarks to SA10, we're working on an experiment that will hopefully provide a broader temporal aspect to Sound American by adding fresh new pages that relate to the issue's topic every 3 or 4 weeks. These pages will be added as the home page for a week and then join the rest of the content, ultimately being archived as the next issue is posted.

This essay by David Kant is the first of those pages. David was suggested to us by Larry Polansky, who contributed some thoughts on the topic of Christian Wolff and improvisation for this issue. Polansky, a professor at University of California at Santa Cruz, was overseeing some project by Kant, a doctoral student, and recommended talking about his computer-assisted realizations of the famously difficult (physically impossible?) For Pianist.

As an editor, I admit I was skeptical, not about David, but about how the idea of a computer assisted anything would fit in with the tonewe were trying to set in talking to and about Christian Wolff. What I thought we were trying to capture was Wolff's ability to capture a certain non-romantic sense of what is human and social about music making, and my, admittedly naive, view of what a programmed version of his piano work would involve seemed to be counter to all the notions we had set out in the rest of the issue.

Almost immediately upon receiving David's essay, though, I could see how misplaced my worry had been. Kant's project uses the computer in ways that ultimately expand the performance possibilities of a piece that may have previously been limited by not only physical constraints, but the tendency of us, as humans, to lock ourselves into a small number of possibilities, patterns, or habits. It's a fascinating way of viewing a piece that is infinite in concept, but limiting if viewed only through the eyes of the possibilities of the human performer.


For (Cyborg) Pianist


I first encountered For Pianist at the Ostrava Days 2009 Festival of New Music when Philip Thomas presented the piece and talked about his experience performing it. I was fascinated by the work: the time bracket notation specified in unplayable fractions of a second; its form, an unpredictable labyrinth of interdependencies; separate pages of pitch collections and performance instructions; and enough in-performance decisions to fry even the fastest supercomputer (OK, but maybe in 1959...). The piece is difficult, or, as Larry Polansky joked, “It's impossible, at least at this stage of humanoid evolution.” But what about this stage of cyborg(-oid) evolution?

For Pianist is a solo piano work from 1959. One of the earlier instances of Wolff's unique and innovative time bracket notation, the piece spans a continuum from determinate to indeterminate. It requires the performer to respond musically to the unpredictabilities of their own playing, and to choose rapidly from changing sets of possibilities and restriction. Its performance is a frenzy of decision-making, listening, and responding.

Time is simultaneously under- and over- specified. The score is a series of brackets. The duration of each bracket is fixed, but the timing of the material within is free - sounds may fill the entire duration or only a short portion of it. Wolff's durations range from 36 seconds to 1/50th of a second. Some are simple divisions of the second, such as 2 and 1⁄2 seconds, while others are more complex, such as 9/40ths, 11/60ths, and 13/20ths. The temporal density (number of sounds per bracket) spans orders of magnitude, ranging from a leisurely 3 events in 36 seconds to a hectic 7 events in 1/4 second.

Each bracket contains a set of symbols indicating what to play. Numbers specify how many events, and letters correspond to one of 6 pitch collections, ranging in size from 3 to 34 pitches (given on a separate page). Other symbols indicate transpositions by octaves and semitones (combinatorially expanding the pitch choices) and playing techniques: tapping, muting, snapping, touching, plucking, pinching, scraping, and hitting the keys without activating the hammers. Fermatas provide exceptions, allowing events to extend before and/or beyond the time bracket boundaries, and the score even features occasional tablature-style notation.


Example notation from page 3. Each box is a time bracket. The leftmost number indicates the duration of the bracket in seconds. To the right of the colon, the number indicates how many sounds to play within the bracket, and the letter indicates the pitch collection to choose from. Additional text indicates playing technique modifications and other instructions. Above the staff, the numbers indicate the absolute time of the piece.

For Pianist applies Wolff's cueing technique to one performer. The program note explains, “For Pianist is an attempt to involve a single player in situations like those of pieces (such as Summer, Duo for Pianists II) in which several players rely on what they hear from one another, unpredictably, for cues.” Where previous pieces require performers to respond to one another, this piece requires the solo performer to respond to unpredictable aspects of their own performance—whether or not/how long a harmonic sounds, how cleanly a note is struck, accidental sounds, and more. These unpredictable aspects set the performer on branching paths, trigger the start of secondary paths, and can even send the performer to entirely different pages of the score. The many possibilities form a structure that both bifurcates and overlaps. For example, the score branches into 3 separate staves according to the performer's effort to play “as soft as possible:” whether the result is inaudible, as soft as possible, or louder than as soft as possible. Another passage features a secondary staff whose alignment with the primary staff is cued when a sound and its harmonics are no longer audible


Excerpt of page 1 showing a branching point. The dotted line points to the three possible paths determined by the outcome of the event “as soft as possible.”


The piece is a complex, ever-changing set of constraints and contingencies, sometimes limiting the player's options, sometimes offering many. The system of constraints is something for the performer to work with and against. Actions have recourse; the performer's decisions at one moment determine their options in the next. In this piece, indeterminacy is not simply what the performer can do in any one moment, but how these choices effect their choices in the next. The score is a dynamic system of possibilities explored in dialog between the performer and the score.

David Tudor, for instance, fully determined the score. Although the piece is understood as an effort to thwart Tudor's practice of determining indeterminate notations, Tudor, as documented in John Holzaepfel's dissertation "David Tudor and the Performance of American Experimental Music, 1950-1959,” prepared a fully determined version—at least to the extent possible. Tudor's version is a meticulous and sprawling working out of the system of contingencies, complete with alternate staves for branching paths and a sliding staff to align systems with unpredictable starting times. He fixed the indeterminacies that he could, deciding pitches, dynamics, and where to apply performance techniques, and he indicated rhythms proportionally on a one-second grid, translating the fractional bracket timings into decimal notation to coordinate with a stopwatch.




Between the precise bracket timings, the large number of decisions to be made in fractions of a moment (some impossibly small), and the need to respond to unpredictable situations, just playing what is written is difficult. The piece demands compromise; the performance indeterminacies are constrained, in fact, by the score's logistics. My work takes interest in the possibilities of a computer to rebalance this compromise, from coordinating timing in a computer-assisted live performance to producing fully determined versions of Wolff's score.

Wolff's timings are beyond human precision, but computers are excellent timekeepers. Interested in the possibility of a computer to coordinate timing in live performance, I made a digital version of the score. The digital score is animated in realtime, visually guiding the performer through the time structure. It scrolls through the piece, highlighting the present moment bracket by bracket. An expanding bar grows to fill the current bracket, indicating how much time is left. In effort to retain Wolff's hand-written notation, the animation is overlayed on scanned images of the original score. Furthermore, while Wolff's notation is roughly proportional, some brackets are stretched and others brackets are compressed. I wanted to both clarify the proportional timing and keep Wolff's original notation. The expanding bar graphically shows the rate of time along the horizontal dimension of the score, according to how quickly it grows. Finally, the computer needed to respond to cues, allowing the performer to choose paths in live performance (just a foot-switch interface for now). The computer functions, in effect, as a sophisticated graphic metronome, pre-programmed to the time structure of the piece, yet able to change paths on the fly.

I hoped this would help the performer devote more attention to choosing what to play, but there was still too much to decide in what was often too little time (some of the time brackets are quicker than the frame rate of my computer monitor). I offloaded more and more to the computer score, displaying the pitch material beneath each bracket (using scanned images from the original score), and even choosing which pitches should be played, in what order, their dynamics, and their articulation, working towards a compromise of the determinate and indeterminate. In order to retain a degree of unpredictability, the computer score used chance procedures, a counterweight against the tendency (at least my own) to settle into familiar musical figures when diverting brain processing power to other performance demands.

An excerpt from page 3 of the computer-assisted score. The current bracket is highlighted in red as a display bar above expands to fill its width.


As my versions became further determined, I began to reconsider Tudor's approach, no doubt a laborious endeavor at the time, yet another task computers are particularly suited to. Due to sheer speed, a computer is an excellent means for exploring the possible realizations of the score—a way of having many David Tudors—and I began to make many different versions, determining everything that I could program such as pitches, articulations, playing techniques, and rhythm. These versions were rendered in a separate (somewhat) standard notation, rather than Wolff's bracket notation. I became interested in exploring the space of possible realizations formally, according to different methods, constraints, preferences, and techniques of determination—the densest realization, the sparsest realization, the most harmonic realization (the list is endless)—to capture a panoptic image of the piece.

At first I was interested in notating alternative paths as Tudor had, and even combining this notation with computer-assisted timing—a technological update for Tudor's sliding staff—but I quickly became interested in deciding paths through the entire piece, start to finish. Fixing a path simultaneously fixes the corresponding contingencies; if the outcome, for instance, of "as soft as possible" is fixed, the corresponding alternative stave must be fixed as well, and vice versa. My attention turned towards computationally exploring this system of dependencies and trade-offs.


Page 3 of the determined version. Time is notated proportionally, and bar lines show bracket borders. In this rendering determinations are made using a uniform distribution.


There are many possible realizations of For Pianist, (infinitely many, perhaps, considering that the score allows any number of pages). While the space of possible realizations is enormous, it still contains some things and not others. One way to describe the piece is through the kinds of things it provides, the kinds of things it doesn't provide, and why—what is its structure? Performances of the piece present possible realizations, but a computer allows access to the space in another way, that is, by distinguishing the impossible realizations from the possible realizations. Computer code provides a way answering the question: is x possible? Is it possible to play a 6 minute version? How many versions are under 4 minutes? How many versions use at most 3 pages? What is the fewest combination of pages that will last at least 15 minutes? Is it possible to play a 5-6 minute version in which page 1 occurs 3 times more than page 7, no page is repeated twice, pitch set c is never chosen, unless pitch set b occurs on the following page, and the dynamic never exceeds mf?

Most importantly, these questions provide a means of exploring the relative significance of parts of the score. Perhaps including page 7 allows for only a small number of new realizations when compared with page 6. Perhaps page 3 alone describes most realizations. Perhaps page 9 can drastically change the nature of the space of possible realizations, but only in combination with page 2. Perhaps it's not a function of specific pages at all, but rather the number of pages total. Or perhaps it changes dynamically, depending on what has occurred thus far. This gives a way to talk about the important features of the piece, and, ultimately, its construction, or composition. It also gives a way to understand how these features interact to determine the piece's possibilities. Moreover, it's an approach unique to computer code (at least barring an extreme [mis]use of human-power). Computers can help us to explore and understand this space. Ultimately, however, For Pianist is not what's written on the page, nor even the totality of every possible realization, but rather the experience of having those possibilities before you.


David Kant is a composer and performer living in the California Bay Area. His work takes interest in music and computation, and includes analysis of chaotic circuit networks, soundscapes of bioluminescent phytoplankton, and machine listening deconstructions of popular music icons. Kant is pursing a DMA in Music Composition at the University of California Santa Cruz with Larry Polansky and David Dunn.