Indeterminacy 2.0: In Which We Agonize Over Terminology

I have a certain tendency to refer to my indeterminate pieces as “my indeterminate pieces.” But wait, aren’t they generative? In this week’s episode, I want to try to hash out some of the terminology floating around this sort of music.

Written By

Kenneth Kirschner


Image from variant:flare by Joshue Ott and Kenneth Kirschner

Discover the recipes you are using and abandon them.

—Brian Eno and Peter Schmidt, Oblique Strategies

I have a certain tendency to refer to my indeterminate pieces as “my indeterminate pieces.” But wait, aren’t they generative? Haven’t we forgotten about Brian Eno?

In this week’s episode, I want to try to hash out some of the terminology floating around this sort of music. This is very much intended as a conversation: I don’t feel I have the right answers myself, and I’d like to hear in the comments below your thoughts, disagreements, and differing interpretations of what all these words mean—or should mean. A certain amount of this is squares and rectangles, and more than one of these terms could apply to any given piece of music. So let me pick a few of the key concepts out there and start to try to pin them down a little…


Let’s start with an easy one: the Cagean distinction between chance procedures and indeterminacy. Chance procedures are the incorporation of a random element into either the process of creating a composition or into the actual structure of the composition itself; as such, they can just as much be used to create a fixed work as an indeterminate one. The classic example is Cage’s own Music of Changes, in which he employed coin tosses and the I Ching to decide the notes of a fixed, fully determined score. Chance procedures can give you a piece that’s indeterminate or a piece that’s not, and an indeterminate piece can be based on chance or on some other uncertain element (such as performer choice, as in Feldman’s graph pieces).


Let’s start by calling an indeterminate composition a piece of music that differs with every realization, whether that realization is a performance or a recording. Or whether that difference comes from chance procedures, performer or listener choice, or a generative process. Cage called The Art of the Fugue an indeterminate composition because, while each and every note is fixed by the score, Bach never specified the instrumentation and so every realization is potentially different. Push this too far and the concept disintegrates: after all, every performance of any score will be different every time, with big huge millisecond differences between even the most robotic human performances. So we need to try to isolate the concept a little more, perhaps by saying that there’s an aspect of the composition’s fundamental structure that opens itself to uncertainty and difference, and that this structural rather than performative element is what properly characterizes indeterminacy.

Throwing out some examples beyond the odd one of The Art of the Fugue:

  • Feldman’s early indeterminate pieces—starting from the Projections series, in which the performer chooses their own notes among “high,” “middle,” and “low” pitch ranges—or the Durations pieces, in which the pitches themselves are fixed but the tempos and rhythms are free.
  • A huge number of Cage pieces, from Imaginary Landscape No. 4 with its radios, up through the late Number Pieces with their wide-open spaces and vast freedoms of time and sound.
  • Stockhausen’s Klavierstück XI, which forms a sort of musical mobile of individually fixed elements that can be permutated into endlessly varying combinations (and which, as we’ll see next week, is similar to the approach I’ve been trying with software-based indeterminate composition).

Or there’s Terry Riley’s In C, there’s Ives and Cowell, Brown and Wolff—the list goes on. But let’s change gears…


Okay, now we get to Eno. His concept of generative music starts with 1975s Discreet Music and runs to the present with interactive apps such as Bloom and Scape. I’m tempted to say that generative music is music that uses a clearly defined process—an algorithm, a set of axioms or rules, a list of instructions—to create a composition that evolves strictly according to that process but not necessarily deterministically; the end result can be fixed or indeterminate, autonomous or interactive. Eno cites wind chimes as an example of a generative music. Or consider Reich’s It’s Gonna Rain: we can think of this as a generative work in that it takes a specified process (two tape loops gradually phasing) and lets that process run—but interestingly, it’s not an indeterminate composition; the result is a fixed recording. Conversely, a generative piece can be indeterminate—through built-in randomness, external inputs, or other means. We’ll need a Venn diagram for all this.

Perhaps one possible direction in helping differentiate generativity and indeterminacy is as a process vs. a result: generativity is a way of making something, indeterminacy is a trait of the thing made. So you can have a generative indeterminate work, or a generative determinate work. Could you have a non-generative indeterminate work? Perhaps Feldman’s approach to indeterminacy might fit the bill: his focus was on performer choice, rather than system or chance. So by the time you try to force a Projections or a Durations into the category of generative music, the whole concept has become blurred beyond recognition.


In a way, interactivity is an even bigger jump than the leap from certainty to indeterminacy. Let’s call an interactive composition a piece that actively integrates the listener or audience member into the structure of the composition itself. Or a piece in which the listener, rather than just the composer or performer, participates in the realization of the work. But perhaps a better word than “listener” would be “user”—because questions of interactivity arise naturally and almost automatically when dealing with indeterminate digital music, in a way that they don’t necessarily in a concert hall. The iPad apps I’ll talk about next week have, as we’ve worked on them, become far more focused on interactivity than on a more traditional, “passive” sense of indeterminacy, all through a process that has seemed both natural and inevitable.

Distinguishing interactive music becomes a question of the “stance” of the listener: Are they an active participant in the realization of the music? Do their actions alter or guide the development of the piece? Or do they experience the piece as they would a traditional work—sitting back, letting it unfold, just listening. Having now worked on both non-interactive indeterminate music and interactive indeterminate music (cue the Venn diagram again), I can tell you that this is a very, very significant difference from a compositional point of view. But more on that next week.

I want to throw out one final term—though more as a proposal, as I’m not sure it actually exists yet:


My indeterminate pieces all use software-based chance procedures to reshuffle their component parts, creating random juxtapositions of different fragments of material—a sort of digital mobile (pronounced like Calder rather than your phone). But in listening to them, I can’t escape the feeling that sometimes the results are better and sometimes worse; the roll of the dice sometimes gets it right—sometimes that random number generator is just on. From this, I got to thinking about how I could cheat—how I could bias the piece toward better results, more reliably, more consistently than just through pure chance alone. One idea was to “weight” the outcomes with perhaps something as crude as a “thumbs up” button: the piece hits upon a good concatenation of material and you hit “yes,” which then statistically biases it to move more often toward that part of its “compositional space” in the future. As you develop the piece, you’d gradually refine these “likes,” and the piece would slowly adapt itself toward a set of outcomes that sound better and better. So it’s random, but a structured, learned, constrained randomness. You could also have different versions or interpretations of the piece: the composer could painstakingly develop an adaptive profile—their vision for the piece—but then the listener could reset it and develop their own interpretation, their own way of weighting the dice and biasing the outcomes of chance toward a better or different musicality. We haven’t tried this yet, and I’m not sure if anyone else has, but I feel like it’s a promising idea.

There are plenty of terms still out there—aleatoric music, stochastic music, algorithmic music—that I don’t have the space or, in truth, the clarity on to start locking down right now. But maybe in the end it’s better to think of all these conflicting and converging words as adjectives rather than nouns—ways of describing a piece rather than static categories or classifications. Because, again, push any of them too far and they become absurd. What piece of music doesn’t have an element of chance back there somewhere in the history of its creation? What performance of a scored composition isn’t innately indeterminate in its microphysics, its performative nuance? And don’t forget that any playing of any recording is indeterminate as well—across different speakers or headphones, in different rooms, amidst different sonic environments, with different interruptions, pauses, and distractions.

And doesn’t every composition, “generative” or not, involve a formal system that structures it, that organizes and limits it within the vast space of all possible music? Consider the following perfectly legitimate set of rules and constraints: Take a harp and knock it on its side. Now, instead of playing it with your fingers, build an elaborate system of mechanical hammers to strike the strings. Tune those strings to a strange compromise in temperament that allows modulation between keys at the cost of twisting certain intervals away from their ostensibly more natural whole number ratios. Oh, and 88 might be a good number of strings to use.

Is this an interactive composition? A generative one? It has a clearly defined system of axioms and rules that constrain the possible space of musical results. But is it really necessary to say that a piano is one big indeterminate composition?

I’d like to see the answers to this and every other question I’ve asked today in the comments below, so that I can get it all figured out myself.