Exhaustive Indeterminacy: Subtraction as Score, Silence as Decision

The Paradox of Too Much

Traditional musical notation aims for clarity. It transmits intent, structure, and expression from composer to performer. Even in indeterminate or aleatoric works, where chance and choice are built in, the goal is usually to open space for freedom while retaining a composed identity. But what happens when the score becomes so overloaded with choices that freedom emerges only through reduction?

Exhaustive Indeterminacy is a radical compositional approach in which every conceivable musical option—articulations, dynamics, rhythms, tempi, gestures—is inscribed simultaneously. Each page becomes a hyperdense matrix of sonic potential. It is not a “play everything” instruction, but rather a mandate to subtract: the performer must whittle this impossibility down to a single thread. The work emerges not from what is written, but from what is removed.

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The Nature of the Exhaustive Score

Imagine a page where each line contains overlapping staccato and legato markings, conflicting tempi, contradictory dynamics, and coexistent gestures: tremolo and sul ponticello and pizzicato, all stacked. It is not chaos, but a systematic completeness—a cartographic atlas of all ways the line could be played.

In this system:

• Notation becomes a field of possibility, not instruction

• Performance is a process of curation and elimination

• The performer is positioned as editor, sculptor, and interpreter

• Each performance becomes singular—an artifact of choices and renunciations

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The Subtractive Gesture: Interpretation as Erasure

Rather than choosing between options in real time, performers of Exhaustive Indeterminacy are tasked with paring down the score in rehearsal, sometimes even physically crossing out notations. This performative editing reflects:

• The aesthetics of negation, where the piece is revealed through loss

• The act of interpreting as destruction, not completion

• A confrontation with musical overload—mirroring the contemporary saturation of options in both digital and cultural spaces

The result is a performance that is irreproducible, non-transferable, and wholly contingent on a singular sequence of subtractions.

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Compositional Methodologies

How can a composer construct a work of Exhaustive Indeterminacy? Strategies include:

1. Stratified Notation

Multiple articulations and expressive instructions are layered, not separated—inviting contradiction.

2. Quantum Measures

Each bar may contain all possible rhythmic subdivisions, and performers must isolate one logic per measure.

3. Instructional Blocks

Pages may feature full sets of performance instructions, from dynamics to bow pressure, in modular boxes—none marked as “correct.”

4. Competing Tempi Maps

Independent tempo trajectories may run parallel, leaving the performer to choose a single acceleration path.

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Philosophical and Artistic Precedents

While Exhaustive Indeterminacy is a speculative compositional technique, its conceptual DNA is traceable to several artistic movements:

• John Cage’s I Ching procedures opened music to chance, but Cage still curated the results. Exhaustive Indeterminacy removes even that authorial control.

• Brian Ferneyhough’s complexist notation challenges performability, but assumes a “final version.” Exhaustive Indeterminacy assumes no finality.

• Hanne Darboven and Sol LeWitt: their serialized systems map every permutation—Exhaustive Indeterminacy shares their impulse toward taxonomic totality.

• Wabi-sabi aesthetics in Japanese philosophy: impermanence, imperfection, and the beauty of reduction.

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Practical Challenges and Opportunities

For Performers

• Encourages a redefinition of virtuosity: not in execution, but in discernment

• Promotes a slow practice ethic, where time is spent not playing, but thinking

• Forces ethical decisions: which voices deserve to live?

For Audiences

• Each performance is a unique reduction, a sonic fossil of vanished potential

• Listeners experience a musical work as negative space—what is heard is shaped by all that is absent

For Composers

• Liberates the score from fixed structure

• Encourages a new compositional humility: the work is complete only when erased

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Applications and Futures

Digital Platforms

Digital scores could incorporate toggles, filters, or sliders to allow performers to digitally erase in real-time—introducing dynamic and evolving versions of the same piece.

AI-Assisted Editing

Artificial intelligence could generate the exhaustive matrix, and assist in the curation—perhaps offering a “ghost performance” of all the lines not chosen.

Collaborative Subtraction

Multiple performers could subtract in stages—each “editor” revising the version left behind, creating a chain reaction of erasure.

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When Everything Is Possible, Meaning Emerges from Less

Exhaustive Indeterminacy is a framework for reclaiming silence, restraint, and the act of artistic choosing. It rejects performance as mere reproduction, and instead invites performers to confront the unbearable richness of musical potential. In doing so, it asks a simple but haunting question:

If everything is possible, what should be heard?