The Sound Cells series is built on a complete enumeration of trichord pair combinations — every way that two trichords can be combined, across all 12 transpositions, in all 18 inversions and permutations. The total comes to 9,240 trichord permutations. No human working alone could generate, verify, and organize this material by hand in a reasonable timeframe. It required computational tools — and understanding how those tools work illuminates both the mathematics and the music.

The Generation Pipeline

The full pipeline from mathematical specification to practice-ready exercise files involves four distinct stages, each implemented with different tools:

Why LilyPond?

LilyPond is a music notation program that compiles plain-text score descriptions into publication-quality PDF scores. Unlike graphical notation programs (Finale, Sibelius, MuseScore), LilyPond is scriptable — you can generate .ly files programmatically and compile thousands of them in a batch without manual intervention.

For the 9,240 permutations project, this was essential. Each permutation needed its own score showing the exercise in standard notation. Generating these by hand in a graphical program would have taken years. LilyPond reduced the task to writing one template .ly file and a Python script to fill in the pitch class arrays — the compiler did the rest.

The tradeoff is a learning curve: LilyPond’s syntax is idiosyncratic, and generating complex scores (multiple staves, specific voicings, accidentals that follow pitch class set conventions rather than key signatures) requires detailed understanding of the language. Much of the development time in this project was spent debugging LilyPond output to match the exact notation standards required for the books.

Why SuperCollider?

SuperCollider is a programming language for audio synthesis and algorithmic composition. It is used in academic music technology programs worldwide and is the tool of choice for generating large quantities of audio from programmatic specifications.

For the Sound Cells series, SuperCollider generates the drone-plus-exercise audio files that accompany each volume — a constant reference pitch (the key center) plus the trichord pair exercises played at a specified tempo with a specified instrument sound. The same parametric approach applies: one template synthesis graph, fed different pitch arrays, produces all the audio needed.

SuperCollider’s pattern system is particularly suited to this task. A Pbind (pattern bind) object schedules note events based on arrays of pitch values, durations, and amplitudes. Changing the pitch array changes the exercise; the rest of the synthesis architecture stays fixed. This separation of content (the pitch class arrays) from form (the synthesis architecture) mirrors the mathematical separation of set content from interval structure that underlies the trichord pair system itself.

// SuperCollider: parametric trichord exercise generation
// trichord_1 and trichord_2 are pitch class arrays
var generateExercise = { |trichord_1, trichord_2, drone, tempo|
    var hexatonic = (trichord_1 ++ trichord_2).sort;
    Pbind(
        instrument, piano,
        
ote, Pseq(hexatonic ++ hexatonic.reverse, 1),
        dur, tempo,
        amp, 0.7
    )
};

The Role of AI in the Pipeline

Several stages of the 9,240 permutations project used AI assistance — specifically Claude — for tasks that are tractable for AI but time-consuming for humans:

Mathematical verification: Checking that each generated hexatonic is genuinely a valid pitch class set (no duplicate pitch classes, correct prime form classification, correct Forte number assignment). AI could process hundreds of these checks in a single session.

Text generation: Each of the 78 volumes in the Sound Cells series includes a book describing the trichord pair system, the specific characteristics of that volume’s trichord pair, and exercises. AI was used to generate drafts of this text, which were then reviewed and edited by Arnold.

Debugging: LilyPond error messages are often cryptic. AI assistance helped diagnose and fix notation bugs that would have taken hours to track down manually — identifying the source of an accidental placement error or a stem direction conflict in a multi-voice score.

The result is a production pipeline that would have been impossible for one person working alone in any reasonable timeframe. The 9,240 permutations, with their associated scores, audio files, and metadata, represent approximately five terabytes of generated material — a scale that only becomes tractable when computational tools and AI assistance are combined effectively.