About
Why this site exists
GAMUT translates a mathematically serious research program into an editorial experience that curious, technically literate readers can actually inhabit.
The public site is not meant to replace the academic paper trail. It is meant to widen the circle of readers who can enter the thesis, follow its development, and see the visual argument unfold.
Essays carry the narrative, visualizations make relationships available for exploration, and papers develop the formal argument. Research dossiers keep documents, score observations and interpretations available for inspection.
Author
Jason St George is the author of the GAMUT (Geometric-Algebraic Music Theory) research program, which develops a layered geometric framework for musical structure rooted in cyclic content, ordered pattern fibers, and symplectic form over the 12-tone system. The project bridges mathematical music theory with public explanation through formal papers, interactive visualizations, and the essay series collected on this site.
The research program
GAMUT separates pitch content from ordered traversal and embeds distinct-note cyclic patterns in Fourier coordinates. The continuous ambient space is equipped with a chosen weighted exact symplectic form; that choice is additional structure, not a consequence of injectivity alone. Cardinality indexes a disjoint family of spaces. The current Lean release verifies selected discrete contracts; the reviewed manuscripts develop the higher geometry.
GAMUT Histories studies the lives, practices and institutions through which music takes form. Its first Mozart dossier examines K. 543, K. 545 and K. 546 through a sourced chronology and selected score passages. It is a working historical study with direct comparative listening still to complete.
How to cite this work
For the public essay series: Jason St George, The Shape of Musical Possibility, GAMUT Research Program, 2026. Available at shapeofmusic.org.
For the formal paper: Jason St George, "Cyclic Autocorrelation, Permutation Fibers, and a Layered Symplectic Model for Pitch-Class Space," GAMUT Research Program, March 2026 (revised September 2026).
Version and data
The September 2026 AMS proof paper (v1.2) is the current mathematical reference. Earlier public volumes and surveys remain historical companions pending alignment. The research overview explains the completed Lean milestone, the Coltrane and Bruckner source studies, the Mozart historical dossier, and the proposed instrument sequence. Musical usefulness remains an empirical question.