Why this site exists

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.

The architecture privileges three content modes: long-form essays, visualizations, and formal papers. Essays carry the narrative. Visualizations make the claims tangible. Papers anchor the work in its rigorous form.

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 argues that the natural exact geometry for cyclic pitch content and ordered traversal is symplectic — not as a metaphor, but as a consequence of lifting the discrete musical seed into its natural spectral coordinates. The framework separates content from order, attaches permutation fibers locally, and shows that the resulting layered space carries a canonical exact symplectic form with unusually transparent Hamiltonian symmetries. The global object is not a single smooth manifold but a stratified symplectic space indexed by cardinality, with orbifold singularities at symmetry-rich landmarks.

How to cite this work

For the public essay series: Jason St George, The Shape of Musical Possibility, GAMUT Research Program, 2026. Available at shapeofmusicalpossibility.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.

Version and data

Current version: 1.0 (March 2026). All essays, papers, datasets, and code are freely available for download from the Papers page.