Theory
ResearchFrontier structures and internal systems
Research

Push into the frontier.

Formal systems, symmetry and asymmetry, pitch-class structures, exhaustive formula spaces, and the unified models that tie them together.

Symmetry

Modes of limited transposition, invariance, repetition, and formal balance.

Asymmetry

Irregularity, directional structure, non-balanced systems, and theory beyond mirror logic.

Set Theory

Pitch-class sets, prime forms, interval vectors, and advanced structural classification.

Formula Lab

Frontier workspace for exhaustive formula families, trajectories, and novelty labeling.

Unified Model

The merged graph across concepts, datasets, and frontier formula systems.

Research Map

How the frontier areas connect

Symmetry to Asymmetry

Move from balance and invariance into directional, irregular, and biased structures.

Set Theory to Formula Space

Go from pitch-class classification to generated formula families and transformation systems.

Formula Space to Unified Model

Connect frontier formula work back into the larger graph of concepts, datasets, and relations.