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.
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.