Johann Sebastian Bach · 1722 · Pitched Music
Core Mechanism
constrain the variables to make the system's rules visible, then prove those rules are sufficient.
Kernel Engagement
Works within the kernel’s native ground; the structural gap is present but never encountered.
Evidence
The work systematically demonstrates that all keys are viable through 24 preludes and fugues, addressing the Pythagorean comma by proving equal temperament works across the entire domain. The structural argument is domain-level demonstration, not work-level resolution.
Territory
The work uses fifths-based harmonic organization as primary language throughout - functional harmony, key relationships, and fifth-generated motion structure both prelude and fugue. The C major prelude and four-voice fugal exposition are paradigmatic diatonic territory.
Constitutive depth
The fifth remains constitutive infrastructure - remove fifth-based relationships and this ceases to be tonal music. The work doesn't generate endogenous constraints beyond those inherent to fugal procedure and harmonic progression; Bach chose the arpeggiation pattern and fugal subject independently.
Legibility
The mechanism is exposed because the audience can perceive the systematic demonstration operating - the work foregrounds its structural logic through constraint (single arpeggiation pattern, harmonic progression as sole organizer) and makes the fifth's operation visible through systematic position-swapping and key traversal.