Hear the Breach
This page renders the Ambient Breach model as sound and image. It does not extend the theory. It makes the model observable: set the parameters, and the system’s state becomes audible and visible. Arrival past durable capacity’s reserve drives the tonic flat as the breach debt accrues; the regime boundary is a line you can cross. Use headphones.
Developed from a conversation with the pianist Elliot on how trained ears track harmonic drift. The sonification maps the model to sound; the visualization maps it to sight. The mapping is faithful, not decorative: every tone and every line reads from the formula.
Part 1: the irreducible residue
Twelve perfect fifths do not equal seven octaves. The gap is the , a . It is : every tuning system absorbs it somewhere; none removes it.
The cycle that does not close
Trace twelve pure fifths around the ring. The arrival does not equal the origin. It beats, and the ring lands short of close. That gap is the debt.
Pure versus tempered
A chord in holds steady. The same chord in oscillates, because the comma is distributed across all twelve keys. The oscillation is the same debt, spread thin. Watch the spectrum below while each plays.
Part 2: live breach simulation
Drive arrival past capacity’s reserve and the tonic drifts flat as the breach debt accrues, while the surface stays active. Reduce arrival and the drift persists: recovery is not threshold-crossing.
Live synthesis and analysis from exact frequency ratios (Web Audio, Canvas). The detuning is breach debt in cents, the tritone tracks (B − 1), the boundary line is B = 1. Every plotted line reads from the model. Return to Ambient Breach Theory.