The canon stroke convention has its short step at the tonic, exactly as the major scale has its semitone at ti-do′. That shortened final step is the leading tone: the mechanism of arrival. A scale with perfectly uniform steps is the whole-tone scale; it reaches the octave number, but nothing marks it as home.
Listen for the pull of the last step in the first scale, and for its absence in the second. This is the argument that adjudicated the convention (doc §8).
The Shepard tone rises forever while going nowhere: chroma cycles, height never changes. The framework calls that the sound of the Inflation Lie (performed ascent without gaining an octave). A true ascent returns in chroma AND gains height: the staggered continuation.
The Shepard tone loops seamlessly and never arrives. The true ascent arrives, one octave higher, singing the same note names.
The fixed point of the α-coupled octave ring (v16) carries momentum q* ≈ 0.3625π per octave: every octave holds identical weight (A3, exact), while the phase advances about 65° per octave. Below, eight octave-nodes with constant brightness and traveling hue; four octave-voices with constant loudness and a traveling pulse. Flip the chirality and the direction of circulation reverses: that flip is i's arrow made observable.
Weights uniform, phase traveling: this is why the structure was invisible to every weight-based probe. Momentum is the phase-sensitive observable that finally saw it.
Real computed data (v16/v18 operators; eigenvalue phase as angle, modulus departure per α as radius). Canon's seven bands, viewed in the folded eight-octave frame, thread through all eight sectors before closing: the helix as spectral flow. The whole-tone operator's fifty-six bands are disconnected closed loops: its −i flux opens gaps (factor ~550) at exactly the crossings canon's octave symmetry protects.
The moving dots are the eigenvalues of T(q) as the Bloch momentum q sweeps the zone; the faint curves are the full band loops. Minimum band separation: canon ~1e-5 (protected near-crossings), whole-tone 5.05e-3.
The ladder's two canonical functions occupy the two extreme spectra on ℤ₇ (exact result): the traversal function A is a Zadoff-Chu chirp (zero self-overlap under every nontrivial shift), the splitting function A′ is a pure tone (identical under every shift), and A′ = dA/dd maps one to the other. Rendered in pitch: A′ is a scale of constant steps; shift it and you get the same shape, in parallel. A is a scale of growing steps; shift it and the two copies walk away from each other.
The exact statement lives in phases mod R (flat spectrum √7, autocorrelation exactly zero); the pitch rendering performs the same algebra. Only the trivial shift returns the traversal pattern: the spectral echo of the single-period lemma.
Map each quarter-turn i-stroke to a minor third, so i⁴ = 1 becomes an octave (4 × 3 semitones = 12: the diminished arpeggio is the i-cycle in pitch). On a ring of n octaves the uniform (whole-tone) stroke field fires 7n/2 strokes per loop. If that count is not a multiple of 4, the arpeggio is interrupted at the seam: the loop restarts mid-cycle, and the mismatch IS the flux, walking the i-cycle as n walks 2, 4, 6, 0 (mod 8). Only at n = 8 does the loop close seamlessly.
Listen at the loop point: for n = 2, 4, 6 the four-note cycle is cut short and restarts wrong (the closure obstruction, spin-structure shaped); at n = 8 the second loop continues as if nothing happened. This is the −i holonomy of the parity double cover, audible.