Scroll

The two piano-roll layouts are timelines: every note is born on a fixed now-line and the whole sheet drifts away from it like a tray on a conveyor. The drift is itself a closed-form deformation — a uniform translation:

$$P_{src} = P - \hat v\,s\,\Delta t,\qquad s = \frac{\text{bpm}}{60}\times\text{roll\_speed}\ \ \text{canvas lengths per second}.$$

roll_speed is canvas-lengths-per-beat, default 1/16 = 0.0625: the full canvas holds 16 beats of history — four bars of 4/4 — so at 120 BPM ink lives on screen for eight seconds. A value of 0.25 would flush the whole canvas every bar, which reads as a waterfall rather than a drifting tray.

Drops born on the now-line drift off the far edge; fresh water enters behind them.open full size ↗

Invariants

• Exact. A translation has Jacobian 1; nothing folds, nothing is sub-stepped.
• Ingress is an explicit shader branch. When $P_{src}$ falls outside $[0, 1]$ the fragment writes fresh water: ink 0, hue 0 and the identity coordinates of its own texel. This cannot be delegated to sampler state — clamp-to-edge would streak the boundary texel’s old ink across the entering region, and clamp-to-border cannot work because fresh water is not a constant: the identity coordinates vary per texel.
• Everything else rides on top. Tines, vortices and feeds still apply after the scroll, so expressive gestures smear downstream like ink in a current.
• Paper stays put. The washi grain is screen-locked; only ink scrolls. The regression check: run a 120 BPM scroll over textured output and confirm the grain does not move while the ink does.

Ownership

• The four piano rolls, named by their now-line: left (pitch → y, now-line at x = 0.12, field moves +x), right (now-line at x = 0.88, field moves −x), top (pitch → x, now-line at y = 0.12, field moves down) and bottom (now-line at y = 0.88, field moves up). Marble-only layouts — “play the now-line” is deferred.
• BPM is host-supplied (a param the host may update live from a DAW or link source); the core never guesses tempo from MIDI. The desktop’s lab bench nudges it with B / Shift-B for syncing against a metronome.