◬ MIMZY · instrument № 14 · the analog–quantum suite · THE SYNC

The Rhythm Sync

The suite's promise, kept literally: a software clock (a numerically-controlled oscillator) listens to a drifting hardware oscillator (the tank) through a phase detector, and a loop filter steers it until the two beat as one — a phase-locked loop, the circuit inside every radio, CPU clock, and GPS receiver. The 3·2·1·0 pulse cadence gates the lock into rhythm.

⊙ EDUCATIONAL & SIMULATION — a genuine 2nd-order PLL: phase detector → loop filter → NCO

The two clocks

hardware tank f₁ 3.0 Hz

software NCO starts at f₂ 4.5 Hz

loop gain K 2.0

hardware drift off

— UNLOCKED —

NCO frequency now

—

frequency error

—

phase error φ

—

beat period 1/|Δf|

—

The rhythm gate · 3·2·1·0

The two waves — watch them slide, then bind

hardware tanksoftware NCO

Phase error φ(t) — the loop pulling to zero

Lissajous — hardware vs software (a circle = locked in quadrature)

How real is this? This is a textbook second-order PLL: the phase detector multiplies the two signals and low-passes the product (≈ sin φ of the phase difference); a proportional-plus-integral loop filter turns that error into a frequency correction; the NCO obeys it. Everything you can see is genuine PLL behavior — the beat while unlocked, the capture, the steady-state lock riding through hardware drift (that is the integrator term earning its keep), losing lock when K is too small, and ringing when K is large. Open the loop and the clocks immediately drift apart again — sync is not an event, it is a continuous act. The cadence row gates the audio with the pulse rhythm 1110·110·10·0000, the house 3·2·1·0 — labeled as the lore it is.