Experiment · moiré / beat frequencies
Beat frequencies
Two rhythms that nearly agree produce a slow third rhythm — a beat. Called moiré when you see it, it appears wherever a fine repeating structure meets another of almost the same pitch: a scanner reading a halftone, a camera filming a fabric, two grids on this page.
The stage
Build the beat by hand
Pull the spacing of the second grid toward matching the first. The slow pattern is the arithmetic made visible: when two frequencies are close, their difference is a third, slower frequency — and that one is slow enough for your eye to catch.
How it works
The slow difference
Add two nearby frequencies and you get four: the sum, which is too fast to see, and the difference, which is slow by construction. Moiré is the difference frequency rendered as space. Two rings whose radii differ by a hair produce a beat ring whose spacing is the ratio of the two spacings divided by their difference — small mismatch, huge beat.
It is the same arithmetic as two tuning forks a semitone apart, humming in and out of phase. And it is a nuisance engineers fight everywhere: a screen's pixel grid moirés the fabric behind it on camera, a scanner's sampling moirés a halftone print, and offset printing rotates its color screens against each other precisely so the beats land out of sight.
The beat is not in either grid. It exists only where they overlap — which is exactly how your eye, a camera, and a scanner all end up reporting a pattern no single source contains.