Hollow

What it is

White noise, plus the same noise a millisecond or two later. Drag to change the delay.

The amber line is what arithmetic says the spectrum should look like, the green line is what an analyser reads off the actual output. They sit on top of each other.

The sound is the point though. A flat hiss becomes hollow and metallic, and it acquires a pitch that tracks the delay, even though nothing tonal was added.

How it works

Two copies of a signal, one delayed by τ. At any frequency where τ is a whole number of periods the copies arrive in step and add to double. Where τ is a half period out they arrive opposed and cancel to nothing.

That gives peaks at every multiple of 1/τ and nulls exactly halfway between, at odd multiples of 1/(2τ). A 1 ms delay puts nulls at 500, 1500, 2500 Hz and peaks at 1000, 2000, 3000. The whole response is |1 + a·e^{-i2πfτ}| = √(1 + a² + 2a·cos(2πfτ)) and everything else follows from it.

The pitch is the interesting perceptual part. A regular series of spectral peaks 1/τ apart is exactly what a harmonic series looks like, so the ear reports a note at 1/τ. Same machinery as day 11’s missing fundamental, except here not one of those harmonics was deliberately played. The pitch is an artefact of the spacing.

What surprised me

Not the physics, which is textbook. It’s how little delay it takes.

At 20 ms you hear a distinct echo, two events. Come down to 5 ms and the echo is gone, instead the timbre has changed. At 1 ms there’s no sense of a repeat at all, just a thin metallic colour, and the pitch it produces is up at 1000 Hz.

Nothing about the arithmetic changes across that range. The same equation describes all of it. What changes is which part your ear reports. Above roughly 30 ms it hears two events in time, below that it stops resolving them separately and hears one event with a different spectrum. The transition is entirely in the listener.

That’s why this is a psychoacoustics day rather than a DSP one. The comb filter is the same object throughout. “Echo” and “timbre” are two different things the same object is heard as, and the boundary between them is a fact about ears.

What I would do next

Feed the delay back on itself, which turns the comb into a resonator and the colour into an actual note.