the interval

the lock: hear the roughness resolve into smoothness.

This is sensory consonance and beating. Two tones close in frequency add up to a wave that swells and fades at their difference — you hear that as beats. A little further apart and they fall inside the ear's critical band, where they clash as roughness. For tones with harmonics — the tones real instruments make — a simple ratio (1:1, 3:2, 2:1, and the rest) lines the overtones up, so their harmonics coincide rather than beat, and the pair sounds smoother. That much is physics — Helmholtz, and measured carefully by Plomp & Levelt in 1965.

The demo above plays pure sine tones, which carry no harmonics. There the effect is subtler — driven by the difference tone and critical-band roughness rather than coinciding overtones — so a fifth or octave is only mildly smoother than its neighbors.

Whether smooth sounds better is partly cultural, not just acoustic: McDermott and colleagues (2016, Nature) found a remote Amazonian people who don't prefer consonance to dissonance. So the smoothness here is real and physical; the preference for it is a proposal about your ears and your upbringing, not a law.

It bestows no health effect. This is acoustics, not sound-healing — the “healing frequency” claims around 432 Hz and the solfeggio numbers have no scientific support. Keep the volume moderate; headphones or speakers are both fine.