Add a second sine a perfect fifth above the first and hear two oscillators fuse into a single richer tone, the first step toward a full harmonic stack.
In the world
Two tuning forks struck together do not blur into mush: their waves add point by point in the air between you and them.
When two sines share the air, they obey superposition: at every instant, the combined pressure is the sum of the two. Tuning one a perfect fifth above the other (seven semitones, frequency ratio 3:2) gives a stable, harmonious shape because their cycles line up every third period of the lower tone.
If the ratio is irrational, the waveform never repeats, the pitch dissolves into beating, and the trace appears to walk across the scope.
Did you know?
Pythagoras discovered the perfect fifth (3:2 ratio) by listening to hammers in a blacksmith's forge. He noticed that hammers whose weights had simple ratios sounded harmonious together - the birth of music theory from a workshop accident.
Explore
Two glowing sources emit ripples into a shared pool. Move your cursor up/down to change the second source's frequency ratio. At simple ratios like 3:2 or 2:1, the interference pattern locks into a clean repeating shape. Click to switch between hearing both sources, cyan only, or magenta only.