Integer multiples of a fundamental form the harmonic series, the physics behind every plucked string, bowed cello, and sung vowel.
In the world
A plucked guitar string vibrates at its fundamental and at exact integer multiples at the same time; that stack of frequencies is the harmonic series. The sounds we love - guitar strings, singing voices, piano notes - are all shaped by harmonic overtones. Even the Western musical scale approximates the harmonic series.
When a string, tube, or membrane vibrates, it does so at a fundamental frequency f and simultaneously at 2f, 3f, 4f, 5f.... These integer multiples are called harmonics or partials, and together they form the harmonic series. The relative loudness of each partial is what makes a violin sound different from a trumpet at the same pitch.
Every pitched acoustic instrument lives inside this series. Additive synthesis lets you build that stack directly, partial by partial.
Did you know?
The harmonic series is built into the physics of the universe. It appears in vibrating strings, air columns, drumheads, even the spectral lines of hydrogen atoms. Pythagoras heard it in stretched strings 2,500 years ago; quantum physicists found it again in electron orbitals.
Explore
A solar system of 8 planets orbits on the right - the glowing sun is the fundamental, and each planet is a higher harmonic. Click any planet to toggle that partial on or off. Active planets are linked by glowing constellation lines. Unmute, then click planets to hear what happens when you remove or add harmonics.