Musical Harmonic Overtone Series (2D)

Fundamental

Fundamental frequency f1 110 Hz

Waveform preset

Harmonics (tap to toggle)

Playback

Click a harmonic or press Play to hear the composite tone.

Live Readout

Selected harmonic n

Frequency f_n

110.0 Hz

Nearest note

Active harmonics

1,2,3

How it works

A vibrating string of length L fixed at both ends can only ring at frequencies f_n = n·f1, where f1 = v/(2L) is the fundamental (n=1) and every higher n is an overtone. Each mode n forms a standing wave with n antinodes and n+1 nodes (including the fixed ends) — that's the "shelf" of individual harmonic shapes shown above the string.

A real musical tone is never a pure sine wave: it is the sum of the fundamental plus a mix of overtones, each with its own amplitude. The lower panel shows that sum as one composite wave shape. Strong odd harmonics with 1/n amplitude give a bright sawtooth-like buzz; only odd harmonics give a hollow square-like tone; fast-decaying 1/n² amplitudes give a soft, rounded triangle-like tone.

This is additive synthesis — the same principle behind synthesizer oscillators, and the reason a violin and a trumpet playing the identical fundamental note still sound completely different: their overtone spectra (which harmonics are strong or weak) differ, even though the fundamental frequency is the same.