harmonic series
The naturally occurring series of overtones produced when any pitch sounds, forming the acoustical basis of harmony
In Depth
When a string or air column vibrates, it produces not only the fundamental pitch but a series of higher frequencies at integer multiples: the octave (2x), perfect fifth (3x), next octave (4x), major third (5x), and so on. This series explains why certain intervals sound consonant — they share low-number frequency ratios. The harmonic series is the physical foundation of Western harmony, brass instrument design, organ stop construction, and the phenomenon of timbre itself.
Brass instruments can only play notes from the harmonic series — every pitch a trumpet or horn produces is a harmonic of its fundamental tube length.