Fundamental and Harmonic Frequencies
Musical sounds consist of a fundamental frequency, harmonics, and overtones.
The lowest frequency of any vibrating object is called the fundamental frequency. The fundamental frequency provides the sound with its strongest audible pitch reference - it is the predominant frequency in any complex waveform.
A sine wave is the simplest of all waveforms and contains only a single fundamental frequency and no harmonics, overtones or partials.
Virtually all musical sounds have waves that are infinitely more complex than a sine wave. It is the addition of harmonics and overtones to a wave that makes it possible to distinguish between different sounds and instruments; the timbre.
A harmonic is one of an ascending series of sonic components that sound above the audible fundamental frequency.
The higher frequency harmonics that sound above the fundamental make up the harmonic spectrum of the sound. Harmonics can be difficult to perceive distinctly as single components, nevertheless, they are there.
Harmonics have a lower amplitude than the fundamental frequency.
Harmonics are integer multiples of the fundamental frequency. For example, if the fundamental frequency is 50 Hz (also known as the first harmonic) then the second harmonic will be 100 Hz (50 * 2 = 100 Hz), the third harmonic will be 150 Hz (50 * 3 = 150 Hz), and so on.
Overtones are frequencies of a waveform that are higher than, but not directly related to, the fundamental frequency.
Two tones produced by different instruments might have the same fundamental frequency and thus the same pitch e.g a C note, but sound very different because of the presence of different amounts of harmonics and overtones.
It is the presence of harmonics and overtones within a soundwave that helps to produce the sounds unique sound.
The timbre describes those characteristics of sound which allow the ear to distinguish sounds that have the same fundamental pitch.
It is due to the timbre that we can distinguish one instrument from another, for example, a piano played at C3 sounds different to a guitar plucked at C3.
The timbre is often described in subjective terms, for example, reedy or golden.