Fundamental & Harmonic Frequencies

Sound sources emit at specific frequencies, including a fundamental frequency, harmonics and overtones.

Fundamental Frequency

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.

The fundamental frequency is the frequency we actually hear the sound at.

A sine wave is the simplest of all waveforms and contains only a single fundamental frequency and no harmonics or partials - see figure 1. Virtually all musical sounds have waves that are infinitely more complex than a simple sine wave. It is the addition of harmonics and overtones to a wave that make it possible to distinguish between different sounds and instruments; the timbre.

The sine wave is the simplest waveform

transverse-wave.png
Fig 1 - Sine wave

Harmonics

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 (volume) than the fundamental.

Harmonics are positive integer multiples of the fundamental. 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.

harmonics
Fig 2 - Harmonic partials f, 2f, 3f, etc. (where f means fundamental frequency).

Overtones

Overtones are frequencies of a waveform that are higher than, but not directly related to, the fundamental frequency.

Differing Timbre

Two tones produced by different instruments might have the same fundamental frequency and thus the same pitch e.g a C note, but sound different because of the presence of different amounts of various harmonics and overtones.

It is the presence of harmonics and overtones within a wave that helps produce the sounds unique timbre.

The timbre describes those characteristics of sound which allow the ear to distinguish sounds which 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.

Most sounds are dynamic events that are continually changing over time. If an instrument’s harmonic balance were to change, the sonic character of the instrument would change also.

Microphone Frequency Response

It is important to understand that the frequency response of a microphone has an effect on the overall sound and timbre of a recorded instrument. If a microphone’s frequency response is shaped as opposed to flat, the sound timbre will change. For example, if the low frequencies are rolled away from a kick drum, the sound will become weaker than it should be. For this reason, specific devices or the use of an equalizer can be useful tools in varying the timbre of an instrument, thereby changing its subjective sound.

Read more about microphone frequency response.