Introduction

We have already discussed the simplest sound, a sine wave, created by a source vibrating in simple harmonic motion. But all natural sources vibrate at a combination of frequencies simultaneously producing more complex waveforms.

Such complex waveform can be thought of as comprising a number of individual sine waves of differing frequencies which interact and interfere with each other in a complex process of summing and canceling (phase) producing a single more complex waveform pattern.

Harmonics

In sounds with a definite overall pitch (such as those that musical instruments produce) each individual vibration is known as a harmonic. The diagram below shows some of the individual harmonics in a square wave (you actually need at least 20 harmonics to approach a squareish shape).

Sample MP3

Square wave 1KHz

Fundamental / 1st harmonic

In a complex sound, the vibration with the highest amplitude (the loudest) and lowest frequency (bassiest) is known as the fundamental. It is also known as the 1st harmonic.

Subsequent harmonics

Additional harmonics, each with a successively lower amplitude and higher frequency, will be named the 2nd, 3rd, 4th, etc harmonics.

Pitch

Sounds which have a definite pitch are distinguished by a repetitive waveform. No matter how complex the waveform is it repeats its pattern at regular intervals.

Overall frequency / pitch

Although complex waves are made from harmonics at many frequencies they have an overall frequency or pitch. This overall frequency is usually determined by the frequency of the fundamental or 1st harmonic. Higher harmonics are often referred to as "overtones" by musicians.

Timbre

The relationship of fundamental and harmonics creates the character of a sound and is known as its timbre. Natural sounds produce enormously complex waveforms. Here are some simpler waveforms as produced by an analogue synthesiser.