Some call it "clipping", others call it "Creative Destruction"!
Dictionary Definition: the act of twisting or altering something out of its true, natural, or original state.
Definition in Audio Terms: a falsified reproduction of an audio signal caused by change in the wave form of the original signal.
Distortion can be a friend or foe in the world or audio. It all depends whether it has been used creatively or not. In audio, the term refers to harmonic distortion, which you see among common amplifier specs as THD, or total harmonic distortion. Harmonic distortion, in amplifiers especially, is usually caused by the amplifier needing more voltage than that of its power supply. It's also caused by a part of the internal circuitry (the output transistors) exceeding its output capacity. So, instead of reproducing the peaks of a waveform, the amp clips them off, hence the term "clipping".
Here's an example of clipping in the oscilloscope chart shown above. You see a sine wave (BLUE), and at top, a heavily clipped version (RED) of the same wave at bottom. The peak of the audio wave is clipped off at the point where the amplifier's power hits its maximum output. Therefore the original sine wave becomes more of a square wave. This creates extra harmonics at multiples to the original tone.
Another thing to keep in mind is the difference between Even-order Harmonic Distortion, and Odd-order Harmonic Distortion.
The best-known form of distortion is harmonic distortion, where the output of an audio signal contains additional harmonics that occur at the natural harmonics of the input. When a source clips, the waveform is generally flattened. Analog devices tend to gently flatten the waveform and produce what we think of as saturation. When a digital device clips, it does so by chopping off the tops of the waveforms abruptly (as shown above). If this 'flattening' is symmetrical, it produces odd-order harmonic distortion at the third and fifth harmonics. Even-order harmonics represent octave multiples of the fundamental note. They thicken the sound, but continue to emphasise the same tone, just with more octaves mixed in, continually reduced in volume as they go up.
Even harmonics would tend to sound very sweet, where as the odd harmonics would sound less sweet, but still interesting.
For a simple example of harmonic distortion, I inserted a Es2 software synth into Logic Pro X. Assigned a Sine wave and held a low D. Here's the spectrum analysis; A plain and simple sine wave compared to a distorted sine wave, with a maxed out input gain:
Sine Wave Test:
Distorted Sine Wave:
With Compressor/Limiters, you can gain a little extra harmonic distortion, using Limiter functions, such as fast release times and maximum limitation. These processors gave the signal a viable characteristic. So for any rock inspired musician, you can easily colour your clean, direct signal, by distorting it this way. A playful tool, especially for rock and metal instrumentals.
As a guitarist, I'm always seeking that dirtier, fuzzier, tonal character, so other than using the obvious pedals at my disposal, the option to utilise gain in a creative way will not be overlooked in my future productions. I love learning new things.
Lussier, G., & Jones, T. (2018). What Is Distortion?. Retrieved from https://www.gizmodo.com.au/2011/08/what-is-distortion/