Distortion is broadly defined as any change in an audio signal between two points. In common use, however, “distortion” usually means harmonic distortion, the addition of overtones to a signal caused by clipping in an electrical circuit. Several other types of distortion also exist, such as envelope distortion, digital aliasing, and intermodulation distortion, and any of these can be intentional musical effects or unwanted corruptions.
Clipping
Clipping is the phenomenon most people associate with distortion, but it’s actually the cause and harmonic distortion is the effect. When the amplitude of an audio signal is too strong for the circuit it’s passing through, the peaks of the wave are “clipped” off, becoming flat instead of rounded and starting to resemble a square wave. This adds high-frequency overtones to the signal, which are harmonically related to the notes being played.
Due to fundamental differences in operation, different types of circuits clip differently. Tube circuits produce “soft” clipping when they’re saturated with signal, creating a gradual breakup as volume increases.
Most transistor-based circuits produce “hard” clipping that takes effect as soon as the signal gets too loud (going from clean to distorted with a sharp cutoff), but tube saturation can be mimicked with clever design.
Harmonic Distortion
Two types of harmonics (even and odd) can be added by clipping, and it's the blend of the two that gives each particular amplifier or distortion effect its own complexity and tonal character.
Contrary to widely-circulated myths, neither tube or transistor-based designs produce only odd or even harmonics. Rather, the topology of the circuit and components used are responsible for the character of the distortion produced. Single-ended circuits produce strong even harmonics, but not without some odd ones. Push-pull designs mostly cancel out even harmonics, leaving the odd intact.
Second-order (or “even”) harmonics are even-numbered multiples of the fundamental frequencies in a signal, with a simple octave being the most prominent. Since even harmonics are always in tune with the notes being played, they lend a pleasing richness to a variety of signals, even complex timbres and dense chords.
Third-order (or “odd”) harmonics are odd-numbered multiples of the fundamental—the strongest being an octave plus a fifth. This gives a harsher, edgier sound prominent in rock and metal music. Because of the fifth, odd harmonics sound flattering on power chords, while other intervals—such as thirds and sevenths—can become muddy and unintelligible.
Total Harmonic Distortion (THD) is a measurement of the overall distortion added by a device—the sum of all the harmonics present at the output compared to the input. This statistic is expressed as a percentage and is calculated for microphones, preamps, speakers, and any other device where a pure signal is favorable. A THD of zero is impossible to achieve outside of a laboratory, but scores less than 1% are common in high-end gear.
Other Types
Saturation is the gradual change in tone when tubes and magnetic tape reach the upper limits of their intended ranges. Saturation often results in a soft, pleasing compression, which many pedal and plugin designers go to great lengths to emulate.
Intermodulation distortion occurs when non-harmonic or sub-harmonic frequencies appear in a signal due to complex relationships between tones. Fuzz pedals can create significant intermodulation distortion when dissonant intervals are played through them, resulting in a muddy, unintelligible sound.
Envelope distortion occurs when the amplitude of a sound is altered over time. Compressors, for example, allow the user to control sounds that have an undesirable envelope by enhancing sustain and de-emphasizing transients. The amp envelope on a synthesizer does the opposite, giving attack, decay, sustain, and release characteristics to otherwise static waves.
Phase distortion is what happens when all or part of a signal’s phase is shifted, often as a side effect of electronic circuitry. Multiband equalizers can cause phase distortion when certain frequency bands are processed and others aren’t, and high-end gear (like mastering equalizer) is designed to minimize this effect.
Noise isn’t technically distortion but rather the addition of unwanted content to a signal, like crosstalk between two radio stations. Noise can creep into a signal through unbalanced cables, single-coil pickups, ground loops, and poor impedance matching. Every circuit has a noise floor, or a constant low-level noise, that can be minimized with proper gain-staging.
Digital clipping is produced when a signal exceeds the limits of the system transmitting it. Just like analog circuits, digital audio systems have an upper limit to the information they can convey (known as Full Scale). When a signal exceeds 0dB Full Scale, it's squared off in a harsh and artificial-sounding way.
Aliasing is another byproduct of digital audio, produced when certain frequencies are interpreted incorrectly—the audio equivalent of those jagged lines in video games. Aliasing can occur when frequencies below or above the range of a system are not properly filtered out. Some plugins and digital gear feature a function called "upsampling," which increases the sample rate before processing a signal, allowing it to be filtered to avoid aliasing.