Assuming that you already know what harmonics are, how they affect our perception of timbre and how critical bandwidth determines pitch dissonance/consonance we can investigate how harmonics are themselves affected by the common processes involved in audio production. Let's start with a basic premise: altering the structure and interrelationships of harmonics is defined as 'harmonic distortion'. Harmonic distortion comes in two distinct forms: linear and non-linear. The former refers to changes in the amplitudes of harmonics while the latter refers to the creation of harmonics that were not previously present within a signal. The occurrence and effect of these distortions shall be considered with relation to three groups of audio processes: EQ/enhancers, compression/limiting and amplification (including dedicated distortion effects).
EQ and Enhancers
EQs are static with regard to frequency and create linear harmonic distortion by cutting boosting the amplitude of a fixed frequency bandwidth. This bandwidth is usually specified as the Q factor and is most commonly found in adjustable form on parametric designs. It is Q that has the most relevance with regard to harmonics and the distortion thereof.
When shaping or altering the tone of a source the choice of EQ type has major implications for linear harmonic distortion. Sources with limited harmonic content (i.e. tend towards a sine waveform) will respond less overtly to EQ cut/boosts unless its amplitude varies with frequency, in which case a simple shelving EQ can be used to even out this amplitude vs frequency shift. Sources with rich harmonic content exist over a large bandwidth which further increases if they possess a wide fundamental pitch variance, such as in a melodic phrase or chords. If a source IS sounding too bright or too dull then its harmonics are either too dominant or too quiet and thus a shelving EQ or filter is a good choice to cut/boost the harmonics as a whole. When trying to lift the presence of a source in a mix (i.e. bring it forward without just lifting the fader) a parametric or bell curve EQ can be a better choice for zoning m on those critical first few harmonics we use to identify an instrument.
If the instrument varies in pitch or plays chords then the bandwidth within which the first few harmonics exist can be large. A Q equal to the range of the second and third harmonics (three octaves or a Q of 0.4) is a good starting point to make sure the relevant harmonics do not fall outside the bandwidth of the EQ filter. A narrower Q will begin to display a more uneven harmonic adjustment response. One method to bring a bass source out in a mix without just increasing gain is to lift or even create harmonics that will cue the hearing system to its presence.
Bass enhancers or exciters do exactly this job, enhancing and creating harmonics from the fundamental frequencies present within a specified bandwidth. The effect of this can be observed when a simple sine wave is processed by an enhancer. A series of harmonics are produced that the brain uses to identify the fundamental frequency that they are produced from. If used excessively these harmonics become highly audible and make the instrument sound closer to a sawtooth waveform and therefore distorted, which may or may not be desired.
Compression and Limiting
Compression and limiting primarily affect the dynamic range of a signal to either increase their perceived loudness or control transients that might distort a proceeding amplifier stage. Though these processors come in many types and topologies (valve, solid state etc.) they all have one thing in common: by altering the relationship of the onset of a waveform to its steady state via the attack, threshold and ratio controls, the harmonic characteristic is distorted.
For most instruments the initial onset of a note, i.e. it's attack or transient portion, is critical to how we perceive its character or timbre. The faster the attack setting on a compressor or limiter, the faster the transient is reduced m amplitude, which then translates as a loss of high frequency response making the source seem duller or less 'present'. The fast attack also defeats the onset of the fundamental frequency and results in a loss of low frequency perception.
To prevent this loss of transient and low frequency perception the attack speed should be set slow enough that the transient is not totally lost, the fundamental frequency can develop but the total dynamic range is st ill reduced. As the brain uses the attack characteristic to identify an instruments timbre it follows that the release setting on a compressor/limiter has a less substantive effect on the perception of harmonic structure. The harmonic distortion effects of compressor and limiter attack times as well as ratio/threshold settings can also produce non-linear effects. With a limiting ratio (i.e. 10:1 or above) and a low enough threshold a compressor/limiter can chop off or flatten the rounded peak of a waveform, the effect of which is to produce a waveform approaching a square shape. This in turn produces odd numbered harmonics which are perceived by the brain as harsh.
A very fast attack speed can also contribute to this effect. If the attack time is set to below a quarter of a wavelength, for instance 3 ms on a 60 Hz bass note ( l/4 wavelength = 4.2 ms based on 60 Hz being equal to l/60th of a second), the gain reduction will occur before the initial onset of the wave has completed and thus square off the waveform, again producing odd numbered harmonics. This 'clipping' distortion is often used to add 'bite' to kick drums but can also be heard as the inevitable by-product of excessive hard limiting used in mastering over the last decade.
Amplifiers are, on the whole, designed to incur as little harmonic distortion as possible, but despite this all amplifiers can and will distort harmonics in both linear and non-linear fashions when driven hard enough or starved of electrons. let's look at a two basic building blocks and what distortion effects they produce to understand what our humble harmonics can be subjected to. The daddy of all distortions is the valve guitar amplifier, a legendary producer of harmonic distortions that started life as a bastardized hi-fi amp.
Nearly every stage of a valve guitar amplifier contributes some degree of harmonic distortion, from the saturation of transformers to the physical limitations of the moving coil loudspeaker, but it is the valves themselves that have received the most attention with regard to their sonic imprint. There are two types of valve commonly found in the guitar amplifier, the low power triodes used in the preamp stages and the high power pentodes used in the power output stages. Both triodes and pentodes can produce linear harmonic distortions within their normal operating regions but when driven by high inputs or starved of operating voltage they become quite unruly and non-linear.
Triodes, due to their internal topology, produce mostly even numbered harmonic distortions, both linear and non-linear, while pentodes will also produce some dominant odd-numbered harmonic distortions, making their effect harsher. One characteristic of valves that makes them a favored device for imparting harmonic distortion is that the transition from 'clean' to distorted is gradual and thus relatively simple to control for small degrees of harmonic 'excitement'.
The valve was superseded by the smaller and cheaper transistor, which are either single components or set out in a specific circuit and miniaturized into an Integrated Circuit (IC). The slew of transistors that appeared during the 1960s and 1970s became commonplace in many audio amplifier circuits. Most transistors display a less forgiving behavior than valves.
As a signal incurs more harmonic distortion it tends towards a squarer waveform. This is perceived as an increasingly harsh and unpleasant tone as the amplitudes of harmonics rise and their numbers increase. Extreme distortion will become more and more like white noise as non-linear harmonic distortion produces harmonics from harmonics to create a wholly inharmonic mess.
Harmonic Distortion - Angel or Devil?
Harmonic distortion can make an instrument come to life, it can also ruin the fidelity of an amplifier, it can make a guitar smg and it can trash a perfectly good mix in mastering.
An awareness of where harmonic distortion is occurring, what effect it may be having and how it may be reduced/increased can make a huge difference to how you record and how you treat your mix. I would highly recommend the study of harmonic structures of signals before and after processing with a spectrum analyser to identify the characteristics of both good and bad distortion, be it due to EQ, compression, fuzz pedals or amplifier stages.