New Harmonics

We look at the processes that can add harmonic content to a sound, for subtle warmth or radical transformation.

You might see a sound engineer as an audio chef, blending the finest ingredients to create the perfect sonic dish. But there’s another food analogy that I think is interesting to consider, that of fermentation. Fermentation is the use of organisms such as yeast and bacteria to transform otherwise innocuous foods into more complex and interesting ones such as bread, beer and chocolate. Similarly, certain audio processes can introduce new frequencies and harmonics that weren’t there before, and which can create spicy new audio flavours and tasty sonic experiences.

Techniques such as distortion, saturation, clipping, resonant feedback and waveshaping are all methods of introducing brand‑new harmonics into a sound. This article will look at a few of the ways to ‘ferment’ your audio in this way, introduce new harmonics and to creatively transform its character.

Distortion, saturation, clipping, resonant feedback and wave‑shaping are all methods of introducing brand‑new harmonics into a sound.

Distortion Overload

The most common method of adding harmonic content to a signal is through distortion. Technically speaking, distortion is a description of what happens when a signal is transformed in a non‑linear way as it passes through a system or a component. Which is a technical‑sounding term for a relatively straightforward idea, as shown in Diagram 1.

Diagram 1: ‘Linear’ just means the signal passes from the input to the output without change: the mapping from input to output is one‑to‑one, creating a straight line, hence linear. So ‘non‑linear’ just means the line is no longer straight, representing the fact that the signal has lost that one‑to‑one mapping between input and output, ie. it’s been changed.

A non‑linear response introduces harmonic content: feed a sine wave in, for example, and you may get additional sine waves produced a fifth or an octave above. This is normally undesirable, and equipment designers vie to achieve the lowest Total Harmonic Distortion, a measurement of how much unwanted distortion is being introduced.

However, it was realised quite early in the history of recording that certain kinds of distortion actually sounded good, and enhanced the power of the music. All kinds of distortion were experimented with, from ‘quite subtle’ to rock music’s full distorted guitar sound, which opened pathways to whole new musical genres.

Brian Eno has written that by distorting a sound, one is subconsciously stating that the music is bigger than the system can even contain, implying its power and might! Which certainly works for rock music, but there are different ways of introducing distortion to a sound and they don’t all have to be as obvious as the kind you get from a fuzz pedal or distorted guitar amp. Applying distortion more subtly can give us the benefits of new harmonics, warmth and a richer tone without totally transforming the signal.

Amplitudinal Clippage

The easiest way to get a non‑linear and hence distorted response from a component or device is to feed it too high a signal level. In this state, it won’t be able to represent the signal accurately, and eventually, we’ll reach the point where it simply can’t produce any more voltage, no matter how much we pile on the input signal. This state is known as clipping, because the top and/or bottom of the waveform gets flattened out.

Synth aficionados will realise that as a signal becomes progressively more clipped, it starts to resemble a square wave. And as a square wave is the theoretical sum of an infinite number of odd‑numbered harmonics, it’s no surprise to find that clipping introduces predominantly odd‑numbered harmonics. In extremis, it can actually turn a guitar or bass note into something that sounds a lot like a synth square wave. It also means, interestingly, that in theory, clipping a square wave has no audible effect! In practice, hardware and software clipping do other things to the signal which may indeed alter the sound further.

Diagram 2: Clipping is easily illustrated using the example of a sine wave. As the top and bottom of the waveform are ‘clipped off’ it becomes more and more distorted, tending towards a square wave.

When clipping starts abruptly at a set level, it’s referred to as ‘hard clipping’. Signals just below the threshold are completely undistorted, while those just over it are clipped. It’s not the most subtle way to introduce distortion, and it’s not typical of most analogue circuits. More often, things become progressively more non‑linear above a certain level, so you can get some distortion before full clipping is reached. This response is referred to as ‘soft clipping’. (‘Hard‑knee’ and ‘soft‑knee’ settings are similar concepts found in compressors.)

Each piece of equipment is different, of course, and will respond differently to different amplitudes and types of material in relation to their thresholds and non‑linear response curves, and so will generate different sets of odd or even harmonics at different rates and intensities. Software emulation of distortion can take this kind of manipulation into very sophisticated realms: dynamic clipping thresholds, variable frequency responses, parallel distortion channels, and so on.

Worth noting is that some classic guitar fuzzboxes use a distortion curve that’s asymmetric. This means the positive‑going and negative‑going halves of the signal are distorted differently, and usually causes the addition of even‑order harmonics to the already present odd‑order harmonics. This manifests itself as a generally fuller tone, with more low end. Symmetric curves, by contrast, generally only generate odd‑order harmonics, which is sometimes better when an already full sound doesn’t need the full odd and even treatment!

Altering the EQ of a signal going into a distortion unit can have quite a significant effect on the distortion behaviour, and is always worth exploring. The low end will usually be driven into distortion more quickly, as it’s where most of the energy lies, so if that bass is distorting too much and overwhelming the rest of the sound, cutting low end before the distortion unit can help balance the resulting distorted tone.

Clipping distortion works well on single instruments as a creative tool. It can produce a thicker, richer tone, with increased high‑frequency content. By the same token, though, it’s often too much on more complex material as every frequency present creates its own set of harmonics, along with all the others. So much high‑frequency content is then generated that it tends towards white noise and send the whole mix into meltdown. For subtler use cases, such as on groups of instruments, mix buses and whole mixes, the gentler type of distortion described as saturation is usually more useful.

Clipping distortion works well on single instruments as a creative tool... but is often too much on more complex material as every frequency present creates its own set of harmonics, along with all the others.

Saturation

Saturation, in the analogue realm, occurs when the signal starts to exceed the level at which a device can represent it in linear fashion. Signal peaks are not clipped, but neither are they represented at their true amplitude. Sometimes the saturation effect is achieved by deliberately overloading a mixing desk, tape machine or tube compressor, but there are also lots of hardware and software products specifically designed to introduce pleasing saturation. As well as sympathetic harmonic content, saturation also reduces the dynamic range of the signal. Transients may also be softened, because these are often the biggest peaks in the signal and so cannot be represented accurately by the component that’s being saturated. Used carefully on a mix bus, saturation can provide that ‘glued’ feeling thanks to the compressing effect, and add richness from the added harmonics.

By modifying the frequency range of the signal going into a saturator, we can create an enhancer: an alternative to high‑frequency EQ that adds harmonic content to the upper frequencies to ‘excite’ the mix. Try boosting a small frequency range with EQ before the distortion effect, then apply the opposite EQ curve to the output signal. The chosen frequency range won’t be louder than before, because the bulk of the new harmonics added by the distortion will relate to that region.

One classic use case is to make a subby bass more audible on smaller speakers by adding distortion to the upper frequencies, filling out the low midrange so that the bass seems louder even though the mix level hasn’t been changed. This can be done through a selective EQ parallel distortion process: create a parallel channel of the bass with plenty of distortion (to taste), cut the low end of this distorted signal so the original low end of the bass is unaffected, but bring in the top end of the distortion over the old signal to boost the higher mids and tops.

In the real world (and in emulations of it) there are some common sources of saturation, such as magnetic tape, tubes, valves and transformers, each of which has its own characteristic response to being pushed beyond its linear range of operation.

Audio tape generates both odd and even harmonics as it runs out of magnetic particles to represent increases in signal level. Interestingly, the level of third‑order harmonics (third‑harmonic distortion) was used to calibrate tape machines, and usually at 3 percent (which is a pretty high level of distortion). An overdriven tube is often particularly rich in second‑order harmonics, and because these second‑order harmonics are relatively lower in frequency than the other upper‑order harmonics, this can sound warmer than other types of saturation.

Saturation can be added when tracking instruments by overdriving the mixer channel or mic preamp, potentially pushing transformers and other components outside their linear range of operation. This is a much‑used technique, but needs to be done carefully, as the saturation can’t be removed afterwards. Overdriving mixer channels at mixdown is another method of achieving a saturated sound, and saturation across an instrument group or bus will give that glued feeling, due to the shared compression effect and harmonic generation. When used across a whole mixdown in mastering, it will generally need to be a lot more subtle and treated more as an enhancement rather than an attention‑drawing ‘effect’.

Wave‑folding

Although distortion and saturation of these kinds are probably the most common ways of adding new harmonics to a signal, they’re not the only ones. Synthesizers have had a method called ‘wave‑folding’ since the late 1960s, and this was used on the earliest Buchla and Serge modular systems.

Diagram 3: The simplest form of wave‑shaping to illustrate is the wave‑fold; ‘reflecting’ back the top of the waveform above the threshold. This introduces all manner of related harmonics. It’s even more effective when the threshold, bias or phase are changed dynamically for a really exciting sound.

Instead of clipping the amplitude of a signal, they ‘reflect’ the waveform back above a threshold by inverting it. Add phase‑shifts and bias control over the precise nature of the wave‑fold, and they can create a huge range of wild and exciting sounds. With the explosion of Eurorack modules over the last 20 years, it’s become a much less niche method and is part of the new vocabulary of synthesis. Frequency modulation (FM) and amplitude modulation (AM) are further methods of cross‑pollinating audio signals to create new harmonics.

Bit‑crushing

Distortion doesn’t have to be added in the analogue domain, either. By reducing either or both of the word length and sample rate of a digital signal, one can add another style of crunchy old‑school digital distortion. Unlike the odd‑ and even‑order harmonics added by analogue distortion, the distortion products of bit‑crushing tend to be unrelated harmonically to the source signal. From a sonic point of view this makes them much grittier or harsher, which is great for sound design, perhaps less so for ‘warming up’ a mix! It’s a commonly found effect in modern DAWs and is often effectively used on drum loops and percussion samples to ‘rough’ them up a bit.

In Summary

So, to return to the culinary analogy, we don’t have to limit ourselves to blending a few basic ingredients or feel stuck with their current nature, we can be audio fermenters, devising new ways to introduce extra flavours into our audio bakes and surprising ourselves — and our audience — with newfound harmonic content, and sometimes brand new genres of music into the bargain! Hopefully the examples discussed here will give you food for thought and some ideas to explore in your own sonic kitchen...