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Basics of Synthesis: Waveforms

Updated: Mar 24

G’day, Tom here with my debut post on the Island tutorial! Whether you’re a bedroom producer or a seasoned veteran making records with world-famous artists, you’ve probably at least fumbled around with the idea of synthesis - creating your own synth patches. But how does it work?

Here, we’ll be running through the basics of building waveforms in an additive context using harmonic (or partial) formulas. We’ll also look at the tonal characteristics of the four different waveforms you’re most likely to be using. And soon, like me, you’ll be making more synth parts than you’ll have DAW tracks to fit them in!

Waveforms are your starting point when you’re building a synth patch. The waveform (or multiple waveforms) you choose to enable will determine the spectral content and overall timbre emitted from your synth. It’s the most fundamental step in tone-shaping your way to a polished, professional sound.

Additive synthesis is about building a synth sound from the ground up. As opposed to subtractive synthesis - where sounds are shaped by removing frequencies from a waveform - additive synthesis involves compiling a specific set of sine waves to create your desired waveform.

This set is made up of a fundamental frequency (your chosen note on a keyboard) and harmonic frequencies (the ones that stack on top) all playing together at once. Those harmonic frequencies are integer multiples of the fundamental frequency. For example, if 440 hz is our fundamental frequency, the second harmonic is at 880 hz (twice the fundamental), our third harmonic is at 1320 hz (three times the fundamental), and so on for the fourth, fifth, and as many as you can count!

The key (no pun intended) to synthesis is that different combinations of harmonics will give you different types of waveform - and therefore different tones. There are four types of waveform in subtractive synthesis that are widely accepted as the standards for music production. The creators of early synths, such as Moog, believed these four waveforms would give the artist the most sonic control, versatility, and diversity. They are the Sine, Sawtooth, Triangle, and Square/Pulse waveforms. Let’s discuss the 4 waveforms individually, in depth.

The Sine Wave

A sine wave is typically quite easy to identify. It’s the most pure, clean sounding waveform of them all, including only the fundamental frequency. If your oscillator is set to produce a Sine wave, and you play an A3 note on your keyboard, a spectrum analyser is going to display a spike at 220 hz - and that’s all. Sub-bass is one of the most common utilisations of the sine wave in modern music. While the multitude of frequencies present in other waveforms create clashes and conflict in the low-end of a mix, the single-tone fundamental produced by a sine wave provides a strong, accurate, ‘phat’ bass. It’s the sort of thing that’ll rearrange the organs in your chest with a decent subwoofer.

The Triangle Wave

The triangle wave is slightly buzzier than the sine wave, but not quite as buzzy as the other two waveforms. Its harmonic structure contains only odd harmonics (i.e. the fundamental, the third, the fifth, the seventh, and so on), and the volume of each frequency tapers off the further away it is from the fundamental. The triangle wave can be used as a good mid-bass oscillator, as it adds a touch of richness and buzz to the sine wave without getting over the top. It’s almost right between a Sine wave and a Square wave, which leads me to the next waveform…

The Square Wave

The square wave has the same harmonic structure as the triangle wave - odd-numbered harmonics - but the harmonics remain much stronger as they move away from the fundamental. This gives you a very rich, buzzy waveform, which is brighter and more ‘in your face’ than a triangle wave, and can be shaped to create a nice vintage synth lead sound.

Square waves are a trademark of the Juno synth, an old-school hardware synth One of its two oscillators is dedicated to the square wave, and blending it with the other oscillator - which provides a saw wave - can birth some pretty staggering pad sounds, especially when combined with that fabled Juno chorus.

The Sawtooth (Saw) Wave:

Saw waves are very commonly used in modern synthesis (and they’re also my favourite waveform). They sound more aggressive and sharp than the other three waveforms we’ve discussed, and that’s because of the wealth of harmonics they contain. In fact, saw waves contain all the harmonics - odd and even. If you multiply your fundamental frequency by two, three, four, and so on, you’ll end up with a saw wave.

We’ve been talking about additive synthesis throughout this tutorial, but it’s worth noting that the amount of harmonic content in saw waves makes them popular in subtractive synthesis. Filters and other tone control measures are often used on saw waves to produce many of the pad sounds you hear in modern electronic music. With a bit of detuning to cap it off, it’s a really beautiful sound.

The world of synthesis branches far further than just waveforms and oscillators - but that’s where we’ll leave it for now! If you’re a synthesis newbie, go and experiment as much as you can with the information in this tutorial. You’ll be able to identify the different waveform sounds on the radio in no time… and that really is power. Have fun and happy synthing!


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