Subtractive Synthesis Part 1

Subtractive synthesis is probably the most commonly used method of synthesis in electronic dance music. It is used by famous hardware synths such as the JP-8000, Nord Lead, and Access Virus, and much-used softsynths like z3ta+, Vanguard, and Albino. It is often the first sort of synthesis that new producers have a chance to play around with, and one that a great many producers use to produce "bread and butter" sounds for tracks, such as the "supersaw" and a huge number of keyboard and bass sounds. But how does this synthesis method actually work?

The basic idea behind subtractive synthesis is very simple, and is hinted at by the word "subtractive": take a raw, harmonically rich unit of sound -- called a "waveform" -- and manipulate component frequencies, change pitch, dynamic properties, and (sometimes) timbre by using the knobs and sliders on your synth. Each of these terms could use some explanation, which I will give. But first it's time to say a little bit about tones, timbre, and how they relate to the mathematical properties of sound waves -- I know, boring, but it's good to know and might make things less confusing later on.

Frequencies, Pitches, Harmonics, and Partials

All waves, including sound waves, have high points (peaks) and low points (troughs). The frequency of a sound wave (or any kind of wave) is the number of times per second that the sound wave repeats itself -- how long it takes to move from trough to trough or peak to peak. Pitch is, for our purposes, the same thing as the frequency of a sound: if a sound wave has a high frequency, you will perceive it as "high-pitched," and if it has a low frequency, you will perceive it as "low-pitched." The frequency of a sound wave is measured in Hertz (abbreviated "Hz"). Nearly any given sound you hear will contain lots of individual waves with different frequencies -- these combine to give the sound its distinct character -- and a sound's fundamental frequency is the frequency of the lowest frequency wave contained within the sound.

A harmonic is a whole number multiple of the fundamental frequency of a sound; as an example, 880 Hz would be the "second harmonic" of 440 Hz, since 440 * 2 = 880; then 1320 would be the "third harmonic," and so on. A partial is a fractional or decimal multiple of the fundamental frequency of a sound; 660 Hz would be a "partial" of 440 Hz. Sounds that people call "rich" have a lot of harmonics and sometimes partials present along with the fundamental frequency: this is what gives them their unique, attractive, or "interesting" character. [1]

What is a "waveform?"

[Note: a very useful tool to use in following along here is Native Instrument's Absynth, because it allows you to edit your own waveforms and view the effects on the harmonics of a wave (and vice versa).]

A waveform is the "basic" sound you start out with when you construct a patch from scratch on a subtractive synth. The four "classic" waveforms are the following:



What does the shape of each waveform represent? The shape represents two characteristics on the following graph: the y-axis of the graph is amplitude (one half the vertical distance from a wave's peak to its trough) and the x-axis of the graph is time:



The four waveforms pictured above each have a characteristic "sound" (or "timbre") that results from the harmonics contained in them. Both the square and saw waves are especially rich in harmonics, making them ideal building blocks for "lead" sounds that can catch the listener's attention. Here are the four classic waveforms being played on Reason's Subtractor synth:

Sine - Triangle - Square - Saw

Now, after this long introduction you are probably thinking, "Okay, fine, but when are you going to tell me the stuff that will actually help me in designing a synth patch?!" Soon, soon! The next installment of this series will cover oscillators, filters, envelopes, and all the other good stuff that will allow you to create nice patches for subtractive synths.

NOTES

[1] It is useful to think of all non-sine waves as the sum of a bunch of sine waves, each one having a different frequency (usually, but not always, an integer multiple of the fundamental frequency). That is, waves such as saws and squares can be thought of as a number of sine waves all interacting with one another; this "summing of waves" concept is the basis for additive synthesis, but that is getting off-topic...