Sine, Square, Sawtooth: Synthesizer Waveforms Explained

A waveform is the shape of one cycle of a sound. A sine wave is a single pure frequency; the other basic waves add harmonics, multiples of that frequency, on top. A triangle has a few weak harmonics, a square has strong odd ones, and a sawtooth has all of them, which is why it sounds the brightest. A synthesizer starts from one of these waves and shapes it with a filter and an envelope.

Why Waveforms Sound Different: Harmonics

Play the same note on a flute and on a violin: the pitch is the same, the sound is not. The difference is in the harmonics. Almost every musical sound consists of a fundamental, the frequency we hear as the pitch, plus a series of quieter tones at two, three, four and more times that frequency. Which of these harmonics are present, and how strong each is, gives a sound its color.

The mathematician Joseph Fourier showed that any repeating waveform can be built by adding sine waves at these multiples. For the classic synthesizer shapes the recipes are simple, as the lab notes of an MIT electronics course summarize: a square wave contains only the odd harmonics, each at a strength of one over its number; a triangle wave contains the same odd harmonics, but they fall away with the square of the number; a sawtooth contains every harmonic, odd and even.

The Four Basic Waveforms

Sine

The sine wave is a single frequency with no harmonics at all. It sounds pure, round and soft, like a whistle or a tuning fork. On its own it is used for sub-bass, which should add weight without color, and as a building block: every other sound is a sum of sines.

Triangle

The triangle wave looks like a sine with straight edges, and it sounds like a slightly brighter sine. Its odd harmonics are there but weak: the third is at one ninth of the fundamental, the fifth at one twenty-fifth. It suits soft leads, flute-like tones and mellow bass.

Square

The square wave jumps between two levels and spends equal time at each. It contains the same odd harmonics as the triangle, but far stronger: a third, a fifth, a seventh. The missing even harmonics give it a hollow, woody tone, a little like a clarinet, and it is the sound of early video games. If the two halves of the cycle are made unequal, it becomes a pulse wave, and the tone gets thinner and more nasal.

Sawtooth

The sawtooth ramps up and drops back. It contains every harmonic, each at one over its number, which makes it the richest and brightest of the four. That is why it is the usual starting point for strings, brass, pads and leads: with all the harmonics there, a filter has the most to work with.

From Raw Wave to Instrument

A raw sawtooth is a harsh buzz. What turns it into an instrument is what happens next. In subtractive synthesis, the most common method, the wave passes through a low-pass filter that removes the harmonics above a chosen frequency, the cutoff. Lower the cutoff and the sound gets darker and rounder; raise the resonance and the harmonics around the cutoff are emphasized, which gives the filter a vocal, whistling edge.

The second tool is the envelope, usually written ADSR: attack, decay, sustain, release. It sets how the loudness of each note changes in time. A fast attack and a short decay give a plucked sound; a slow attack and a long release give a pad. The same sawtooth can be a bass, a string section or a bell-like pluck, depending on the filter and the envelope.

A third trick is detuning: two oscillators playing the same wave a few cents apart drift in and out of step, and the result is a wider, livelier tone than either gives alone.

Hear It for Yourself

The quickest way to learn the waveforms is to switch between them while you hold a note.

To see how the pitch of a note relates to its frequency, the Frequency to Note Converter shows both.