How does a synthesizer work?

A synthesizer makes sound from electricity alone. Nothing vibrates until the very end, when a loudspeaker turns the voltage into moving air (see Faraday's law for how a speaker works).

This is a classic analog synth, laid out like the Minimoog of 1970. Read its front panel from left to right and you follow the sound. The oscillators (VCOs) make a buzzing tone. The mixer blends them. The filter (VCF) takes away the bright parts. The amplifier (VCA) makes it louder and softer, steered by an envelope. Then it goes out of the output jack.

The keyboard only sends two signals: which note (a control voltage) and when a key is down (a gate). The pitch wheel bends the note and the mod wheel adds wobble from an LFO. Under the panel are the circuit boards that do the real work.

Early synths were modular: separate boxes joined by patch cables, so you could wire them any way you liked. The Minimoog wired the most useful path inside, so musicians could take it on stage.

An oscillator makes a wave that repeats, and how many times a second it repeats is the note's frequency. A3 repeats 220 times a second: 220 hertz (Hz). But the shape of the wave matters too. That is why a flute and a violin playing the same note sound different.

In 1807 Joseph Fourier showed that any repeating wave can be built by adding up plain sine waves, at 1, 2, 3, 4… times the main frequency. These are the harmonics. Each wave shape is just a recipe:

A sine wave is one harmonic alone: a pure, soft tone. A sawtooth has every harmonic, the nth one 1/n as strong: bright and buzzy, like brass or strings. A square has only the odd harmonics (1, 3, 5…) at 1/n: hollow, like a clarinet. A triangle has the odd ones too, but they fade as 1/n², so it is much softer.

The layers behind show each harmonic. The glowing line in front is their sum: the wave the speaker plays. The boards show the live signal when you play: a scope for the shape, a spectrum for the harmonics.

Most classic synths use subtractive synthesis. The oscillator makes a bright wave with lots of harmonics, like a sawtooth. Then a filter takes some away, the way a sculptor carves stone.

The usual filter is a lowpass: low frequencies pass, high ones are cut. The cutoff is where the cutting starts. Above it the harmonics fall away steeply: this filter loses 24 dB per octave, so each doubling of frequency leaves only a sixteenth of the strength. Bob Moog's ladder filter of 1965 had this slope, and it is a big part of the famous Moog sound.

Resonance (Moog called it emphasis) feeds some of the output back in, so harmonics right at the cutoff get a boost. Turn it up and you hear a sharp, singing peak. Move the cutoff while a note plays and you get the wah of a filter sweep.

An envelope can open the filter on every note and let it close again. That makes a note start bright and turn mellow, just like a plucked string: see GuitarClear.

A real instrument's note has a shape in time. A piano note starts with a bang and fades. A violin can swell slowly and hold. A synth copies this with an envelope generator, and the most common kind has four settings, ADSR:

Attack: how long the sound takes to rise to full strength after you press a key. Decay: how long it takes to fall to the sustain level. Sustain: the level it holds for as long as the key is down (a level, not a time). Release: how long it takes to die away after you let go.

The key sends a gate signal: on while held, off when released. The envelope turns that simple on/off into a smooth curve, which drives the amplifier (VCA). Here it also opens the filter a little, so the note is brightest when it is loudest, as in real instruments.

Short attack and no sustain gives a pluck. A slow attack and long release gives a soft pad. Everything at full gives an organ, which is on or off. A quick swell with a bit of decay sounds like brass.

Decay and release fall fast at first, then slower and slower. The times here are how long they take to get 98% of the way.

In 1967 a composer at Stanford, John Chowning, found another way to make rich sounds. Take a plain sine wave, the carrier, and wobble its frequency very fast with a second sine wave, the modulator. This is frequency modulation (FM), the same idea FM radio uses, but at audio speed.

When the wobble is fast enough, you stop hearing a wobble. You hear new frequencies, called sidebands, spaced evenly on both sides of the carrier: fc ± fm, fc ± 2fm and so on. Two numbers control them. The ratio of modulator to carrier sets where the sidebands land. Whole-number ratios give harmonics, like an instrument. Other ratios give clanging, bell-like sounds. The index (how hard it wobbles) sets how many sidebands are strong. Their heights follow maths called Bessel functions.

Chowning published this in 1973, and Stanford licensed the patent to Yamaha. In 1983 Yamaha's DX7 put FM in a keyboard musicians could afford, and its electric piano and bell sounds are all over 1980s pop. It was digital: its six "operators" are sine waves computed by chips.

Two other ideas followed. A sampler, like the Fairlight CMI of 1979, records real sounds and plays them back at any pitch. A wavetable synth, from the early 1980s, steps through a list of stored wave shapes as a note plays.

In 1983 synth makers agreed on a common language: MIDI, the Musical Instrument Digital Interface. It was pushed by Dave Smith of Sequential Circuits and Ikutaro Kakehashi of Roland, and it still works today. MIDI sends no sound at all, only messages, as a stream of bits down a 5-pin cable.

Press a key and the keyboard sends three bytes: Note on plus the channel (90 in hex for channel 1), which note (60 is middle C) and velocity, how hard you hit it (0 to 127). Let go and it sends Note off (80). The cable runs at 31,250 bits a second. Each byte takes 10 bits, so a note-on takes under a millisecond.

A sequencer sends those messages for you, on time. This one has 16 steps, each a sixteenth of a bar, with a row for each drum and one for the bass. Its coloured step keys copy the Roland TR-808 drum machine of 1980, whose booming synthesized bass drum is all over hip-hop and pop. Roland's TB-303 bass machine, with its squelchy resonant filter, started acid house.

An arpeggiator takes the keys you hold and plays them one at a time in a pattern. Today a DAW (a music program on a laptop or phone) does all of this in software: its software synths do the same maths as the oscillators, filters and envelopes in this box.