How a synth makes sound

Take the A above middle C, 440 vibrations a second. Play it on a violin, then on a flute. The frequency is the same, the loudness can be made the same, and still you could not mix them up with your eyes shut. So a note is more than a frequency. There is something else in it, and a synth can build that something out of nothing.

What makes a violin sound different from a flute on the same note?

This chapter is the instructions for a build-it-yourself synth kit. Each section adds one block: the oscillator, the filter, the amplitude envelope, the filter envelope, the LFO and glide. Each section has the synth itself, with exactly the knobs built so far, and a separate bench that shows what the new block does to the sound. Keep a hand on the keys: a MIDI keyboard, the A S D… row on a computer, or the keys in the strip at the top of the page. Headphones help a lot: a phone speaker plays almost no bass.

One note, different sounds

In chapter 1 a string sounded not one frequency but a whole stack: the fundamental, then twice, three and four times as high. These are the overtones. Every musical sound has them, and what the ear cares about is which of them are loud and which are quiet. Below is an organ where each overtone of the 440 Hz A is a bar of its own. Tick "The keyboard plays this sound" or press "Hold a note", then drag the bars.

Try the presets. "Flute-like" puts nearly everything in the first bar and a trace in the rest: the sound is soft and round. A real flute sounds like this, especially when played quietly, because its fundamental is much louder than everything above it. "Clarinet-like" has a strong first, third and fifth harmonic and almost nothing in the even ones. That is the sound of the clarinet's low register: its tube is closed at one end, which mostly supports the odd harmonics, and the sound comes out hollow and woody. "Violin-like" has every harmonic in a row, each quieter than the one before: the second is half as loud as the first, the third a third as loud. At once the sound turns bright and dense.

This set of bars has a name: the spectrum. The wave above the bars is their sum. Different spectra add up to waves of different shapes, even though the period, and so the pitch, is the same for all of them.

Now leave the bars alone and switch "Over time". "Steady" holds the sound still, like an organ. "Bowed" lets it swell over two or three tenths of a second and waver slightly in pitch. "Plucked" gives a strike and a fade, and the upper harmonics die away faster than the lower ones: watch the bars on the right melt first. Choose "violin-like" and "plucked" and you get pizzicato, the violin played by plucking the string. The spectrum is the same, yet it seems like a different instrument.

That answers the course's second question. On a violin the bow drags the string in jerks, so it vibrates almost like a sawtooth, and the sound has plenty of strong upper harmonics. It swells within a fraction of a second and trembles with vibrato. On a flute nearly all the loudness sits in the fundamental, and the sound stays level for as long as the breath lasts. A synth knows nothing about wood or strings. What it controls is exactly these two things: the spectrum and time.

The synth you played by drawing the spectrum

The Soviet engineer Yevgeny Murzin came up with his instrument around 1938, but could only build it by 1957–1958. He called it the ANS, after the initials of the composer Alexander Nikolayevich Scriabin. The ANS was not played from keys. Its sound was drawn: the composer scratched lines into an opaque mastic coating on a glass plate, and every point up the plate was a frequency of its own. It is the same organ of harmonics, only with hundreds of bars that change over time. Eduard Artemyev used the ANS for the sounds of Tarkovsky's Solaris (1972). The only surviving instrument is kept in Moscow, at the Museum of Music.

Block 1: the oscillator

Setting dozens of overtones by hand takes a long time. So the first block of a synth is the oscillator: it puts out a ready-made wave in one of a few shapes. Each waveform has its own spectrum, and that spectrum can be worked out exactly. Pick a shape, slide "Harmonics" down to one, then back up.

A sine is one harmonic and nothing more: the purest and dullest sound there is, like a dialling tone. A triangle has only the odd harmonics, and they fade fast: the fifth is 25 times quieter than the first. The sound is soft, a little like a flute. A sawtooth has every harmonic, and the nth is n times quieter than the first: the same "violin-like" spectrum as in the organ above. A square wave has only the odd harmonics, like a clarinet, and that is why it sounds like one.

The slider shows that the waveform and the spectrum are one and the same. Add harmonics one by one and the corners of the sawtooth or the steps of the square slowly grow out of the sine. How any wave breaks down into sines is shown in detail in the Fourier series tool.

Here is the synth's oscillator, on its own for now. Tick "The keyboard plays this sound" and play something while you switch the waveform.

Now by ear, with no picture. The sine is easy to spot. The sawtooth and the square are the pair people confuse most: the sawtooth is brighter and buzzes, the square is duller and sounds nasal.

If you keep mixing them up, try the "Timbre by ear" trainer: its levels go from two shapes up to four.

Block 2: the filter

The oscillator gives you four sounds. That is not many. You could build a sound out of sines, as in the organ of harmonics. That is called additive synthesis, and it is hard work: every overtone has to be set separately. A classic synth works the other way round. It takes a wave with overtones to spare, a sawtooth or a square, and cuts away what it does not need. This is subtractive synthesis, synthesis by taking away: the sculptor does not model clay but carves stone.

The carving is done by a low-pass filter. It lets through everything below the cutoff and muffles everything above it, more and more the higher you go. Below is a sawtooth on A2 (110 Hz): the grey bars are its harmonics, the coloured ones are what got through the filter. The dark line is the filter itself. Press "Hold a note" and drag the dot.

Cutoff down, and the sound darkens, as if someone put a pillow over it. Cutoff up, and it opens out, with "air" coming in. Press "Sweep the cutoff": a filter sweep like this runs through a huge number of electronic tracks.

The second knob is resonance. It raises a narrow hump right at the cutoff, and the overtones that land on it sound louder than the rest. With a little resonance the filter just darkens the sound. With a lot you hear a whistle, and when the cutoff moves, a typical "wow", as if the sound were saying vowels.

The oscillator is playing a sine, and you slowly lower the cutoff: from far above at first, then closer and closer to the note. What do you hear?

Almost nothing until the cutoff reaches the note itself. Then the sound simply gets quieter The sound darkens, as with a sawtooth The sound gets higher

A sine has no upper overtones, so there is nothing to cut. The filter only starts to work when it reaches the sine's single frequency: with resonance that frequency first gets a little louder, and once the cutoff drops below it, quieter. That is why subtractive synthesis starts from a sawtooth or a square: you need something to take away.

Here is the first "match the sound" exercise. The target is a sawtooth through a filter. You get two knobs: cutoff and resonance. Turn them, listen and compare until the two sounds agree, then press "Check". The course compares the knob positions, shows the match as a percentage and tells you which way to turn.

Block 3: the amplitude envelope

So far the synth sounds like an organ: press a key and the sound is at full strength at once, let go and there is silence at once. Yet the organ of harmonics showed that a pluck and a bow differ in how the sound lives over time. That is the job of the third block, an amplifier controlled by an envelope.

The envelope on almost any synth has four knobs, named by the first letters of their English names, ADSR:

• attack (Attack): how long the sound takes to rise from silence to its peak after you press the key;
• decay (Decay): how long it takes to fall from the peak to the sustain level;
• sustain (Sustain): the volume the sound holds while the key is down. It is a level, not a time;
• release (Release): how long the sound takes to die away after you let go of the key.

Press and hold the button or any key. A solid dot runs along the curve: attack, decay, sustain, and release as soon as you let go. Drag the three circles: the first sets the attack time, the second the decay time and the sustain level, the third the release time. You can move the sustain while the note is still sounding.

Go through the presets and listen to what one and the same oscillator turns into. "Organ": instant attack, sustain at the top, short release. "Pluck": instant attack and a long decay down to zero, so the sound fades even if you hold the key, as on a guitar or a piano. "Bow": an attack of about a third of a second, and the sound floats in. "Pad": an attack of more than a second and a long release, a backdrop that trails behind the chords. "Hit": everything shorter than a fifth of a second.

The envelope did not arrive all at once. First Deutsch asked Moog to make the notes swell and fade smoothly instead of switching on like a light bulb. In 1965, for the composer Vladimir Ussachevsky of the Columbia-Princeton Electronic Music Center, Moog built a module with four knobs: rise time, initial decay time, sustain level and final decay time. The letters ADSR came later. The four knobs stayed.

Now by ear: a phrase plays, and you name the envelope. A hint: listen to the start and the end of each note.

And a second sound to match: a bell. What matters here is the waveform and the envelope. A bell has no attack and no sustain, only a strike and a long ring.

Velocity: louder and brighter

A MIDI keyboard tells the synth not only which key you pressed but how fast. That is velocity, covered in detail in chapter 3. The simplest thing is to make a hard note louder. But on acoustic instruments force changes the timbre too. Strike a piano key harder and the sound gets not only louder but brighter, with more upper overtones in it. The felt hammer turns harder under a strong blow and touches the string for a shorter time.

A synth copies this with one knob: velocity opens the filter a little. Press the pads from pp (very quiet) to ff (very loud), or play the keyboard. On the left is the spectrum of the last note, and on the right (below, on a phone) every note is a dot: the harder you press, the further right the dot and the higher the cutoff.

Set "Velocity → brightness" to zero and play the same pads. Now the quiet notes are just quieter than the loud ones, all with the same colour, and it sounds cheap, as if someone were turning a volume knob. When velocity opens the filter by an octave or two, the playing comes alive. On a computer keyboard every key has the same velocity, and you change it with C and V.

Block 4: the filter envelope

Remember the pluck in the organ of harmonics: the upper overtones died away faster than the lower ones. The sound starts bright and then darkens. The amplitude envelope cannot do that, because it turns all the overtones down equally. So a synth has a second envelope that moves the cutoff. The filter envelope opens the filter the moment you press a key and closes it again at its own decay. The "Amount" knob says how many octaves the cutoff rises at the peak.

This is easier to see than to describe. Below is a spectrogram: time runs from left to right, frequency from bottom to top, and brightness is loudness. Play the pluck with the filter envelope, then the same pluck without it.

With the envelope, every note flares up into a tail several kilohertz high that dies straight away. Without it you get a flat dark band. "Slow opening" is the same envelope with an attack of more than a second: the sound unfolds like a flower in time-lapse. The spectrogram shows everything playing on the page, so you can use the keyboard too.

The pluck is one of the most common sounds in electronic music. Match it: there are four knobs here, and two of them belong to the new envelope.

Block 5: the LFO

When a violinist holds a note, the finger rocks on the string and the pitch wavers slightly up and down. This is vibrato. String players usually rock at about 5–7 times a second, with a width of 20–60 cents from the lowest point to the highest, less than a semitone. Without vibrato a long note sounds dead, like a test tone.

On a synth, vibrato comes from the LFO, the low-frequency oscillator. It is the same kind of oscillator, only slow, from a fraction of a hertz to a little over ten. You do not hear it as a sound. Like a hand, it turns another knob back and forth. Point it at pitch and you get vibrato, at the filter cutoff and you get a "wah".

"Violin vibrato" is 5.5 Hz and ±12 cents, and the sound warms up at once. "Wide" is ±50 cents, which is already a siren or an old tape. "Wah" puts the LFO on the cutoff. Turn the rate up to 10–12 Hz: the sway stops being a sway and turns into a rattle.

A pad is a backdrop sound: a slow attack, a long release and a filter that breathes quietly under the LFO. Here there are four knobs from three different blocks.

Block 6: glide and the second oscillator

The last block is a very small one. Glide (portamento) makes the sound slide to a new note instead of jumping to it. The knob sets how long the slide takes. Set it to 100–200 ms and play two notes far apart, one after the other: this is the signature move of a synth solo.

The second oscillator lives here too. Two oscillators slightly out of tune with each other make beats, the same ones you tuned by in chapter 1: the sound drifts and grows wider. A detune of 5–10 cents gives a warm chorus, 30–50 sounds out of tune. A second oscillator an octave lower gives a bass weight.

A bass by ear

The final exam. A bass is a low sawtooth or square, a partly closed filter, some resonance and a short filter envelope that puts a click at the start of every note. Five knobs from three blocks. Listen to the target on headphones: on a phone speaker the low end all but disappears.

Don't lose heart if your first check shows 50 %. Sound engineers spend years learning to hear where the cutoff ends and the resonance begins. The "more" and "less" hints under the knobs tell you which way to go, and in three or four checks the sound usually comes together.

Your sound

Here is the whole synth: two oscillators, a filter with its own envelope and velocity sensitivity, the amplitude envelope, the LFO and glide. Start from any preset or from scratch and make a sound you like. When it is ready, press "Save my sound" and give it a name.

The full set of knob positions is called a patch, a word from the days of modular synths, when a sound was literally set up by connecting cables. Your patch is stored in this browser and plays in the Notebook.

Next

Now you know why a violin can't be mistaken for a flute: they have different spectra and live differently over time. You can tell the waveforms apart by ear, you know what the cutoff, resonance, envelopes and LFO do, and you have matched five sounds by ear. These are the knobs you will find on any synth.

But all this time the synth has been taking orders from the keyboard. Which note to play, how hard, when to let go, which way to turn the wheel: all of it reached the synth as messages. What exactly a MIDI keyboard sends when you press a key is the subject of chapter 3.

The Notebook has your first sound: saved sounds appear in each track's sound list next to the presets, such as pad, bass and pluck. The tracks are still empty. In chapter 3 the Notebook starts recording what you play on a MIDI keyboard, and it will record it with your sound if you choose it.