Worksheet: Digital Synthesis in Music

Cover teacher — you need no subject knowledge

Print: this sheet, one per pupil. Headphones needed for Part C — one pair each, or pupils work in threes and share. Parts A and B are paper and can be done with no computers at all, so if the room or the network fails, cross out Part C and use the extensions.

Run: 6 min — read the facts box · 10 min — Part A, the waveform table · 14 min — Part B, design three patches on paper · 15 min — Part C, build them in a browser synthesiser and write down what you actually heard · 5 min — swap and check. Part A has right answers and they are all in the facts box. Do not let pupils skip straight to Part C; designing before touching a knob is the point.

Collect: this sheet. Headphones back in the box.

What you are doing

A synthesiser does not play recordings. It builds a sound from scratch: a raw waveform, a filter that removes part of it, and an envelope that shapes how it starts and stops. You are going to design three sounds on paper — a bass, a pluck and a pad — then build them and check whether they came out the way you predicted.

Facts box — everything you need

Harmonics. Every note you hear has a lowest frequency called the fundamental, plus quieter tones at whole-number multiples of it — two times, three times, four times, and so on. Those are the harmonics, and which ones are present is what makes one waveform sound different from another at the same pitch.

Sine — the fundamental and nothing else. No harmonics at all. Pure, smooth and slightly hollow, like a tuning fork. Almost invisible in a mix, which makes it perfect for a sub bass.
Triangle — odd harmonics only (3rd, 5th, 7th…), and they fall away fast, as 1 divided by n²: the 3rd harmonic is about one ninth as loud as the fundamental. Soft, a little hollow, brighter than a sine but far darker than a square.
Square — odd harmonics only, falling as 1 divided by n: the 3rd is a third as loud, the 5th a fifth. Hollow and buzzy. A clarinet and an old games console both sound like this.
Sawtooth — every harmonic, odd and even, falling as 1 divided by n. The brightest and buzziest of the four. Brass sounds and big string pads are built from saws.

Low-pass filter. It lets everything below the cutoff frequency through and removes the harmonics above it. Turn the cutoff down and the sound gets duller and warmer, because you are deleting its upper harmonics. Resonance boosts a narrow band right at the cutoff, which is what makes a filter sweep "sing" or whistle. Starting with a rich wave and filtering bits away is called subtractive synthesis.

The envelope (ADSR). Attack = how long the sound takes to reach full volume after you press the key. Decay = how long it then takes to fall back to the sustain level. Sustain = the volume it holds at while you keep the key down — this one is a level, not a time. Release = how long it takes to fade to silence after you let go.

Step by step

Part A — The waveform table

Take the fundamental as 1. Write the relative loudness of the 2nd, 3rd and 5th harmonics for each waveform, using the rules in the facts box. Write 0 where a harmonic is absent.

Put the four waveforms in order from darkest to brightest, and say what "brighter" actually means in terms of harmonics.

Part B — Design three patches

Give real numbers. Attack, decay and release are times in milliseconds or seconds; sustain is a percentage; cutoff is a frequency in hertz.

Part C — Build it and listen

Use the browser synthesiser your teacher has set up, or the synth instrument in the school's music software. Headphones on. Build each patch from your own Part B numbers.

Test	What I actually heard
Play the same note as a sine, then a sawtooth, without changing anything else.
On the sawtooth, sweep the low-pass cutoff from the top down to about 400 Hz.
Do that sweep again with the resonance turned up.
Set the attack to 1.5 seconds, then back to 2 milliseconds.
Set the sustain to 0% and hold a key down.
Which of your three patches came out furthest from what you predicted, and what did you change?

Success criteria

I can say which harmonics each of the four waveforms contains, and use that to explain why one sounds brighter than another.
I can explain what a low-pass filter removes, and what resonance adds at the cutoff.
I can explain that sustain is a level while attack, decay and release are times.
My three patches use real values, and each choice of waveform is justified by the job the sound has to do in a track.
I compare what I heard with what I predicted, and I say what I changed as a result.

Setting	Patch 1 — sub bass	Patch 2 — bell pluck	Patch 3 — slow pad
Waveform, and why
Filter cutoff (Hz)
Resonance (low / medium / high)
Attack
Decay
Sustain (%)
Release
Effect to add, if any
Where it would sit in a track

Digital synthesis in music