Harmonics and Timbre

Play an A2 on a piano, then the same note on a sawtooth synth, then on a very simple wave. Your DAW shows the same row three times, the same frequency, and yet you hear three sounds that have nothing in common. This difference has a name, timbre, and a little theory explains it very well. In this part of the course, we're leaving scales and chords behind for a while to look at sound itself, because that's where theory and sound design meet.

Listen to these four buttons. They all play the same note, which vibrates at 110 hertz. The first one is round and almost faint, the last one is bright, almost aggressive, and the two in the middle sit somewhere in between. The note doesn't change; what changes is what the sound contains on top of that note.

A sound is a sum of frequencies

At the very start of the course, we said that a sound is a vibration, and that its pitch depends on the number of vibrations per second. That was true, but incomplete. Almost every sound you hear vibrates at several frequencies at once. The lowest one, which gives the note, is called the fundamental. The others, higher and usually weaker, are called harmonics.

The only sound that contains a single frequency is the sinusoidal wave, simply called the sine wave. It's the purest sound there is, and that's why it seems so simple, almost dull. Every other sound is a blend. Its timbre is the recipe for that blend: which harmonics are present, and how strong they are.

To hear it, let's build a sound by hand. The first button plays a single sine wave at 110 hertz. The second adds a sine wave at 220 hertz, the third adds two more, at 330 and 440 hertz, and the last one stacks eight sine waves. Listen to the same note get fuller, a little nasal, then brighter and brighter.

Notice something surprising: even with eight frequencies, you don't hear an eight-note chord. You hear a single note, the lowest one, with a different color. Your ear fuses the harmonics with the fundamental, because they're lined up in a very particular way.

The harmonic series, a ladder that never changes

Look at the frequencies we just stacked: 110, 220, 330, 440, and so on. Each one is an exact multiple of the fundamental. The second harmonic vibrates twice as fast, the third three times as fast, the fourth four times. This ladder of multiples is called the harmonic series. It's the same for any note: only the fundamental changes.

Read the last column from top to bottom: A, A, E, A, C♯, E, then a slightly flat G, then A again. The first six harmonics form an A major chord, spread over several octaves. So every note in your piano roll carries a kind of very discreet major chord inside it. Harmonics 5 and 7 don't land exactly on a key; we'll see why that gap matters in the lesson on equal temperament.

Four waveforms, four recipes

Synths almost always start from a few basic waveforms. Their names come from the shape they draw on a screen, but what matters to you is the list of harmonics each one contains. Here it is, with the strength of each harmonic relative to the fundamental.

Now you understand what you heard at the start. The sine wave has nothing above its fundamental. The triangle has only odd harmonics, and they fade very quickly: the third is already nine times weaker than the fundamental, which explains why it sounds almost like a sine. The square has the same odd harmonics, but they fade much more slowly, and it's the absence of the even harmonics that gives it that hollow sound.

Finally, the sawtooth contains all the harmonics, and each one loses only a little strength compared with the one before: the tenth is still only ten times weaker than the fundamental, not a hundred times. That's why it's so bright. It fills the whole spectrum, from lows to highs, and that's also why it's synths' favorite waveform: it gives you a lot of material to sculpt.

The low-pass filter removes harmonics

Now that you know a sound is a stack of harmonics, the most famous knob on your synth becomes very easy to understand. A low-pass filter lets low frequencies through and attenuates high ones. Its cutoff frequency, the cutoff, tells you where the attenuation begins: above it, the harmonics are weakened, and all the more so the farther they are from the cutoff.

Take a sawtooth on A2 and set the cutoff around 500 hertz. The first four harmonics, at 110, 220, 330 and 440 hertz, pass through almost untouched; the following ones are more and more attenuated, and the sound gets darker and more muffled. Bring the cutoff down to around 150 hertz, and almost nothing but the fundamental is left: you're back close to a sine wave. Listen to this descent, imitated here in a simplified way by removing harmonics from the top.

That's exactly what happens when you close the filter on a pad during a breakdown, or open it slowly during a build-up: you're taking away or giving back harmonics, without touching the note. The row stays the same; only the brightness changes. The resonance control, found on most filters, boosts the harmonics just around the cutoff, which gives that characteristic whistling sound when you move it.

In the next lesson, we'll put precise numbers on the low notes of the piano roll, so you can tune a kick, an 808 or a sample as accurately as possible.