Set eight mixer faders to the 1/n amplitude series and a bright buzzy sawtooth appears, the same waveform at the heart of every classic analog lead.
In the world
A bowed violin string produces a near-perfect sawtooth: the bow yanks the string until it slips, then yanks again, a process that mathematically generates every harmonic.
A sawtooth contains every harmonic, with amplitudes falling off as 1/n. The 2nd harmonic is half as loud as the 1st, the 3rd is a third, the 8th is an eighth. This simple rule gives the saw its bright, brash, piercing character - it struggles at bass where the dense harmonic stack can muddle together, but at treble it cuts through anything. That is why the sawtooth is the workhorse of subtractive synthesis.
Eight VCOs are tuned to harmonics 1 through 8. A ninth VCO provides a real sawtooth on CH2 for comparison. Your job is to dial the first eight mixer channels to the 1/n series and watch the traces converge.
Did you know?
The sawtooth wave gets its name from its shape, but its sound is everywhere: a bowed violin string physically traces a sawtooth as the bow grips and slips. Every orchestral string section is a wall of sawtooths slightly detuned from one another.
Explore
Eight rain columns fall on the right, one per harmonic. Click any column to toggle it on or off and hear the harmonic vanish from the mix. A waveform ribbon at the bottom shows the composite shape in real time - watch it approach a sawtooth as you activate all eight.
Listen to the slight differences between CH1 and CH2. With only 8 harmonics, the additive saw is gentler than the real one - the missing upper partials soften the buzz.