Additive synthesis, sixteen sines.

What you are hearing

Sixteen sine oscillators run in parallel, one for each integer multiple of the fundamental. The amplitude of each one is whatever the matching bar is set to. The signals are summed, scaled by the master volume and sent to the speakers. There is no filter and no envelope in the chain, so the tone is set entirely by the heights of the bars.

The presets

A square wave is the Fourier series of odd harmonics falling as 1/n: bar 1 at full, bar 3 at one third, bar 5 at one fifth, and so on. A sawtooth uses every harmonic, also at 1/n. A triangle keeps the odd harmonics but rolls off much faster, at 1/n². The clarinet preset is closer to a real measurement of a clarinet's spectrum: the same odd-heavy stack, with traces of the even harmonics that a real bore leaks through. The whole difference between these timbres lives in the bar heights.

Things to try

Start on Sine and walk the bars up one at a time, in order. The pitch never changes; only the tone gets brighter. Set Sawtooth and lift bar 2, then drop it. The brightness barely moves but the quality of the sound does, because the even harmonics carry no information about pitch and a lot about character. Then switch to Square: dropping every even bar to zero takes the sawtooth's hollow snarl and turns it into the transistor-radio hum of a square.

A note on phase

The bars only show magnitudes. The phases of the sixteen sines are all locked to zero, which is one of infinitely many phase assignments that share the same spectrum. The ear is almost insensitive to phase for a steady tone, so the timbre sounds the same; the waveform on the scope, however, changes shape entirely with phase. A textbook sawtooth uses alternating signs across harmonics; this page uses all positive ones, which still converges to a sawtooth, just shifted along the time axis.