Modulation

Everything so far has been a setting

Lesson 1 already made this case from the other direction: a spectrum and an envelope are both needed, and the envelope carries more of the identity than anyone expects. Every figure since has been a sound that holds perfectly still until you move a control.

The fix is to have something else move the control for you. Whatever does the moving is a modulation source, whatever it moves is a destination, and the amount is called depth. That vocabulary covers every modulation routing on any synthesizer ever built.

An LFO is an oscillator you left running slowly

LFO stands for low frequency oscillator, and the expansion is worth taking literally. An LFO is the same oscillator from lesson 2, set to a frequency below hearing, with its output connected to a parameter instead of to the speakers.

In the figure below that is exactly what it is: an ordinary oscillator node, wired into a pitch, a gain or a filter cutoff. The code has no notion of a control rate and no branch that treats slow signals differently from fast ones, because no such distinction exists in the machine.

It exists in you. Drag the rate upward and somewhere around 20 Hz your ear stops resolving the individual cycles and starts hearing their effect as tone colour instead. That is the whole of the boundary, and the figure lets you walk across it.

What the sidebands are telling you

Set the destination to amplitude, the rate somewhere above 100 Hz, and watch the spectrum. Where there was one partial there are now three: the carrier, and one either side of it at exactly the carrier plus and minus the modulation rate.

Those are sidebands, and they were always there. At 5 Hz they sit at 435 and 445 Hz, which is far too close to 440 to be heard as separate tones, so the three of them beat against each other and you perceive one wavering note. Nothing appears as you speed the modulator up. The sidebands simply move far enough from the carrier to be resolved as pitches of their own.

That single fact is the seed of an entire synthesis method. If modulating fast enough puts new partials into a spectrum, then modulation is not only a way to animate a sound, it is a way to build one, and a very cheap way, since two oscillators can produce dozens of partials. Lesson 7 is about doing this on purpose.

Envelopes are the same thing, once

An envelope is a modulation source that is not periodic. Instead of repeating forever it runs through a shape when a note begins and unwinds when the note ends. That is the only difference. It occupies the same slot in the architecture, connects to the same destinations, and has a depth control just like an LFO does.

The classic shape has four numbers. Attack is how long it takes to reach full value, decay how long it then takes to settle, sustain is the level it settles at, and release is how long it takes to fall away once you let go. Sustain is the odd one out and worth noticing: three of the four are durations and that one is a level.

The figure below sends one envelope to two places at once. The same four numbers shape the volume and open the filter, and only the depth differs.

Why this is the lesson that makes it sound like music

A filter envelope is the single most characteristic gesture in subtractive synthesis. A fast attack and a short decay into a low sustain gives you a plucked, percussive note whose brightness collapses immediately, which is what almost every synth bass is. A slow attack on the same filter gives you a pad that opens.

Both are one shape pointed at one parameter. Nothing has been added to the oscillator or the filter since lesson 3; the only new thing is that a number is now changing over time, and that turns out to be the difference between a tone and an instrument.

Two things worth knowing that the figures do not show

Modulation sources can modulate each other. An envelope on an LFO's depth gives you vibrato that fades in, which is what a string player actually does. An LFO on another LFO's rate gives you something that will not sit still. This is where modular synthesis gets its reputation, and it is why the architecture is a graph rather than a fixed list of slots.

Not every modulator is a waveform. A very common one is sample-and-hold, which takes a random value at each tick and holds it flat until the next, giving the stepped, unpredictable movement of a lot of 1970s electronic music. Velocity and key position are modulators too: play harder, open the filter more. None of that changes the model, it only adds sources.

Also worth flagging: the envelopes here use straight-line segments, because the shape drawn above the sliders is drawn from the same numbers and a picture that disagreed with the sound would be worse than no picture. Real analogue envelopes are exponential, since they come from a capacitor charging, and the difference is audible on long decays. It is a fair criticism of the model rather than something the model needs.