There are many ways to operate a modular synthesizer but one of the important methods of sound synthesis is called subtractive synthesis. To accomplish that you’re going need a filter.
All sounds that have ever been heard can be simply described as patterns of air waves. When a bow is dragged across the string of a violin, the friction creates tiny vibrations which get amplified by the body of the instrument. When that violin’s sound is recorded by a microphone, the waves in the air vibrate the microphone’s membrane resulting in an electrical signal, similar to the voltage coming out of a synthesizer’s voltage controlled oscillator. A VCO can typically output basic waveforms but those can’t imitate the the complex sound of a violin by themselves.
In theory, you could imitate any sound with enough sine wave oscillators set at different frequencies, a method called additive synthesis. In practice, however, you would need hundreds of oscillators to make a convincing imitation of a rich harmonic sound. With subtractive synthesis you can get a lot of variety with one oscillator generating a sawtooth or square waveform followed by one or more filters.
What a filter does is eliminate, or subtract, certain frequencies. A lowpass filter lets the low frequencies pass through unchanged and eliminates the high frequencies. The point at which the high frequencies are removed is called the cutoff frequency. Above that point the higher harmonics begin to fade to silence. A high-pass filter does the same but inverted across the frequency spectrum so that the high frequencies pass through while the low frequencies are eliminated.
Lowpass Filter:
This subtractive approach can be useful because it can be much easier to simulate a sound by taming an oscillator with too much harmonic content than to create all the harmonic content using additive synthesis. The sawtooth wave is a common wave type because it’s audio spectrum contains both even and odd harmonics of the fundamental frequency, which gives the filter a lot of content to work with and shape into something new.
A square wave is an alternative waveform that has mostly odd integer harmonics, making it good for simulating wind instruments. A sine wave, on the other hand, has no harmonic content and so a filter has nothing to clear away. The most a filter could do to a sine wave is turn down it’s volume, whereas with a sawtooth wave, the synthesist has a large degree of control over the darkness and brightness of the sound. In fact, if you have a precise enough filter, you can in theory reduce any waveform to just a sine wave at the fundamental frequency. Generally, the filters of synthesizers are resonant filters, where a peak with an adjustable amount exists at the cutoff frequency, giving even more control over the character of the sound.
Common ways to modulate a filter include patching from the pitch output of a CV keyboard into the cutoff frequency input of a lowpass filter, also called pitch tracking, where higher notes make brighter sounds. Another common way is to patch out of an envelope generator into the filter cutoff frequency, causing each pressed key to create a dynamic motion of the filter.
Watch the following video view different waveforms being filtered on an oscilloscope: