Synthesis
In music, synthesis is the process of creating artificial sounds, either electronically or digitally. This means that they generally don't touch the acoustic realm until they're reproduced through playback. In contrast, recorded sounds are most commonly either fully acoustic or played on magnetic strings and converted to electrical signals by a microphone or pickup respectively.
1. Types 🔗
There's many types of synthesis, and a lot of it is probably marketing. There's no issue in mixing types, and many of them overlap to an extent.
1.1. Subtractive synthesis 🔗
Subtractive synthesis, the most primitive form of synthesis, though arguably not the simplest. If you take an oscillator, you can control it by running it through an envelope to give it attack and decay, and cut harmonics using a filter, etc.
A good example of subtractive synthesis is any basic modular synth.
1.2. Additive synthesis 🔗
Additive synthesis flips the idea of subtractive synthesis. Instead of taking a complex waveform and simplifying it, you take a simple waveform and add to it.
A good example of an additive synth is ZynFusion.
1.3. Frequency modulation synthesis 🔗
Frequency modulation (FM) synthesis is the act of controlling the pitch of oscillators with other pitched oscillators. It is arguably the logical conclusion of modular synthesis.
By varying the pitch of an oscillator with a low frequency oscillator, you get a vibrato. If you increase that frequency of that LFO, its frequency eventually becomes audible as a distinct tone. If the oscillators frequencies are consonant, they will generally produce some form of pleasant sound. If they are dissonant, they can instead produce some of the harshest noise you'll ever hear.
FM synthesis was popular in the 80's, where it allowed for more complex waveforms and a great deal of variety in sounds without needing samples, which the tech wasn't quite there for yet.
A good example of FM synthesis is the Yamaha YM2612, found in the SEGA Mega Drive.