3. Additive Synthesis#
In Chapter 2, we synthesized our first sounds, but they were all sine waves. A sine wave is a useful starting point, but it sounds thin and featureless compared to richer sounds we encounter in music:
Hopefully you agree that the second has a fuller, brighter quality. How do we get from one to the other? Here we will explore additive synthesis, a technique for synthesizing richer tones by summing multiple sine waves together. It is the first synthesis technique we’ll study that’s capable of producing non-trivial, musically interesting tones.
This chapter develops additive synthesis end-to-end, from mathematical principles to algorithmic implementation. We start with the sine wave as an elementary building block, formalize the mathematical result (the Fourier series) that lets us decompose any periodic sound into sine waves, and then introduce wavetable synthesis, an efficient algorithm that makes additive synthesis practical.