I go into detail about the foundations of digital synthesis to illustrate how phase modulation is implemented, how it differs from frequency modulation, and how a small change in the code from one to the other has a big effect.
Ken Shirriff's blog: https://www.righto.com/2021/11/reverse-engineering-yamaha-dx7.html
Compiled DX7 PDF: https://www.dropbox.com/scl/fi/mvghikdapnw0cf24an2xg/kenshirriff_dx7.pdf?rlkey=3d9j0vkcl12mawfqxg2j7wz7n&st=2vp52rv1&dl=0
Analog's DDS article: https://www.analog.com/en/resources/analog-dialogue/articles/all-about-direct-digital-synthesis.html
3 Blue 1 Brown Fourier Series: https://youtu.be/r6sGWTCMz2k?si=Jfbu0Iqt1Bj41sFr
00:00 Intro
04:57 Part 1.1 - DDS: Let's get sinusoidal
08:35 Part 1.2 - DDS: Structure of DDS
15:14 Part 2 - Frequency modulation
19:23 Part 3 - Phase modulation
23:46 Part 4.1 - Upward vs downward phase ramps
30:48 Part 4.2 - PM with non-sinusoids
41:40 Part 5 - PM vs FM feedback
45:11 Extras: Coming full circle...
47:59 Extras: A true new FM synth (Fors Dyad)
55:31 Outro