What is the right way of thinking about frequency modulation for musicians? I know some of the maths but I can't operate the bitwig FM-4 synth. Do you just screw around with the thing until you can operate it?

Shallower algorithms sound have fewer overtones and the overtones tend to be harmonic.

Deeper algorithms have more overtones and often those overtones are enharmonic.

But also how you tune and mix plays a role…a shallow algorithm witH carriers tuned one way will sound consonant and with a different tuning will sound dissonant.

Or to put it another way, FM is awesome for sound design but like everything in music it is hard to learn quickly.

I find it essential to have a MIDI CC knob box of some kind with FM. My MPC works in this capacity, I also bought an external one. Most FM synths support a huge number of MIDI CCs and FM really comes alive if you twiddle with the knobs during patch design, same as with other synths.

This link is a great practical guide, which has you look at waveforms in an audio editor and clone them using FM, one operator at a time. He walks you through making clones of several real life instruments, 6 operators is enough to sound quite good and 8 is even better. FM has a reputation for being computer-y sounding but it doesn't need to be. A lot of that is just baggage from default patches introduced decades ago with that fresh '80s sound, those patches from the DX-7 are still on the newest Yamaha flagship workstations. And as everybody knows the grand majority of sounds you hear in music are barely- or not-tweaked presets.

https://csclub.uwaterloo.ca/~pbarfuss/FM_Synthesis_of_Real_I...

Honestly the best way to think about any sound design concept as a musician is as platform for creative experimentation. Most of my favorite patches I have come up with have been happy accidents.

I recommend this video from mixed signals, it shows how a few commonly used and known fm sounds are made: https://www.youtube.com/watch?v=0S6NXIe_NyA

I imagine you are vaguely familiar with subtractive synthesis; oscillators, filters, envelopes, modulation. It wouldn't hurt, although the building blocks are laid out differently in an FM synth.

Anyway, I found these hands-on demos on the DX1 to be some of the most "aha" moments I've had trying to understand how FM patches are made.

TLDR, an FM "operator" is an oscillator. A carrier is the oscillator you hear, its modulator is an oscillator that wiggles the carrier and brings out different harmonics. You can stack more modulators and you can have multiple carriers going in parallel, the various combinations of operators available in a synth being the different algorithms.

https://www.youtube.com/watch?v=YV9vQGqoO5c

https://www.youtube.com/watch?v=k0xGyR_lKoM

https://www.youtube.com/watch?v=1-boGIxRZ_s

There was also one from Venus Theory about how to get musically useful stuff out of frequency/phase modulation: https://www.youtube.com/watch?v=wqc8rZnzTVI

My mental model is : each carrier is a sound (a harmonic). I can stack the sounds by chosing an algorithm with multiple carriers. So I start with one carrier and sculpt it by chosing frequency and envelope. This is the time I also activate it's modulators and try to tweak them to make the sound better. Modulators have very complex effects on the sound and I don't try to have a mental model of what they do, just empirical outlines. The next step is to add another carrier to the sound and continue tweaking the current and all the previous carriers.