Okay so I understand each operator separately. I understand envelopes. What I can't fathom is how on earth the operators interact. I've tried to look up tutorials online and they just give a brief description of each algorithm and kind of skip over what happens in between the operators.
The VGM music maker helpfile goes into great detail on the envelopes and then just lists the algorithms. Certain operators are called 'slots' because they are combined to create the final waveform. Combined how? "Modulation is a frequency modification of modulated operator depending from the output level of a modulation operator." (Thanks, help file.) Okay so the frequency of a sine wave gets changed somehow based on the current value of another sine wave... this is about where my understanding ends.
The closest I've come to finding an actual helpful explanation is this

. I think I understand how the low frequency sine wave can cause the main tone wave to go up and down in frequency/pitch. Then you start increasing the frequency of the modulating wave and you introduce envelopes and multiple operators all feeding into each other in different ways and my brain just gives up.
Maybe a more maths based explanation would help? I understand maths. Or if anyone knows a good video tutorial with lots of simple pictures and animations that my brain might be able to grasp. Or maybe a free oscillator emulation program that allows me to mess around with more freedom. I even studied software engineering for a year (many years ago now though). We had whole lectures on signal processing. And I still can't put everything together in my head.
For the people more experienced in YM2612: do you actually have an intuitive understanding of how the operators work, or are you like me with no idea and you just mess around until something cool happens?

If you understand how 2-op FM works, then it's easy to understand how 4-op FM works just by applying the same principles recursively and/or in parallel. The "algorithms" you're taking about (if I understand correctly) are just configurations of which operators are the carriers and which operators modulate other operators.

After writing a lot of music for the YM3812, I do have an intuitive understanding about how its 2-op FM synthesis works. But give me four operators and I'm partially back in the realm of "mess around until something cool happens".

Mathwise, you might find it easier to thing think in terms of phase modulation, which is mathematically equivalent:

• A lone sine wave has the function sin(t), obviously.
• A sine wave modulated by another sine wave of the same frequency, and at maximum amplitude, has the function sin(t + π*sin(t)).
• You can apply this recursively and get sin(t + π*sin(t + π*sin(t))), etc.

Sigh...

I'll need to finish up a basic video tutorial. I will start with Algorithm 4, and move on from there.

The program I will use is Deflemask. You can download it and go along with my tutorial when finished.

With more time and practice, you will develop more of am intuition and understanding of how it works. I think we all start off with presets and random dial flipping, but that's all apart of the process.