The Genesis's main audio processor was the YM2612, which is a Yamaha chip. Like a lot of sound processors from that era, it used FM (frequency modulation) synthesis. FM Synth is not as common in these days because sampling synthesizers (like what the SNES had, or what a MIDI-type synth is effectively) are now higher-quality and can make some sounds that FM synths can't.
More:
http://en.wikipedia.org/wiki/FM_synthesisThe YM2612's specs were that it had six channels (two sets of three), two of which could operate at special frequency multiples for each FM waveform component (each sound would be made up of four components); these two could be used for drums or melodic percussion.
In addition, though they are not supported by the tracker that I used, there were two other main sound chips. One was a tone generator based off specs from the Master System's sound chip. It had three simple squarewave-type channels and one tone channel, basically the same type of setup of the NES. This was primarily intended for backward-compatibility with the Master System, though it also added 3-4 additional sound channels for Genesis sound and music. The jump sound from the Sonic the Hedgehog games (Sonic CD notwithstanding) used this chip to make its sound. Typically it did square waves for tone.
The other main chip was a digital audio converter (DAC) that could replace one of the two special channels on the 2612. Normally when it was used it limited the number of YM2612 channels available at any time to 5, though all of this would be dependent on the software used for sound timing and such. According to official documents, if I recall correctly, the timing might make it impossible to use the other channels at the same time depending on how it was manipulated. It was primarily used for percussion samples and sound effects like voices. It is also not supported in the tracker I was using.
There were a few major such sound drivers, two in particular were GEMS (which was a driver by Sega that came with development kits used in games like Vectorman and Chakan; it is generally considered inferior to most other drivers as a lot of sounds that came from it were very hissy or distorted. It could be used to make nice techno-type music but had limited other uses) and SMPS (which was a driver used in a lot of Genesis games including the Sonic series). SMPS is a driver that a lot is known about, largely due to its use in Sonic as well as many other notable games -- the format has been cracked and one can convert XM files into that format, to potentially be used in homebrew games.
These sound drivers are typically based on minimizing their own inadequacies. Every driver is in some way ineffective. GEMS just doesn't sound very good under most circumstances and is probably why the Genesis sound hardware isn't always well regarded. SMPS puts limits on the number of usable PSG channels at any time -- no more than 3 of the available four.
There's better information out there. If you'd like to know what sound driver your favorite game uses (and I suspect that the tracker I used is based on GEMS), you can check that out
here. If you would like to know more about the SMPS driver, there's some info
here. A GEMS devkit has been found and leaked; check it out
here. For nearly every Genesis soundtrack in VGM logged form, go
here. Basic info on the YM2612 in different form is
here. Info on the VGM format can be found through
here.
