I’m not sure why sound card manufacturers don’t list the number of simultaneous hardware channels their cards are capable of. Sure, they list 5.1 and 7.1, but not the true maximum number of simultaneous audio samples they are capable of playing.
As far as figuring it out, guess work mostly, digging through audiophile forums, basic knowledge of how older sound systems worked ,NES, C64, keyboards and sound cards with a Yamaha YM-3812 sound chip, a lot of which can be summed up in the following Youtube video:
8-Bit Guy - How Old School Sound/Music Worked
While the hardware mentioned is very old, the CPU still has to not only send the audio samples to your sound hardware to play, but if needed it must also pre-mix sound samples ahead of time to fit them all in the available channels, which can create excessive CPU overhead and stalling if there are a very large number of audio samples to mix and/or your CPU isn’t fast enough to handle the additional load.
Computers these days for the most part are powerful enough and can handle the extra overhead of mixing any audio samples together to cram them into the available hardware channels. However I believe Diablo 3s fast pace is pushing the limits with cheaper audio components like Realtek audio. The problem becomes more apparent if the other system specs aren’t fast enough to handle everything else plus that extra audio mixing overhead.
I’m not sure, but I’d guess 64 channels for both. If you have multiple monitors, bring up task manager on one and play Diablo 3 on your main. To establish a base line, start out with an in game setting of 32 channels, get into a big fight (higher greater rift) to cause a bunch of audio sounds to play.
Crank it up to 64, repeat… 128, repeat, and so on until you start seeing noticeable spikes in CPU usage and drops in FPS in big fights.
One thing worth mentioning is that one single channel only applies to one speaker. A stereo audio sample would use two hardware channels.