When I first got my Emscripten port of DOSBox working, I was happy with the sound. It was not perfect. There were occasional small glitches at some CPU intensive moments. However, it was perfect most of the time in Firefox and pretty good in Chrome. (IE 11 does not support sound and IE 12 will hopefully support it in the future.) Then Firefox discontinued its Mozilla Audio Data API, and Emscripten began using the Web Audio API in both. That made Firefox sound significantly worse. When I recompiled Em-DOSBox with a recent version of Emscripten, sound was very bad.
[ Update: The SDL 2 version described below is old. SDL 2 is now part of Emscripten ports. To use it, simply add
-s USE_SDL=2to the command line arguments and Emscripten will take care of the rest. ]
I just found that SDL 2 has been ported to Emscripten. It is an actual port of SDL itself, not an SDL-compatible library like what is currently found in Emscripten. Looking at its audio code, I saw it using ScriptProcessorNode, and I decided to give it a try.
There is DOSBox SDL 2 patch by NY00123. It's based on a later version of DOSBox, but Git makes dealing with such things fun. First I merged with that revision of DOSBox, and then I merged the patch.
At first, sound was totally terrible. Then I found that the SDL callback needed float data, because ScriptProcessorNode needs floats. When I made that change, the sound was pretty good. It still isn't as good as old Firefox with the Audio Data API, but I think it's acceptable.
There is a problem with red and blue being swapped, and DOSBox won't run in IE, but SDL 2 for Emscripten definitely shows some promise. It may even be faster than Emscripten SDL, because more of it consists of C code which gets compiled into asm.js. Here is the Em-DOSBox branch.