In Windows, the little speaker button that should be on the bar at the bottom right should open your sound settings. Depending on how your sound is set up, the first button may open more than one "volume control" but the button at the bottom of the "speakers" adjustment, if that's what comes up, should turn sound off completely, or back on, without changing your volume settings.

Not very helpful. That site is an index page to a large collection of separate tune pages. The whole point of it is that you can listen to the MIDIs on each tune page. You'll have to turn the sound back on to listen to them - at which point the background sound on the index page will come back, unless you've closed its window or tab (does IE have tabs?), and you'll have two tunes playing simultaneously.

I wonder if I just copy their BGSOUND link (adjusting the URL of the MIDI to point to their site), will it autoplay on IE when reading this thread?

...answer: can't do it. "Your post contains a forbidden HTML tag".