We're talking about acoustics.

In my very basic understanding of things (feel free to correct me Ted...or add, for that matter) a room that is 24x24x12 would indeed be very bad for acoustics. This wouldn't necessarily mean that it's bad at keeping noise out or in, just that the sound QUALITY within the room would suffer greatly. We're talking lack of clarity in the big, inspirational speech in your favorite movie. The kind of garbling that can make you rewind the movie, and listen to that same speech again, and again....and again...

Acoustics may be ever so slightly off topic in this thread, but of course they are truly important in your home. In a home theater, you'll want to hear every word...but that might not be the case with noise from your half loft.

Ok, well let's say the 24x24x12 room is used like an office and a workshop. There may be the occasional music being played by the computer, sometimes an electric drill being used, but no home theater. Would it make it any less noisy to change the dimensions of the room? Would it make it any better for the rest of the house, in other words would the noise from that room be better isolated if the room dimensions were changed?

You have that about right, Matthew. In-room acoustics are accomodated by room dimentions and floor / ceiling / wall treatments. These condition the sound for the reasons Matt described.

Generally a separate issue would be the acoustic isolation (soundproofing) of the room.  Two different animals.

In terms of being less noisy INDSIDE the described room, I would think that would likely be the case. At least, for the intensity of the noise percieved. As far as noise being transmitted to other rooms, as Ted suggested, likely not much would change.