It's not just the fact that the walls are 15' and you have windows- it's all about proximity and acoustical characteristics. Hard, flat, smooth surfaces reflect. Soft materials absorb. Heavy materials can block some bass from going through. The right percentage of absorptive, reflective and diffusive materials is the key to a good sounding room. Also, eliminating initial reflections makes everything more accurate when it comes to directionality.
I worked for a mid-high end dealer and they signed up for a system called FROX, who basically told them that the store needed a dedicated demo space for the system. It had 7.1 surround, 8 dedicated audio channels, a modified Sony 200 disc CD changer, RGB + separate luminance and chroma video to the industrial Sony projector, software based controls for all switching, levels, EQ and all audio outputs were digital. It even had an RF remote control that could be operated with right or left hand. It was a really cool system and I installed it at the store in late '93. Personally, I think they were a bit ahead of their time. However, as good as it looked, and it really looked great, because the room was all drywall, not very large, had painted acoustical ceiling tiles and had a good sized window, it sounded terrible. It wasn't the electronics, it wasn't the Canton Carat speakers and that kind of problem can't be EQ'd out. It was reflective on five surfaces and when I clapped my hands, the reflections were almost as loud as the original sound and in quick succession, called 'flutter'. I told the owner that there's no way they would sell that $72K system in that room and I explained why, with them checking it out for themselves. I bought Armstrong rigid fiberglass panels and found the spots that caused the initial reflections and covered them with some of the panels. Then, I found where the second reflections were coming from and covered those spots. I added more on each wall, listened as I went and pretty soon, it sounded very good. Imaging was much improved and the SPL could be increased to get a good effect without having objectionable reflections.
The point is, walk through and clap, snap your fingers, bang a pan with a ladle and mostly, listen. If the sound takes a long time to die out, it won't sound good. Cathedrals are supposed to have a longer decay rate because they're really large but when a small room has a long decay rate, it will never make you happy. It can be tamed, though. If you need to keep the sound from escaping from that room through the walls and ceiling, that transmission can be reduced, too.
