I was lucky (I think!) I designed my own home. When I built my home I set up a floor plan with a more traditional living room and family room well separated from each other. The thought was that it was a floor plan that would resell easily to anyone not looking for a great room/open home style. I made the family room large and family friendly and that is where we live. I made the living room dimensions audio friendly and that is where I have my music/audio room. It is off the hallway/entry and can be closed off by pocket doors. Not perfect, but it works well.
I think a 13x15 audio only room could work but you'd have to scale back expectations a little bit on big/loud music, and to optimize results you'd probably end up with a near(er) field listening setup so you would have to be very careful in selecting speakers and avoiding any with an uptilted mid-high FR or that is too 'fast'.
FWIW. Hope that helps a bit. BTW, my audio room is 13.5 x 19.5 x 9 and my setup sounds pretty good - 10'equilateral triangle with speakers 5.5ft from the back wall.
I think a 13x15 audio only room could work but you'd have to scale back expectations a little bit on big/loud music, and to optimize results you'd probably end up with a near(er) field listening setup so you would have to be very careful in selecting speakers and avoiding any with an uptilted mid-high FR or that is too 'fast'.
FWIW. Hope that helps a bit. BTW, my audio room is 13.5 x 19.5 x 9 and my setup sounds pretty good - 10'equilateral triangle with speakers 5.5ft from the back wall.