Reflection, Diffusion, Absorption
Sound behaves in much the same way as light. Shine a flashlight at a mirror in a dark room, and a hard glare will be reflected right back into your eyes. Shine the same flashlight onto a frosted piece of glass, and you'll notice that the light is evenly distributed in a pleasing circle on the surface of the glass, which will also reflect more light around the dark room than the mirror did. Apply this to music in an enclosed space, and you can understand why diffusion — the random scattering of sound — is far better than hard reflection. The latter makes the music itself sound hard and brittle, while diffusion provides clarity, warmth, and an evenness of sound throughout the room. And because diffusion more evenly distributes high- and mid-frequency sound throughout a room, it adds greatly to musical clarity.
Absorption is useful in reducing the amount of sonic energy in a room. Many people make the mistake of cutting down reflections by deadening their music rooms with heavy draperies, thick carpets, and overstuffed furniture. However, this will not absorb all frequencies evenly, and can make a room sound dull in the upper octaves and too heavy in the bass — or the other way around. While in "live" rooms some absorption is desirable, even necessary, I suggest a combination of absorption and diffusion. This can be done by placing books, bookcases, artworks, chairs, and other randomly shaped objects along the walls to break up reflections, as well as scattering around the room some soft surfaces, such as upholstered furniture. Some of the best music rooms have mostly hard surfaces with little absorption, but they all have many diffusive surfaces that break up the reflections, which keeps the sound live, warm, and resonant. Partially closed wooden blinds or other irregularly shaped treatments for windows and glass doors will help diffuse reflections coming off of those glass surfaces. Note that flat artworks, even when not covered with glass, can cause degrading reflections unless they have a very irregular diffusive surface. Fabric wall hangings, especially quilts and other thick, soft, irregular surfaces, can absorb a lot of high-frequency reflections, when used in moderation — but not heavy drapes, unless the room is especially "live" and reverberant.
Building a Dedicated Music Room
When building a music room, it's best to use multiples and divisions of 3 or 5 for interior dimensions (rather than 1, 2, or multiples of 2). For example, let's say you plan to buy a Steinway model B grand, which is 6 feet 10 1/2 inches long (I'll round that off to 7 feet for purposes of discussion). Applying the principle that the total wall length should be at least 10 times the length of the piano, this gives us a minimum total wall length needed of 70 feet (10 x 7). If we take one-fifth of 70 feet (=14 feet) for each of the two short walls, that would leave 42 feet, or 21 feet each, for the two long walls. The ceiling height would be calculated as one-fifth of 21 feet (the long wall), x 2 = 8.4 feet. Therefore if your room is approximately 14 feet by 21 feet by 8.4 feet high, the piano should sound good, particularly for practice purposes. However, if you want a room in which you can perform for others on the same piano, or play chamber music with your colleagues, I suggest that your minimum total wall length be 15 times the length of the instrument. This could give you room dimensions of 21 feet by 31.5 feet by 12.6 feet high.
These specific proportions are offered only as examples. Unless you're building your room from the ground up as a dedicated piano studio, you may not be able to strictly adhere to this formula. If your chosen piano room doesn't come close to any optimal proportions (using the 3 and 5 multiply/division formula, you can come up with quite a few), all is not lost. It might take a little more time to get the sound right, with the possible addition of some acoustical treatments to absorb coincident low-frequency room modes. But the larger the room, the less critical of an issue this becomes.
If you're building your piano room from scratch, I suggest you consider making all of the interior walls nonparallel, in order to avoid the typical flutter echo often produced in small and medium-size rooms with parallel walls. Splaying the walls (sort of like a trapezoid) at angles of 5° to 10° can do a lot to prevent flutter. You'll hardly notice that the room isn't a perfect rectangle, and it will sound a lot better.
Something else to consider when building a dedicated piano studio: Don't make the inside walls of the room too stiff by using several layers of gypsum drywall or similar material. The interior walls of your music room should be able to flex a little bit to allow them to resonate—like the skins of a huge drum—and absorb the low frequencies produced by a larger piano in a smaller room. The more the walls can flex, the more excess sound energy they can absorb. For walls, use one or two layers of drywall set on 16-inch centered wood studs (or metal studs, in most high-rise and commercial construction). If you need to acoustically isolate your piano room from the rest of the house, build an additional, heavier, outer wall separated from the inner wall by at least 6 inches of air space. Suspend your music-room ceiling from the ceiling joists using "Z-channels" or a similar system, so that it, too, can flex a bit.