Vertical pianos are designed to work optimally in smaller rooms. They are usually placed up against a wall, and present relatively few problems in the typical domestic environment. The same is true of small grands. But the amount of sonic energy produced by anything larger than about a 6-foot grand can present some big problems in smaller rooms. While concert halls and piano showrooms are big enough to allow the sound of a larger grand to properly resonate, small rooms can't absorb so much sound, and will easily overload when the instrument is played full out. Like other fine musical instruments built to be played in large spaces, a large grand sounds best from some distance away. For instance, stand next to me when I play my contrabassoon's lowest B-flat (half a step above the lowest A on a piano), and while you can physically feel the power of that note, you won't be able to decipher its actual pitch until you walk several feet away from the instrument. The same thing occurs with a double bass, tuba, or pipe organ. At the opposite end of the scale, a really fine violin won't sound its best until the listener is several feet away, when the sound becomes more resonant, with more clearly defined pitch. This is the situation we face when placing a large piano in a room smaller than it was designed for. While we can do many things to just about any room to make it more friendly to a large piano, there are limits, dictated by the laws of physics, that we can't break without paying a price in quality of sound.
How large a piano room needs to be depends on the size of the instrument. Empirical data indicate that the combined length of a room's walls (assuming that the room's ceiling is 8 feet high) should be at least 10 times the length of a grand or the height of a vertical piano. For example, a 15 by 20-foot room (15+15+20+20=70 feet) should accommodate a 7-foot grand. This formula doesn't take into account openings into other rooms, irregular room shapes, etc., but it's a good starting point.
Low frequencies have the longest wavelengths and cause the most problems in smaller rooms because the length of the wave exceeds the largest dimension of the room. The lowest A on a piano has a frequency of 27.5 Hz (cycles per second), which translates into a wavelength of about 41 feet! For this reason, the lower two octaves of a 7-foot grand, having less sonic power, will probably sound clearer in a small room than those of a 9-foot instrument in the same space, even though the larger instrument has the potential for greater low-bass clarity. This is the same principle that applies when designing audio systems and home theaters. In a smaller room, a smaller loudspeaker that pressurizes less air to reproduce a given frequency will actually sound clearer and deeper than a far bigger speaker in that room, even if the larger speaker's bass can go a bit lower in pitch. Therefore, common sense tells us that putting a full-size 9-foot concert grand into a 12 by 15-foot room with an 8-foot ceiling will probably not yield the best results without a huge amount of dedicated acoustical treatment, and probably not even then.
If your piano room is L-shaped, or opens into another large space, this can help your piano's low-octave bass response — the much-longer low-frequency soundwaves can travel through large open spaces. This is one reason why, in a small room, opening the doors to adjacent rooms can often make your piano's low octaves sound a bit clearer. (Because the shorter, high-frequency waves tend to bounce off any flat surface closest to the piano, the extra space won't improve their clarity.)
Try to avoid square rooms, or rooms with wall lengths and ceiling heights having a relationship of 1:1, 1:2, or multiples thereof (for example, 16 feet long by 8 feet wide by 8 feet high). Such rooms exacerbate the buildup of low-frequency coincident modes (resonant frequencies caused by standing waves), which can make the lowest octave of your piano sound uneven, overemphasizing some notes while making others virtually disappear.
Greater ceiling height is always desirable for resonance, but be careful with this. As mentioned above, it's best that the ceiling height not be the same as the length of one of the walls, or that length divided or multiplied by 2 or a multiple of 2. For example, if one wall is 16 feet long, the ceiling should not be 8, 12, or 16 feet high. If your ceiling is more than one-and-one-third times the length of the shortest wall, you may have a problem of reflected soundwaves that will require some dedicated acoustical treatments, though not necessarily. I've worked in some rooms with very high ceilings that sounded fabulous, mainly because the extra headroom helped the low notes sound more full and deep. It all depends on how "live" (resonant) the space is, and exactly which room surfaces are reflecting the sounds of the piano. If you have a sloped ceiling, the best results will likely be achieved by placing a vertical piano against the wall where the ceiling is lowest, or a grand piano facing out from the same wall and into the area where the ceiling is highest.