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Steve,

The reverberation time of your living room space is given by a very simple equation:

Reverberation Time = [(0.161 x cubic volume) / (total sound absorption)]
(total sound absorption in the room is the sum of all the areas of the materials in the space multiplied by their absorption coefficients.)

So... you have two options for reducing the reverberation time in your living room/piano room space. Either reduce the cubic volume OR increase the area of sound-absorbing materials.

I assume that you're not going to change the cubic volume of the space. Doing so would require building new walls, etc.

So... going under the assumption that the volume of your space is fixed, the only choice you have left is to increase the areas of sound-absorbing materials.

You haven 't given a complete description of the furnishings of your space, but you mentioned wood floor and plaster walls. Those are mostly sound-reflecting materials. Examples of sound-absorbing materials are carpet, window drapery, wall tapestries, cloth-upholstered furniture with cushions, people with clothing, kittens, and so forth. There are also commercially available sound-absorbing wall panels in various finishes. You will need to keep adding sound-absorbing materials to the space until the reverberation time is reduced to your satisfaction. It is unlikely that a carpet just under the piano will work. It may provide a just noticeable difference in the acoustics local to your position as the pianist, but is unlikely to make a noticeable change in the overall reverberant character of the space.

You mentioned that this space is your "second living room of [your] house and [you] have to respect design and furniture that are [in] it." If you're not willing to make a dramatic change in the room's finish materials, you won't make a dramatic change in the room acoustics. Sorry. The laws of physics trump your interior decor.

Chris S.
RPT and Room Acoustician

The 1/4 wavelength thing is important, especially if you are looking at the low-mids. C3 is about 130Hz, which has a wavelength of about 2.6m. Any sound absorbing material will not effectively damp this frequency if it has a depth of less than a quarter of that wavelength before encountering a reflective surface (a wall). So you would need a 65cm thick panel of fiberglass, or to hang a thinner panel of fiberglass with a gap behind it so there is 65cm between the front and the wall. Preferrably air-tight for maximum effect!

This is the thing people forget when accoustically treating a room. If you are having problems with boomy low-mids, then you will need to think more carefully about the problem. If it is higher frequencies, the general-purpose treatments will work very well.

Are there specific resonances that are a problem? If certain notes are being accentuated, then you are probably exciting standing waves. If that is the case, then you may have good results simply moving the piano. If you find a particularly troublesome frequency, then move the piano by a quarter-wavelength in any direction for that frequency, and you should be relocating the piano to a node, which will cancel out the effect. (but at the same time you might move it to an anti-node for another frequency, so creating another resonance - it is a trial-and-error thing!) Some rooms have particularly troublesome standing waves at certain frequencies, locating the nodes of these standing waves is the way to get round that.