Is mass necessary to lower the absorbtive frequencies (I mean no matter what thre shape of the material , i.e. acoutical foams, if the mass is not enough, the frequency absorbtive (!) range is above "250 Hz"
No. You're confusing two principles. In general, increased mass is used as a way to BLOCK sound from going from one space to the next through a wall or floor. Blocking sound is difficult at low frequencies, and requires special techniques which may include increasing the mass of the partition separating the two spaces. Sound is ABSORBED by thick, porous materials, generally with very little mass. Absorbing low-frequency sound is also difficult, and requires its own set of special techniques (bass traps, membrane absorbers, etc.).
Do you know if a room can be tested for its own resonant frequencies with a single computer producing white (or pink ?) noise, and recording the noise at the same time with a (good !) mike ?
Just to find the peaks ... I have seen once a software allowing that, but i dont recall where ...
Now you're talking about room modes, which is entirely different than the previous two principles. Room modes occur when a wavelength of a particular frequency of sound corresponds to the physical dimensions of the room in question. They most often occur between parallel surfaces (there are three pairs usually in any given rectangular parallelpiped space), and can occur at integer mutiples of the fundamental frequency. The resulting audible effect one hears from room modes are hot spots and dead spots in particular locations at specific pitches. One can try and reshape the surfaces to avoid the parallelisms, make the surfaces sound-absorbing instead of sound reflecting, change the surfaces to sound-scattering, or just tolerate it. Steinway's selection room at the New York factory has one wall that's canted out of perpendicular, I presume to avoid the room modes between the parallel walls. Again, as an acoustician, I'm bemused because the other pair of walls is still parallel and the floor is parallel to the ceiling.
There are room mode calculators on the internet. They generally identify the room modes for rectangular parallelpiped spaces. These are the tools many recording studio designers like to use, but they don't have much practical application to the real-world living rooms we work in. One can also go to a built space and measure the room modes, but you wouldn't use noise for that.
I once had a client who was really disturbed by the room modes he heard in his living room. When I told him what was needed to correct the problem, he quickly decided he'd learn to live with the room modes. He moved the position of the piano to get his head out of the acoustical hot spot he was hearing, and then promptly found another hot spot at another pitch.
PS also .. did you separe the casters from the floor ? I noticed that some floors can be OK (even wooden floors) and wondered to what point grand pianos can be sesigned for some floor transmission (raising the lower frequencies by solid transmission) I often install rubber or decoupling goodies under the casters on wooden floors, but on any stage the floor participate to the tone (not on US university stages as you use dollies/trolleys, the name escapes me, unless ome wooden blovs are used to restitute some solid transmission the vibrations may be reflected within the instrument and I wonder up to what level it is good for tone...
Again, I'm bemused at caster cups being sold as some kind of vibration isolation for pianos. Some of the hard plastic or wood cups I see provide no vibration isolation whatsoever - none (except maybe the psychosomatic acoustical relief they may provide which seems to be directly proportional to their cost). The softer rubber cups would only be effective at high frequencies. Most of the ones I've seen aren't calibrated to the weight of a piano and don't provide the appropriate deflection to even perform well at that. The piano overloads the rubber such that it's essentially a rigid block. The way to vibration isolate a piano is to put it on a raised platform supported on SPRINGS. Only springs have the deflection necessary to isolate low frequencies. How likely is it that one could get a piano owner to build a platform for a vibration isolation problem? Not likely.
With regard to resonant coupling of pianos to stage floors, and whether that affects tone: It depends on whether the piano's on a dolly or not, rubber wheels or nylon wheels, and whether or not the floor is constructed of soft hardwoord, (or hard softwood), or too thick, or too thin, how far apart the joist spacing is, finished, or unfinished, the weight of the pianist, and the type of nails used to secure the floor, or whether Beethoven himself might have once walked across it....I've heard it all. Good luck scientifically determining the factors which affect tone. Tell me what you think you hear. I'll probably just smile and nod knowingly.
Now! Piano techicians. Go! And use your newfound acoustical knowledge for good!