Thanks for suggestions! The winner so far is grandma's tablecloth!
I will digest and absorb your wisdom. But before we go further: Is there a METHOD to the madness? I mean, I have a suspicion that my stone rack is adding some hardness and extra treble to the sound. Some of you say yes, others no. But what can I do, to test if the hypothesis is true? Maybe the rack problem is very marginal, the hard sound is mainly due to - for example - my somewhat hot tweeters?
Here are some ways I have tested. 1) Hand clapping in front of rack, vs other parts of the room. Result? Not conclusive, perhaps marginally more echo. 2) Listening with a stethoscope on the stone shelves, while playing loud music. Result: cannot hear any clear ringing. They ring when I strike them with a hard object, of course, but not sure if it plays a role with music. However the large volume from the speakers makes it hard to hear whatever goes on in the stethoscope. 3) Varying the basis of the shelves by dampers on the steel supports. Some effect maybe but not a lot, and it lowers stability so again, not sure. 4) Using a variety of footers, including Cerapucs, Walker valid points and large ceramic cones. Some effect, yes, but not so great as I first thought. It seems that the more massive the stone shelf, the less is the extra bonus of good footers. I have some massive stones at the bottom of the rack, and have a tendency to think "i don't bother" with footers there. 5) Try to measure, using REW. So far, not very helpful.
Other suggestions for method are welcome. I know what some of you may answer. Just throw a huge sound-damping cloth over the whole rack! If I don't hear a clear improvement, the "stone rack is bad" hypothesis can be laid to rest in my case. I will consider it.
