What is the informational density of a piano? It's primarily known for 88 distinct sets of data (not specific frequencies as each note is impure: containing different overtones), with a specific access mode. Here's an example of information retrieval on a piano, so what is stored here? Clearly the piano brings some base set of information from which one may extrapolate the performance using a set of meta-information. This meta-information would consist of data as to how the keys were pushed. If we knew nothing about the instrument we might assume a list of total presses for keys might do it. Perhaps greater insight would lead us to a list of the keys in order: but even that's not sufficient. We begin to approach a situation in which way be able to actually grasp the desired output when we include time as a recorded factor. But we also discover the speed at which each individual piece of information is recovered is also an essential part of the overall effect, and now more data is needed. A complete set of retrieval information (or meta-information) would include the time of any key-press, press-intensity most likely measured as velocity of key depression, and release time. In a standard piano knowledge as to pedal action would also have to be included.
Armed with this meta-information we would now be able to recreate past knowledge events (play pieces) given a specific knowledge set (the piano). The meta-information we've obtained has no inherent value, it is useless to use directly and can only be accessed itself through the use of the base information. The fact that likewise the base information is useless to us without the meta-information is not a paradox but a wonderful example of symbiosis of knowledge. Once applied appropriately we find a piece played that goes beyond the meta-information we brought to the appearance: resonance between strings, as an example, not being expressed in the text itself.
The actual information has a real physical appearance in the form of the strings, the soundboard, the case, etc... But the meta-information we've discussed is purely abstract, having no physical reality. It may be stored on paper in the form of sheet music (a rather impure form) but then the reality is the ink and the paper and additional meta-information is required to translate that to our version of knowledge. This sets up an infinite recursion of required knowledge that has not been explained. No true end point has been found, we only know there is one, and that it is not infinite, because we are capable of making sense of these things, and we can translate information. But for the time being we see that the piano itself is the only "true" information, and the rest is an abstraction that requires the piano to become a physicality.
So what information does a piano really store? We discussed its 88 notes, but is that the reality? What if we did not know what information to look for, how many ways could we attempt to access the information locked within? We could put the piano in a compression test in which we loaded the top and bottom until it failed, deriving a force versus strain curves and giving us all sorts of information like elastic constant, plasticity and ultimate load. Is not this information 'stored' in the piano just as much as musical notes? Burning it we would determine caloric makeup, speed of combustion, chemical composition and so forth.
Perhaps a question that should be asked is: what does a piano mean? What's the totality of its meaning, what is it in and of itself and what does add up to? Most likely any intelligence would recognize in a short time that it was designed, and that the purpose of the design included use of the keys (cats certainly prove this with frequency). Is that it's meaning? Would it be more meaningful if it were later to be used to perform an notable task? Is a piano more meaningful if it has in the past performed a meaningful task (which we each must decide the definition of)? If so what information is stored that has value? If none then how could meaning be determined if a zero change in information allowed a change in meaning? That would force us to admit that an object does not contain its own meaning, or that it is impossible to determine the meaning of anything as it may or may not have been impacted by the events that generated its meaning.
How does this apply to the meaning of us, of a person? Do we contain meaning inherent in ourselves or must it be forced upon by another intelligence? If so then where does that recursive process end? If we do contain meaning, where can we find it, how can we determine our own sum total? What must we look at, and how would it be stored as it happened to use?