A. Jewish law has an interesting approach to dealing with potential nuisances like this. We can get a hint of what is going on by examining the three first tractates in the Talmudic order dealing with monetary law.
The first tractate, Bava Kama, begins with the words: "There are four archetypical kinds of damage". This tractate deals with outright damage, such as a goring ox, a raging fire, and so on. The only relationship between the parties is that one has committed a tort against another and must pay.
The second tractate, Bava Metzia, begins with the words: "Two grasp a cloak." Now the two people are still at cross purposes, but no one is harming anyone. They merely need the judges to resolve who is the true owner of the garment.
The third tractate, Bava Batra, begins with the words: "The partners who desired to make a partition." Now the parties are partners, working in cooperation to resolve their interests, without any involvement of the court.
This last tractate also discusses laws of damages, but these damages are of a different nature. "Damages of neighbors" are not destructive of property but rather of communal harmony.
Annoying neighbors by noise belongs to this category. The mishna in Bava Batra states:
[If someone opens] a store in the courtyard, [a neighbor] can protest and say to him: I can't sleep due to the noise of the people coming in and going out. But [a workman] may make utensils and go out and sell them in the marketplace, and [the neighbor] can't protest and say, I can't sleep due to the noise of the hammer or the noise of the millstones and the noise of the children.
The two kinds of noise have a substantive difference and also a legal difference. Having crowds in the courtyard is so annoying that a neighbor can protest at any time. But having someone do work in his own home, at a volume characteristic of a normal (though loud) activity, can obtain an easement; permission is needed at first but once it is given the person can proceed. The exception would be if there is someone with a special need, for example a sick person whose health will suffer from the noise.
If your piano playing is heard by neighbors at a volume, and at a time of day, characteristic of many everyday activities, then there is no need for you to seek special permission from your neighbors. If they are bothered, they can contact you and you should do your best to accommodate them. It's not that hard to find the source of the noise.
Most communities have local ordinances dealing with loud noise and other disturbances and it would be a good idea to find out if you are in accordance with these as well.
SOURCES: (1) Bava Batra 20b. (2) See Tur and Shulchan Arukh Choshen Mishpat 156.
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