We've heard of singing in the shower, but a singing toilet? This has got to be one for the home improvement journals! We suppose that depending upon the number of toilets that one has in one's home, one could have quite a concert--a sort of symphony of the johns if you will. In the event that this style of entertainment doesn't appeal to you, relax help is on the way.
The singing that you refer to is most certainly originating from the small valve contained in the toilet tank that regulates the filling of the tank. This rather simple (yet important) device is called the Ball Cock Assembly. It is designed to work in harmony with a flush valve assembly which controls the flow of water from the tank to the bowl.
A flush of the toilet via that little lever creates quite of chain of events. It's something like a major mousetrap. The trip lever raises a chain (or lift wire) which is connected to a stopper at the bottom of the tank. As the stopper goes up water is allowed to escape from the tank into the bowl. Then with a little help from a couple of laws, (physics and gravity) the water and hopefully everything else is siphoned out the trap.
Once the tank is empty, the stopper drops back down into place and the tank begins to fill via the ball cock assembly which is activated by the float ball. The float ball rises in unison with the water level until it is high enough to shut off the ball cock assembly. And so we have arrived at your problem. Contained in the ball cock assembly are a couple of minute rubber washers called ball cock washers. Over time these little buggers become dry and may split causing a singing sound nothing like Sinatra, not even close to the Mills Brothers.
Replacing these washers is relatively simple and very inexpensive. Make a visit to your local hardware store, home improvement center, or plumbing supply shop for examples of the device you have and for a little one on one training. It may help if you are prepared to share the name of the toilet manufacturer with the stores representative. Often times this will assist him or her in locating just what you need. And remember, our today's advice is "On the House"!