Do singing water pipes mean there is air in the pipes?

If you mean there is a "tone" like sound coming from the water pipes see if it corresponds to each time you flush a toilet. The fill valve of toilets as they come close to being completely filled can vibrate causing a sympathetic vibration on either the cold water line or the waste line depending on certain conditions. The resulting tone can get so loud as to almost be deafening. The solution is simply to install a new fill valve in the tank of the suspect fixture. Hope this helps I had a problem that sounded identical to yours.