Apparently there was a special on TV about music being heard by the Apollo 10 astronauts while coming around the far side of the moon. Conspiracy theorists had a field day with this as have the usual array of Facebook pages that poorly understand science and engineering. As is the case with most things explanation for the noise is a bit more mundane than aliens.
For the uninitiated NASA has posted an MP3 of the recording. There is a lot of noise from equipment, probably some of the whine is due to power inverters but at around the 2:40 mark you can faintly hear some noise. Personally I wouldn't call it music but whatever. You can hear the lunar module pilot Gene Cernan commenting on it.
If you ask me it sounds like pretty standard feedback or interference from local electronics. The command and lunar modules used VHF radios for communication which are pretty susceptible to interference from a wide range of appliances, inverters, lights, etc. Put your WiFi router near a leaky old microwave and see how far the range gets cut for a demostration of this interference. Apollo 11 reported the same noise, but once the LM touched down Collins reported the woo-woo noises ceased. To me that sounds like some sort of ground issue or feedback, not aliens. Just the sheer amount of noise in that recording would lead me to think it was just some leaky electronics or feedback.
As to the classification of these recordings lending credence to the aliens theory: it was the middle of the Cold War, everything was classified outside of school lunch menus.
Turns out space is a pretty noisy place in the radio part of the spectrum. The gas giant planets have very active magnetic fileds and are very loud radio sources. Cassini has provided us with "sounds" from Jupiter and Saturn. They're kind of creepy too:
So, it's not aliens or a government cover up. With most people these days using digital methods of telecommunication that are relatively noise free these sort of things may seem strange. However noise and interference are common to analog radio signals. Anyone else remember static on the TV or radio stations fading in and out with certain weather conditions? It's the same sort of stuff here.