From the Store description:
Pocket Singer turns your Windows Phone into collection of ready to sing to tracks and a built in recording studio — so you can make music anywhere you go.
• Record your voice using the built-in microphone
• Play your Windows phone like you're at the studio
• Save your Songs
• Fast Record/Playback/Re-Record
• Be a Singer Now
• Be a Songwriter Now
• Be a Rapper Now
I gave it a whirl (I'll spare you my warblings*), here it is in action:
There's clearly work to do here, from at least one of the backing tracks being blank, to the strange filename entry screen, to the slightly unresponsive folder icon, but there's potential here, so stick with it.
The developer does go over the top a little in the rest of the description though, including this gem:
Pocket Singer takes song creation to the next level.
!! It's a great tool for very short song ideas, but let's not get too grandiose here! You can try Pocket Singer for yourself in the Windows Phone Store here.
* cough. Shed Music, now sadly defunct!