Go to http://keepvid.com You can past the Youtube URL in their box and it will make the video available for download in .flv and .mp4 You will want to download it in .mp4 format. I'm sure you can find a program online that will then convert the video to audio only. Search for mp4 to mp3 Hope this helps a little
Not legal but...
Audacity is a free sound editor download. One of the settings records "what you hear" on your PC.
If you download an additional little thing called LAME you can export the recoring or edited recording as an MP3 file.
Much You Tube stuff has a high quaility soundtrack.