youtube-dl can be installed easily:

sudo apt-get install youtube-dl ffmpeg
Then simply:

youtube-dl -t --extract-audio --audio-format mp3 YOUTUBE_URL_HERE

(As shown here by duffydack.)
https://askubuntu.com/questions/115587/how-can-i-download-music-from-youtube-and-not-the-video-film/115597#115597