sudo apt-get install youtube-dl ffmpeg libavcodec-extra-53
# Save all music from a playlist as mp4 and mp3 with High Quality
youtube-dl -i --write-info-json --keep-video -o "%(title)s(%(id)s).%(ext)s" --extract-audio --audio-format=mp3 --audio-quality=0 --max-quality=1080p https://www.youtube.com/playlist?list=ID-PLAYLIST

You can put your playlist as Unlisted to not make them public.