There are many tools out there for converting video soundtracks into MP3 files; Peggo is one of them, a free web service that, with no need to register, extracts the audio from YouTube videos or SoundCloud podcasts so you can store them locally.
Peggo lets you record the sound from these platforms using a very simple interface, with the advantage of saving yourself an entire installation process. The way it works, basically, is that you copy the clip links you want into the search bar and click ‘intro’. A player will appear where you can edit the audio fragment that you want to download, whether from start to finish or a certain interval of seconds. Here is an example from YouTube:
With this small tool you can also normalize the sound to avoid large swings in volume and remove the silences at the start and end of the video. Once all the details have been confirmed, including the artist name and song title, you just have to click ‘Record MP3’ and Peggo will download your new MP3 file.