Ditto on Audacity ... it will record anything your computer is playing and has a HUGE assortment of tools.Download Audacity, ( https://www.audacityteam.org/ ). It first seems to be too complicated. You get used to it. You can also tweak settings. It records what comes out of computer speakers. ("What you hear" under pc audio settings.) You can record the entire broadcast as one file. Be aware. When you stop recording, it is going to be one huge file. When you save it, make sure you save it as an mp3 file with the bit rate of your choice.
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