It's probably an error in how the site is coded. If you want to use Safari, control-click on the little speaker icon next to the track and choose "download linked file". Then just remove the HTML from the file name so it just ends in .mp3 and it will work without problems (at least the couple I tested did).
It's difficult to know for certain, but from what you describe, what you've downloaded is the web page the file is embedded in, not the music file itself. If you can post the URL of the page of the track you are trying to download, perhaps someone here can take a look and determine where things are going wrong.
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How to convert music html file?
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