This small script adds a button inside the audio iframes found in common Tumblr posts with music in them.
The script will wait for Tumblr to load the mp3 song (this happens the first time you press play) to catch it and provide you of a link to the file, which can be saved with a quick right-click > Save as. You'll know the download link is ready when the button turns in yellow.
If you find an iframe to small for you to see the button this script generates, don't worry, it's still there. Simply right-click the play button and find an option to open the iframe contents in a new tab (This frame > Open frame in new tab in Firefox). That way the opened tab will provide enough space for you to see and use the link button with no problem.