Well, if you use Google Chrome, you’re in luck. There’s Tumtaster.
All you have to do is download the following extension (it’s sort of like an app on your phone, but for your browser) : https://chrome.google.com/webstore/detail/nanfbkacbckngfcklahdgfagjlghfbgm .
After you do so, all songs on tumblr will have a second bar under it that says download. Clicking on it will open a new tab with just the song, but you can right click and “save as” the song. You’ll be able to find the song in your download folder (CRTL + J).
Another thing you’ll notice is that there will be a tiny icon next the wrench on your toolbar. Clicking on it will show you all the songs you have scrolled by or seen, even if you didn’t play them. It’s handy if you missed any songs and you want to go back to it. It’s supposed to be a music player, but for some reason, it’s not working correctly. I blocked my friends’ tumblrs for privacy reasons, but you get the idea.
You can do this on Mozilla Firefox too, but I don’t use that browser so I didn’t look into how it would work. You would need to download two programs though - Greasemonkey & tumtaster.
I didn’t make this nifty invention, Bjorn Stromberg did, so give your gratitude to him! Reblog, spread the word, and tell your friends.