Now you can use Firefox add-on called Tumtaster to download music which are posted on Tumblr blogs.
TumTaster for Mozilla Firefox
Tumtaster adds a functionality to download music and videos from Tumblr to your computer. You just need to install respectively addons on your Firefox Web browser.
If you are using Google Chrome then you will need to install TumTaster for Google Chrome extension from here.
Note: Please read Tumblr Community Guideline before installing any Web browser extension or addon.