You can actually post music or audio post, using the Text post using the Grooveshark widget.

This can be an alternative to Tumblr default player and also make it easy for you to just share what you listen from your Grooveshark playlist, rather than searching for it in the Soundcloud, or upload it yourself.

To do this here are the steps :

1. Select the song that you wanted to share. Click on “Share Song” option and a menu will pop-out. 
2. Select Widget  
3. Next customize the player as you wish. After that click copy to clipboard. 
4. Go to Tumblr and create a new text post. Click on the HTML icon. 
5. Paste the code into the editor and click update. 
6. After that you can publish the post and check it out on your blog. OSOM.

You can also use this as a audio player widget for your blog.