There was once a time when music streaming was still a cool new idea. Why buy every song on iTunes when you can just pay a little each month to have every song? This was at a time when people other than your coworkers or teachers actually used Pandora, back when last.fm actually had music[1].
Now, you're Twitter, and you notice that not only are a lot of people sharing music on your platform, but you also have a bunch of big name artists on your platform already. Taking advantage of both the rise of streaming and also the amount of stuff shared to your platform, you decide to make a dedicated app for music, powered by Twitter. That app would become #Music.
About two months ago I wrote a blog post about obscure Twitter features, and I'm a little shocked I missed this.
Launch
Announced in a blog post, #Music was an app created by Twitter that was optimized for discovering music based on Twitter. It would gather songs that were popular on Twitter and give you a dedicated place to listen to them. Not only that, but you could also view artist profiles in the app. Music would play from the iTunes preview, but you could connect Spotify or Rdio to listen to full tracks as well.
The way I'm guessing this worked was by gathering the metadata from Spotify and iTunes links people Tweeted. Additionally, you could quickly Tweet what you were listening to directly from the app, and it would add #NowPlaying to your Tweet. This was a special hashtag, as #Music had a feed that would show you songs people you follow recently Tweeted using the hashtag.
Something like this made a lot of sense, especially back in 2013. People used to Tweet a lot more. Obviously everyone uses Twitter differently, but people would post just about anything. Announcing they're hungry, what they're doing, it was basically a small little blog (hence why Twitter is a "microblogging" service). Some business conferences would have hashtags and then put displays around the building the conference was hosted at showing a live hashtag feed. Additionally, the internet was a lot more connected. You could post to Instagram, and it would automatically share the picture to various other social networking platforms like Twitter, Tumblr, and Flickr. People would setup things that would automatically Tweet whenever they for example liked a YouTube video.
#Music was released for iOS and also had a web version. An Android release was planned, but as far as I know that never ended up happening. The main app interface would be split up into different pages with this collage interface:

The pages were[2]:
- Popular - New music trending on Twitter
- Emerging - Hidden talent found in the Tweets
- Suggested - Artists you might like
- #NowPlaying - Tweeted by people you know
Additionally, you (yes, you!) could view profiles for artists, giving information such as who they follow on Twitter.

I also want to show off the now playing interface, which I think looks so cool.

Shutdown
Twitter #Music was somewhat doomed to fail from the start. While it was a cool experiment, most people would rather listen to music on a dedicated streaming app. Plus, the novelty will eventually wear off.
On March 21, 2014, Twitter announced the following:[3]
Later this afternoon, we will be removing Twitter #Music from the App Store. If you have the app, it will continue to work until April 18.
We continue to experiment with new ways to bring you great content based on the music activity we see every day on Twitter.
Twitter #Music was already obscure, but after this shutdown the app was basically forgotten about. While its sad it shut down, its still cool to see it looking back. I love it when social media companies try really dumb things.