James Martin/CNET

SEATTLE--T-Mobile wants to set your streaming music free.

The wireless carrier on Wednesday unveiled "Rhapsody UnRadio," a premium streaming music app available on iOS, Android, and on a browser developed with Rhapsody that is free for unlimited data customers and $4 a month for all other T-Mobile subscribers.

For those uninterested in UnRadio, T-Mobile said it would no longer count streaming music data from the most popular services against its customers' cellular data limits.

The music announcements represent Uncarrier 6.0, following up on T-Mobile's Test Drive news from earlier at the conference. The moves are part of the carrier's broader campaign to shake up the wireless industry and win over new customers. T-Mobile is just the latest to embrace streaming music in a big way, and it hopes its unique take on the service will help it stand out.

UnRadio follows a wave of music-related announcements by the carriers over the last few months. Sprint hosted a music-themed event last month, in which the carrier partnered with Harman Kardon to introduce the audio-optimized HTC One M8 Harman Kardon edition. It also teamed up with Spotify to offer a discounted music service to new customers, with the discounts rising as more subscribers join its Framily plan, with a price range between $5 and $8 a month.

AT&T, meanwhile, has an exclusive deal to offer Beats' fledgling streaming music service, which costs $10 a month for individuals or $15 a month for families. The music service is one of the reasons that Apple agreed to pay $3 billion for Beats.

T-Mobile believes it is one-upping its competitors with the data offer. Customers listening to Pandora, iHeartRadio, Slacker, iTunes, Spotify, and Rhapsody won't see the data counted against its plan.

While T-Mobile doesn't employ data caps, it will throttle, or slow, the connection speed once customers hit a predetermined level. The data-free music is a boon to music lovers who subscribe to a plan with limited high-speed data.

When looking at annoyances in the industry, one concern customers expressed was the fear that streaming music would eat into their data caps, T-Mobile CEO John Legere said in an interview.

T-Mobile will also ask what other music services should be included in this program, and will post a poll on Facebook. Other services under consideration include Google Play, Beats, and Rdio.

For Rhapsody, the deal marks a coup for the pioneer in subscription streaming music. While it has been around since 2001 and owns famed file-sharing service Napster after it transformed itself into a copyright-kosher -- and struggling -- operation, Rhapsody has been overshadowed in recent years by tech giants and hot startups as streaming quickly becomes the music industry's segment of strongest growth.

Rapidly growing startup Spotify; marketing powerhouse Beats Music, in a deal to be acquired by iTunes-download giant Apple; and streaming services from Google and Amazon all tend to outshine Rhapsody in the public eye, while Rhapsody has focused recently on growing overseas through telecom partnerships like the latest with T-Mobile.

"We set out to create the world's best Internet radio service, and with UnRadio, we've succeeded," Paul Springer, chief product officer of Rhapsody, said in a statement.

UnRadio Rhapsody customers on T-Mobile will be billed through the carrier. But the service will be available to any users. The price of the service for everyone else is $5 a month.

The service allows customers to listen to any song they choose, and are able to skip as much as they want without any commercials. They can also mark songs as a favorite and save for listening later, or download them for offline listening. Subscribers can choose from a catalog of 32 million songs through Rhapsody.

There's also a radio option that allows customers to choose from a number of local radio stations.

UnRadio boasts one more feature, TrackMatch, which allows customers to use the service to identify songs played at a bar or on TV and create a station around that song or save it for later listening, taking the Shazam audio-recognition app to the next level.

CNET's Joan E. Solsman contributed to this report.