As a streamer, streaming copyrighted music may result in a DMCA takedown notice from the copyright owner, as well as portions of your videos being muted.
The safest way to avoid your stream or videos getting muted (and potential penalties or copyright infringement claims) is to play royalty-free music. Here's some examples of services that can help you make that happen.
Pretzel – Royalty-free music for your monetized streams and VODs. Use on Twitch without having to worry about content ID strikes & muted content.
Monstercat Twitch Channel – A 24/7 VoD friendly music stream.
We will not mute VODs that contain Monstercat's music. While Twitch's Audio Recognition system only allows for audio muting, we ask that you only include Monstercat music in your VODs if you have purchased a Twitch whitelist license.
If you include Monstercat in your streams we ask that you purchase a Twitch whitelist license.
You can tune into our Monstercat FM channel during your Twitch streams without your VODs being muted, but please include our track listing bot in your channel by typing !join on the Monstercat FM channel at http://www.twitch.tv/monstercat
If you are not listening to Monstercat FM, we ask that you use XSplit, OBS, or similar tools to show your audience which songs are being streamed live.
If Monstercat music accounts for the majority of music used in your stream, we ask that you link to http://youtube.com/monstercat.
Popskyy – Mega Pack 1 contains 106 electronic/chiptune songs for free (name your price). Additional albums available for purchase. All songs can be used for streaming, videos, etc but link attribution is required.