Music.
Napster API is a free Music API that requires apiKey authentication, is served over HTTPS and supports CORS, so it can be called from the browser.

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List of internet radio stations
Yes. The Napster API is listed in the Music category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The Napster API uses apiKey authentication, so you need to register for credentials before making requests.
Yes. The Napster API supports CORS, so front-end JavaScript can call it directly.
Yes. The Napster API is served over HTTPS, so it's safe to use in production.