Why isn't my favorite radio station listed in the Music app?

Re: The thread you suggested was good but did not really speak to my issue. The type of radio station I'd like to add is an existing radio station that broadcasts from a U.S. city as well as on the internet.

Thank you for trying that, and for replying with more info.

Wondering if you tried the tips below from the article: Listen to radio stations in Music on iPhone - Apple Support, eg: ask Siri to "Tune in to {your broadcast station} or try a "search" for your existing radio station.

"Play broadcast radio stations

1. Go to the Music app on your iPhone.
2. Do any of the following:

• • Use Siri: Activate Siri, then say something like, “Play Wild 94.9” or “Tune in to ESPN Radio.”

• • Search for a station: Tap Search, enter that station in the search field, then tap a result to play the station.
  • You can search for stations by name, call sign, frequency, and nickname."

Seems you don't need a Music subscription to listen to Radio in Music.

You may need to be signed in to your Apple Account to do some things.

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Re: "There's another radio station I listen to often but to get to it I have to open my browser and go to the station's website".

Sorry I don't know whether or not you can add stations to Apple's existing list.

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Re: "I do this at least once a week but it never shows up in Recently Played."

If you find success in listening to your particular radio station(s) in the Music app

You may find recently listened to radio stations on the "For You" tab in the Music app.

Re: Playing favorite radio station from Music app

See if the answer provided in this discussion thread on a similar topic can help:

Is there a way to add a Radio Station to … - Apple Community