radio stations are not allowed to tell you when they're going to play certain songs.

Having worked in the radio broadcasting business for the last 30 years, I can tell you that this is urban myth. Perhaps this has been propagated by lazy DJs who didn't want to go to the trouble of looking something up for a telephone caller, and instead told the caller that he "...wasn't allowed to."

Announcers frequently (nearly always, actually) do pre-announce their music. They don't say "Be sure to listen at 11:42 this morning because we're going to play <song title>", but they do say something like "Coming up in the next hour are songs by <artists names> and the new hit <song titie> by <artist>."

Also, radio stations are supposed to pay for songs that they broadcast,

And indeed, they do -- through payments to BMI and ASCAP. These payments are made monthly, and are based upon the net revenue of the station. For some stations this can run into hundreds of thousands of dollars annually.

but that's mostly irrelevant because of the ``rebates'' they get from the record companies.

The only "rebates" we receive from record companies is the occasional free CD that they would love for us to play. If it fits our format and is (in the opinion of the music director) worthy of airtime, it'll get get played. But 99% of our music comes from our music service -- in this case, Clear Channel Radio (yes, I know, the Great Satan of the airwaves, determined to destroy any vestiges of originality in its desire to air only bland, inoffensive music) and from that point we have a computer program (RCS, for Radio Computing Services) that sets up the actual playlists, blending tempos, artists, vocals/instrumentals, etc., with frequency of play based on national ranking of the song.

Despite the apparently commonly-held view that the radio business is a nefarious den of payola working hand in hand with the record labels to make absolutely certain that no worthwhile song from an independent artist is ever aired, the reality is much more mundane. It is very much a "nuts and bolts" business, appealing to the lowest common (and thus the largest) denominator. It is a straightforward game of numbers, and the music that the most people want to hear is the music that will get played. To put it another way, two competing stations would each rather have half of an 80% pie than have 100% of the remainder.

tanstaafl.
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"There Ain't No Such Thing As A Free Lunch"