I was thinking this would qualify as a derivative work, while the original would enter the public domain.

https://www.copyright.gov/circs/circ14.pdf

EX: https://en.wikipedia.org/wiki/Pride_and_Prejudice_and_Zombie..., https://en.wikipedia.org/wiki/Aladdin_(1992_Disney_film)

I don’t know if publishing 1/2 a book would protect the first half or not, but presumably the second half would have entered the public domain in your hypothetical example.

> Half of a book is still under copyright of the whole thing

But what was described isn't "half of a recording". Imagine the "publish to extend copyright" applied to books too - would publishing the book with half the text blacked out still extend the original book's copyright?

That's just my naive take on it (i know nothing about copyright law). Your movie music argument might already be enough to show that I'm incorrect.

What I meant was, the recording is half dial tone and half music, because they're overlaid with each other.

Subtract the dial tone and the music part is "half" the total copyrighted work (which includes the dial tone).

But the music part is still 100% copyrighted. Same way that if you publish a book with 200 pages, pages 1-100 are still 100% copyrighted even though they make up only half of it.