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How do you even start writing counterpoint? What's the actual theory there?

I mean: if you're looking to go straight to theory, the classic textbook is Johann Joseph Fux's, from 300 years ago. But if you're familiar with writing melodies (with some voice leading) over chord blocks, try eliminating the chords and composing a second melodic line. This line should imply the original harmonies, while maintaining a unique rhythm and contour—and you can then add more melodies as needed. Many theory rules, such as avoiding parallel 5ths or 4ths, are essentially design patterns ensuring melody distinctiveness.

Of course, it also helps to listen to a shit-ton of counterpoint (the right suggestion here is "Bach", but personally it was Brad Mehldau's music that got me interested in this).

Gradus ad Parnassum of Johann Joseph Fux http://www.opus28.co.uk/Fux_Gradus.pdf
Everyone reads Fux (see sibling) but nobody, including my counterpoint professor, thought it was super useful.

Piston has this book that's more approachable: https://www.goodreads.com/book/show/445366.Counterpoint

But ultimately, learning counterpoint is 10% reading and 90% writing.

The short version: have your harmony or bassline go down when your lead melody goes up, or vice versa.

(It’s not that easy in theory but that is the gist of it.)

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