> The math looks easy enough, but I know nothing about music. Nothing. And I'd love to learn, of course, but I can see myself buying a keyboard and plinking out some of these transformations

read musictheory.net, get musescore, and then you can start experimenting with some of this. don't need a keyboard.

if you do decide to spend some money on hardware, the r/piano folks have some information on the terminology of such things https://www.reddit.com/r/piano/wiki/faq#wiki_choosing_a_keyb...

> without a payoff

no problem, just redefine payoff and you're all set