I'm considering creating a music transcription service as a side hobby project. With this service, clients could request that I transcribe a song (or parts of a song) for them in exchange for a fee. I would then send the client a PDF version of my transcription.
From my understanding, it is illegal when you sell or give away any derivative form of a copyrighted song (including sheet music). With this service, I do not intend to publish or sell sheet music. I would merely create the transcription, and give it to the client that requested it for a fee.
I understand it is perfectly legal to transcribe a song you purchased yourself, as long as it is for personal use. Does this become copyright infringement when someone else pays you to transcribe a song they've purchased, and this person is the only one who will get the transcription?