The full Acrobat program, which is needed to produce PDF files is rather expensive for a once-in-a-while use.

Acrobat Standard (list $229 US) is mainly intended for creating pdf files from other kinds of "documents." Adobe does not list "editing pdf documents" as one of its capabilities. It does indicate that you can export as a Word document, which you could edit. You could of course use Acrobat Standard to make a new pdf from the Word document after adding your notes.

For full capabilities, inluding direct editing of pdf files for which you do not have the original files, without going to another format, the "Professional" version (list $449 US) is needed. Even Adobe doesn't actually recommend editing pdf files for permanent use. The pdf is used to collect comments, the ORIGINAL files are edited, and a new pdf is made.

The person producing the original pdf can choose whether to allow editing, or addition of notes, comments, etc., but the default setup generally results in a "fixed" output that "resists changes." (The options to save a copy or to export as another format can be "turned off" but I don't know how commonly this is done.)

Even if one has Acrobat Professional, a pdf that the original creator has not deliberately set up to allow editing may be difficult or impossible to modify as a pdf. The default is to "not allow changes" so you're actually unlikely to find many "editable" pdf files on the web. One of the options is to allow "comments" - which are not visible in the document except to the one adding the comment or to another person who has Acrobat to turn on the "view comments" mode. The "other person" who can see your comments can be limited to the originator of the document so that several people can comment on the same document but can't see comments made by others.

Some graphics programs have the ability to extract images from pdf files, and a music score in a pdf would usually be an image, but most such programs will generally ignore text surrounding the image. Photoshop Elements can do this, and I would expect that Photoshop (also too expensive for mere mortals to own) probably can do the same. I'm not inclined to believe that Photoshop can import a "whole" pdf file, but since I can't afford the program I'm too lazy to check it out.

Text contained in a pdf file can usually be copied and pasted, as text, to another kind of document. Separate extraction of images and copying/pasting text can easily become "labor intensive."

For occasional use, just printing and scanning may actually be the most practical method, and there's little to complain about if it works for you.

A method I've used some for adding notes is just to make a Word document with the same title as the pdf, and then try to remember to keep the two together. Put the notes in the separate Word document. If you like, include, in the Word document, a hyperlink that will open the pdf with a click after you read the notes. (Usually the critical info I've been interested in where I've used this method is just the URL for where the pdf came from.)

John