Can a music accompaniment part be recorded ahead of time for a performance as long as the school or library has a copy of the sheet music? Can a few modifications be added to the accompaniment as long as the heart of the work is preserved? Can this recording be shared among schools and libraries as long as each organization has a copy of the sheet music with performance rights?
This question came in from a school system, and it triggered a lot of memories for me.
My junior high school music teacher was a very nice man. From deep within mid-1980's Central New York, he tried to cobble together an orchestra from an array of students whose skills and practice habits ranged from "Julliard-bound," to "who is torturing that cat in the third violin chair?"
Back in 1986 (when I was 13), I saw this guy as "old." Because of the way he tirelessly started the music over (and over) until the brass section entered at the right bar of "Star Wars", I also saw him as a font of endless tolerance.
Now that I am older, my memory portrays my former teacher as a pretty young guy (I think he was in his early 30's). And by now I have worked with enough educators to know that his tireless tolerance of our incompetence was passion.
So, this question has stirred a feeling of nostalgic gratitude. Because of that, I want to give this member an answer that is really solid, helpful, and clear. But as they say in the construction biz when people ask for a job that is quick, quality, and cheap: I can give you a combination of any two, but not all three.
Here is the part of the answer that is solid and clear: Making a recording of a copyright-protected composition, unless the recorder has the permission of the copyright owner, or the recording falls under an exception, is copyright infringement…even for educational purposes.
Is there helpful and solid authority on that? Yes. Circular 21, the long-standing guidance on the relevant copyright laws, makes it clear that for educators, only the following recording of musical compositions is allowed under "fair use":
A single copy of recordings of performances by students may be made for valuation or rehearsal purposes and may be retained by the educational institution or individual teacher.
A single copy of a sound recording (such as a tape, disc, or cassette) of copyrighted music may be made from sound recordings owned by an educational institution or an individual teacher for the purpose of constructing aural exercises or examinations and may be retained by the educational institution or individual teacher. (This pertains only to the copyright of the music itself and not to any copyright which may exist in the sound recording.)
So, at first blush, the answer to the member's first question (and thus, all the following questions) is: NO.
Now, the core guidance in Circular 21 is OLD. It pre-dates streaming, it pre-dates file-sharing, and depending on what start date you give the web, it pre-dates the Internet. But insofar as case law and legal commentary is concerned, it abides.
So, while I have to answer a resounding NO to the question just as it is asked, I can offer a few helpful and clear solutions.
First, it never hurts to ask. Depending on the copyright holder, you may be able to get a "limited license" for the very thing you want to do. Some owners might even be charmed. Others, of course, will just refer you to their manager. You never know until you try. Just make sure you get it in writing.
Second, while the Circular 21 guidance quoted above gives clear examples of what fair use permits, on page 7 of Circular 21, just before listing those guidelines, it states "There may be instances in which copying which does not fall within the guidelines stated below may nonetheless be permitted under the criteria of fair use."
So, if a version has been recorded for performance as part of a clever mash-up, for purposes of commentary and criticism, or another use that might meet fair uses' four factors, this approach is worth considering. Sadly, since that is a case-by-case analysis, I can't say what precisely when that is allowed! An education institution should perform such an analysis using its fair use form.
Third--and I can't believe I am suggesting this--it may be that a combination of different licensing can arrange this precise permission for you.
We'll call this the "Two-Step Shuffle" solution. It is meant to be helpful, and it is solid, but I am concerned it might not be too clear. But let's give it a go.
NOTE: to use the "Two-Step Shuffle" solution, your institution MUST have a public performance license from a licensor like ASCAP or BMI. So, if your school doesn't have one, just stop reading, right now. But if you do…
Step one: see if the song you want to record is licensed for "covers" on a publicly accessible "host site" like YouTube. If the host site has the license, you can record the accompaniment as a "cover," and put it on the host site.
Step two: With your "cover" recorded, you can then play it from YouTube at any premises that has a license for public performance (this is why you need that license from ASACP or BMI…which is also what covers playing music at a high school dance, music over the loudspeaker during halftime, etc.).
Of course, this being an Internet solution, the "Two-Step Shuffle" solution could disappear at any moment! But this being the Internet, something else will take its place.
Now, in suggesting a school to make use of a commercial video hosting service (like YouTube), I would like to take a moment to discuss those two important legal concepts: "Coulda," and "Shoulda."
Just because a school can upload content to a site like YouTube, and get a license for a cover, doesn't mean it should. After all, when using a service like YouTube, an institution agrees with these terms:
By providing Content to the Service, you grant to YouTube a worldwide, non-exclusive, royalty-free, sublicensable and transferable license to use that Content (including to reproduce, distribute, prepare derivative works, display and perform it) in connection with the Service and YouTube’s (and its successors' and Affiliates') business, including for the purpose of promoting and redistributing part or all of the Service.
In other words, you're feeding the beast; you're commodifying the content you've chosen to share. If it's student work, there are privacy and further intellectual property concerns (students own their copyrights, after all). None of these are things an educator should take lightly.
That said, if approached with the right balance of attention to legal details and commitment to artistic excellence, the "Two-Step Shuffle" can also show future artists and performers how to respect copyright law and engage in self-promotion (which seems to be a critical skill nowadays). So "woulda, coulda, shoulda?" If you undertake the "Two-Step Shuffle" solution, do it with an "ethics buddy" (preferably an administrator who has your back).
And of course, a "Two-Step Shuffle" solution can only be used if you can answer these questions in the affirmative, and you preserve the documents from which you derive your answers:
That second part pertains to any other school or place that wants to publicly use your recording, as well.
So, there you have it. Was this solid and/or helpful and/or clear? In keeping with my Junior High memories, I give myself a "B."
I do wish this answer was a little less like trying to get the brass to come in at the right bar of "Star Wars," but copyright, fair use, and licensing take time and attention to detail to get right.
That said, with enough passion to fuel the effort, I am confident you'll hit the right note.
 That was me. I played trumpet. And had braces. NOT a good combo.
 And because I have high standards.
 Circular 21, "Reproduction of Copyrighted Works by Educators and Librarians," which has been in use since my days playing trumpet, and arguably, could use some updating. You can find it here: https://www.copyright.gov/circs/circ21.pdf
 How old? It was first contained in a joint letter written by representatives of the Music Publishers’ Association of the United States, Inc., the National Music Publishers’ Association, Inc., the Music Teachers National Association, the Music Educators National Conference, the National Association of Schools of Music, and the "Ad Hoc Committee on Copyright Law Revision" on April 30, 1976. Of course, if I tell my younger sister that something from 1976 is "old," I'll catch hell, but fortunately, she teaches religious education, not music.
 A scenario such as the one depicted by the member doesn't even get any slack from educators' other great copyright reprieve: section 110. While 110 does allow a variety of exceptions for musical performances, it doesn't extend its tolerance to recording.
 Something no not-for-profit educational institution should be without, since it can help your institution limit damages under Section 504 of the Copyright Act.
 As of January 13, 2020, YouTube maintains a list of licensed songs you can record and upload at https://www.youtube.com/music_policies?ar=1578920053089&nv=1. And, also as of this January 13, 2020, YouTube (unlike Netflix or HULU) enables businesses to use their services (rather than restricting them for "personal" and "home" use).
 Insofar as I know, only YouTube does this. But I need to get out more, and of course, this type of thing evolves quickly in cyberspace.
 This is different than permission to perform the musical composition!