Yes, there are libraries that collect this material.  I would post your
query to the email list of the Music Library Association, MLA-L.  You can
subscribe here:

Some information that could help libraries decide whether to take this
music is:

1) what kind of music is it?  You say dance band, but depending on the
period that could be any number of styles (country, swing, jazz, ordinary
pop, etc.)
2) How much is there?  You say a plastic tub - just one?  Can the person
supply photographs of the material?

My guess is that more local or state libraries would be the best bet.
Something like University of Illinois at Urbana-Champaign which has a good
music department.

Good luck.

Bob Kosovsky, Ph.D. -- Librarian, Rare Books and Manuscripts,
Music & Recorded Sound Division
The New York Public Library for the Performing Arts - Dorothy and Lewis B.
Cullman Center

40 Lincoln Center Plaza, New York, NY 10023

On Thu, Apr 15, 2021 at 9:43 PM Chris Bishop <[log in to unmask]> wrote:

> From a facebook 78 group post - if there's particular interest I can put
> you in contact with her:
> My grandfather Ray Mayhew had a dance band in the late 1930s and 1940s.
> His band was mostly a family band based in northern Illinois. My mother
> played the piano and sang. My grandfather was the oldest brother to Wendell
> (Gus) Mayhew, Jack Mayhew, Bob Mayhew, and Nye Mayhew, who were all
> professional musicians from the late 1920’s on
> My sister inherited all of his orchestrations ( I think that is the correct
> term) for the music that was popular at that time. This music may only be
> the piano arrangements. I know nothing about this, just guessing.
> She wishes to dispose of them as she is selling her house and moving into
> an apartment. My question is: are there people who collect this and would
> be interested in having this.? All of it has been in a plastic tub in a
> garage for many years and is somewhat fragile.