Bruce Grimes asks about Theremin accompaniment rolls in MMDigest
080413 and suggests that there were such rolls for Ampico.  The
"Complete Catalog of Ampico Reproducing Piano Rolls", by Elaine
Obenchain, lists accompaniment rolls for cello, violin, voice and
piano duet, but none specifically for Theremin.  My guess is that
the Ampico accompaniment rolls for Theremin which Bruce heard about
were just vocal accompaniment rolls.  There were lots of similar
accompaniment rolls for the Duo-Art.

I think any music that does not move too fast would be appropriate 
for accompanying a Theremin.  Pieces like "Ave Maria", Schubert's
"Serenade", and many of the other vocal pieces.  Some of the more
lyrical violin pieces should work well on the Theremin.  In fact,
there is a Duo-Art accompaniment roll presently on Larry Norman's
auction list [http://www.home.earthlink.net/~rollertunes/] which
should work well -- it is "Après un rêve" by Fauré.  As the title
implies, the music is slow and dreamy, which should fit the
Theremin well.

Four vocal accompaniment rolls just sold on eBay and it would be
worth checking eBay occasionally, although the accompaniment rolls
are not as plentiful as the standard rolls.

David Sharpe
Western Massachusetts, USA