This is really quite cool.
There is a program on WFMU radio in NY/NJ (archived for streaming on the web) that airs pre-LP recordings.
Since they are a listener sponsored radio station, they have fundraising and have offered a “new” Edison cylinder recording as a “gift”.
Edison’s Attic:
The audio curator at Edison National Historic Site rummages through the archives of the legendary Edison Laboratory of West Orange, New Jersey. Tune in for Edison cylinder and disc record rarities, many not heard since “the old man” himself stashed them away, featuring: Tin Pan Alley pop songs, ragtime, vaudeville comedy sketches, flapper dance bands, old-time country tunes, historic classical music, laboratory experiments and other artifacts - all dating from 1888 through 1929.