Gerhard von Breuning, a friend of the composer, wrote about Beethoven telling his father how the work would have a "new gravitational force" that would go beyond even his celebrated 9th symphony, one of the most revolutionary works of its time.
But Beethoven left behind only a few fragmentary musical sketches of what he planned. The new project aims to use a computer to create the full work he might have composed.
"The quality of genius cannot be fully replicated, still less if you're dealing with Beethoven's late period," Christine Siegert, head of the Beethoven Archive in Bonn and one of those involved in the project, told the German broadcaster Deutsche Welle.
"The project's goal should be to integrate Beethoven's existing musical fragments into a coherent musical flow. That's difficult enough, and if this project can manage that, it will be an incredible accomplishment."
Machine learning software is fed the musical sketches Beethoven left behind for the symphony and also other examples of his work and of the composers who influenced him.
"Take a particular Beethoven work, one for which extensive drafts still exist, like the Eroica symphony. If you feed the computer both the sketches and the final product, it can figure out how Beethoven works with sketches and where he goes from there," Ms Siegert said.
The project is being funded by Deutsche Telekom and is headed by Matthias Röder, director of the Karajan Institute in Salzburg.
"No machine has been able to do this for so long," Mr Röder told Frankfurter Allgemeine Sonntagszeitung.
"This is unique."There will be some human input. While the computer will write the music, a composer will orchestrate it.
