So that takes care of the winds. The violin and cello represented the strings.

“And the piano is very good at filling in the horn part and the brass part,” Mr. Norris said. “It can be quite brassy at this stage. It’s really a clever way of picking out the fewest number of instruments that can sound a little like the orchestra.”

The vivacious performances on the recording — the textures gentle but the details piquant and the energy palpable — conjure a period in which amateur musicians were integral in the dissemination of would-be masterpieces.

Piano concerto arrangements, like the two Johann Baptist Cramer versions represented on the album of Mozart’s No. 21 in C (K. 467), might have been reserved for virtuosos. But the overtures — here “Die Zauberflöte” and “Le Nozze di Figaro,” both arranged by Johann Nepomuk Hummel — would have been fun for less exalted players to read through. And Mr. Norris speculated on how an excellent amateur pianist like Jane Austen’s sister-in-law, Eliza Hancock, would have approached Clementi’s “Jupiter” with a group of friends.

“She would have perhaps enjoyed beginning the ‘Jupiter’ Symphony and playing the beginning as far as they could, and then they could have said, ‘Well, let’s have a look at a slow movement,’” he said. “The Minuet through, perhaps — under tempo. It would have been a way to experience the music for themselves, even if they didn’t give a great public performance.”

As the century went on and the piano kept gaining in popularity, arrangements for four-hand keyboard began to supplant the quartet formation, which withered by the 1850s. And then, with the proliferation of orchestras, the rise of radio and recordings, and the related decline of amateur music-making, the orchestral originals — and the professionals who played them — finally triumphed.

It is impressive to have access, with a click of a button on Spotify, to dozens of full versions of the “Jupiter” Symphony. But “The Jupiter Project” allows an imaginative leap to a time long before that, when the circulation of music was the job of listeners who were also performers.