So I came along this lesser-known composition by Beethoven, "Cantata on the Death of Emperor Joseph II. And wondered how many instruments did this work score for. Like for example, you have 3 flutes, 2 oboes, timpani..etc. And so on. But the composers don't write it down on the score, my question is. How do I know how many instruments is the work scored for?
Most full scores have pieces have the instruments listed in front of their staves at the beginning of each movement. For example, the score that's posted to IMSLP for the canata you mention lists for the first movement:
Flauti, Oboi, Clarinetti, Fagotti, Corni, Violino I, Violino II, Viola, Coro, Violoncello e Basso
which translates as
Flutes, Oboes, Clarinets, Bassoons, French Horns, Violin I, Violin II, Viola, Chorus, Cellos & Basses
Moreover, you can see how many of the winds are required by looking at the staff and seeing how many voices are written. In this case, there appear to be two parts for each woodwind instrument, at least in the first movement. To get a full list of instruments needed for the whole piece, you would need to look over each of the movements and check that extra instruments weren't added in later movements. (In this particular piece, it does not appear that there are.)
You may also run across orchestral instrumentation shorthand, particularly when looking through catalogs of sheet music. This lists the instruments required in a standard order:
- Woodwind instruments: flutes, oboes, clarinets, bassoons
- Brass instruments: horns, trumpets, trombones, tubas
- Timpani, percussion, piano, harp etc.
- String section: violins, violas, celli, basses
In the case of the cantata, the shorthand would be "2,2,2,2 - 2,0,0,0,str". (There are other ways to write this—sometimes with periods between the numbers, sometimes omitting the dash, or using a semicolon—but the order of the instruments is always the same.)
Beethoven did write a few pieces for wind band, where more than one player might well have taken each part. But I think the piece you mention uses the orchestral method where one part = one player.
I seem to remember hearing of some orchestras, doubtless in the German tradition of 100-odd years ago, who would sometimes put two players on each part in search of a bigger sound. Brahms, etc. might even have known of and approved this practice! Not, I think, Beethoven.