This is some kind of a complementary question to Are there any composer instructions on how to play a melody?
How can we (in modern times) know how a piece of classical music was actually intended to sound by the composer? We all know a specific musician's interpretation that recorded this piece of music at some point but is it correct that the initial composition although describing through musical notation its "feelings" would be a bit different from what we know it to be today?
I cannot provide a complete answer. In fact, the answer might be that we cannot know what an ancient composer intended their music to sound like. As an example I'd cite some fairly common renaissance era Lute music arrange for guitar. There are many interpretations of how to play the music and it is common to add ornamentation that is not explicitly present in the music. Another common embellishment is to arpeggiate chords with 3 or more notes rather than play them as chords. Though some performers choose not to do this.
In contrast I would say that in many orchestral scores the composer would not only provide very explicit notation for rhythm and dynamics but also written instructions in words regrading how the sections are to be played and what "feeling" the music should invoke in the audience. Mahler's symphonies are written like this. So in some cases there is less room for interpretation. That doesn't stop modern conductors from making changes but in many cases the "intent" is there.
We can make an educated guess from our knowledge of the instruments, contemporary reports etc. But styles of performance have changed even within the era of high quality recorded music. Listen to 'classical' orchestral recordings from the 1950s. Same 'dots', essentially the same instruments, sometimes a quite different style. Changes in style of vocal performance can be even more marked.
And, in all eras, there's the composer's intention - his 'inner ear' - and there's what the performers deliver. Even the most accomplished composer must often get a surprise - hopefully a pleasant one!
We're told of music being delivered to the first performance - whether it's the overture of a Mozart opera or a Sinatra recording session - with the ink still wet. I'm not sure if this amazes or horrifies me!
