Recently, I've been seeing a weird "style" of eighth notes, where there are clearly way too many to fit within the measure as determined by the time signature.
Moonlight Sonata, third movement:
Chopin, Op. 28 No. 24
Moonlight Sonata is in common time, and the Chopin is in 6/8 time. How are these eighth notes supposed to be counted/played?
These should be played "ad lib", which means the performer is quite free to play them as they wish.
Especially over long tones (first example), that means that you can stretch time quite a lot. Often the long tone has a fermata, and the eights notes are like a cadenza. I'd play it as if there was such a fermata even if it's not there.
In the second case, where the left hand has a specific rhythm, you may want to keep time. But even there you can play "ad lib", you're fairly free to move the beat around.
These "cadenza" mean freedom! :)
My recommendation: listen to a recording you like!
The notes are generally played as a set of un-measured grace notes (except that the total time should fit the measure pretty well.)
Grace notes in general can be recognized by the smaller print.
