It occurred to me that musical interpretation is much like meaningful speech. We can read a sentence in a monotone, so that its sense is obscured, or we can read it with the correct intonation, making it sound right, ie meaningful. An example is, "Fruit flies like a banana." We can read this to make the word "flies" sound like a verb or a noun, changing the meaning completely. When we read aloud we choose which words to emphasise, how fast to read them and when to pause. We raise the inflection when reading a question. These differences are readily apparent when I read Italian aloud. If I do not understand the meaning of the Italian sentence then I will read it incorrectly. If I read a sentence of Icelandic then even if I pronounce the letters correctly (cf play the correct notes), I will be reading it without comprehension, so that it will sound wrong to someone who speaks Icelandic.
The pianist does something similar when they play the notes of a piece, ie they vary the way they play in accordance with their personal understanding of and feeling for the piece. The score cannot say exactly how fast to play, how long to pause nor how hard to hit the keys.
How you say something can be more important than the actual words, eg the tone of voice can indicate that your are joking, or that you intend the opposite of the literal meaning. Similarly, in music the way you play the notes might be more important than the notes themselves.
An actor has to invest their lines with feeling, and so does the musician. The script of a play is like the score of a piece of music. Both have to be brought to life by the performer.