This is a very intriguing topic for me. Because like everything else, interpretation has levels of insight, perception and process. And these depend on the depth and power of the connection of the interpreter. Are there wrong interpretations of books, poems, music and everyday conversations with others? Most would say yes. But I would say, as another way of looking at it, it is a matter of the consciousness and angle of incidence of the interpreter into the subject matter that would determine how close to the truth the actual interpretation is. Having said that, that does mean that certain interpretations can be very far away from where the actual point or core of the truth is? In fact, it could be so far away, that it is totally disconnected to what the piece of music, poetry, movie, or anything else is about, that it creates it's own separate little reality.
How about when someone says, "that is a very dry interpretation." Someone else might 'warm' to that 'dry' version of that piece of music. Others might feel it lacks emotional content. There might be a group of people that would say it was 'appropriate' in the context of the music. Here is a big question, IS IT ALL IN THE EYES OF THE BEHOLDER? And this begs the question and further enquiry into what is IN the beholder?
There are people who are considered great experts or authorities in a particular field. A Bach expert or an authority on the music of Mahler. Is knowing something about a piece of music or a work of art important before playing it or listening to it? What happens to you before you know about a piece and you play it or hear it? How does, if it does, change or alter your feeling and interpretation of the piece after you know something about it? I have found that knowing something about a piece then playing it, can make a profound difference in the way I approach it.
Here are some crucial things to consider: When you interpret, WHAT is interpreting? Your academic references? Your emotions? Your 'practical' mind or your 'abstract' mind? Your former or current teachers' concepts? Your instincts? Is there bias? Your likes and dislikes? This is a big subject and is not complicated for the sake of complication. IT IS WHAT IT IS.
In my looking at this, I see an amazing opportunity for deeper personal growth. It is best to be simple with it perhaps in a childlike way. How does it make you feel? How does your body feel when you hear the piece? Does it bring up thoughts of a certain kind? Do you feel energized or drained of energy? There is a good one to look at!
Musicians often say they want to be true to the composers wishes. Do they know what those REALLY are? That is the quest. And this is where letting yourself be free for a while to go on some journeys, some mystery dreaming and let your thoughts soar. This will thicken your interpretation. It will make it richer and more vivid because you will be playing with more connections.
The actual written music, depending on what you connect to when you are playing it or thinking about it, is a URL to the site in the life of the composer and to the Universal Web of what he or she was ACTUALLY CONNECTED TO, WHETHER THEY KNEW IT OR NOT. This is of course, one of those things that I would say is science fiction until you can prove it to yourself as fact. I have NO DOUBT about it's reality through my own experience and process of many, many years.
In the very end, maybe it is the process and journey of what happens to us that is more important and vital to our lives than what would seem to be a 'correct' interpretation. It's in the process that we evolve.