Unlike jazz and popular music, classical music is meant to be played exactly as written. Improvisation is rarely used in classical music. The question though is that if classical music is meant to be played as written, do you have to play every single note written.
The answer is yes if you are planning to sit piano exams or if you want to be able to play classical music properly. However, the vast majority of people wanting to learn to play the piano and play specifically classical music, are doing so for their own personal enjoyment and realistically don’t have to play every note.
I realize what I have just said is somewhat controversial because with classical music you are taught that you must play every single note exactly as written. You are not allowed to alter anything. This is certainly the way I was taught and when I am teaching classical music, this is the way I teach.
The reasons for me stating that you can alter classical music to suit you is firstly because older hands are not always as dexterous and nimble as young hands. If playing classical music is what you want to do, then why can’t you alter classical music so your hands can physically play the notes? I think it would be ridiculous for someone to be prevented from adapting a piece of music, simply because their hands are not able to move in a certain way.
Even though the concept of playing classical music is to play every note exactly as written, there are a few times when it has been written on the music that the piano player must improvise. There is also a type of piece called ‘theme and variations’ or ‘air and variations’, where the composer writes a melody and then varies the original theme or melody in each of the variations, which could be perceived as a quasi improvisation.
Lastly and perhaps the most important reason for not playing classical music exactly as written is; why not? Why shouldn’t we tamper with music to suit our needs and our tastes? And if we did tamper with great music – who is going to know anyhow? Besides, music over the decades and centuries has evolved and taken different directions because there has always been musicians that have proverbially thrown away the rule book – the best example of this that comes to mind is that Beethoven decided to do the ‘never been done before’ radical thing of adding a choir and vocal soloists to a symphony, specifically Symphony No. 9, 4th movement, which most of us would recognize today as ‘Ode to Joy’.
To summarize, you must play every note exactly as written in a classical piano exam, but in other circumstances – do what you would like to do.