I was wondering, is there a color representation of music? If someone ever tried to represent frequencies with colors could the whole music piece be represented by color somehow?
What do Beethoven's pieces look like if represented as color diagrams or images?
I know this may sound silly but maybe someone thought about it and did eventually try.
Check out the wiki article on the Scriabin Colour Organ - the very earliest precursor of coloured lighting accompanying a performance.
What you're looking for is probably music visualization.
Talking about color representation of music may be a bit basic. There are too many combinations and it depens on how you create the relation note/color. There isn't a unique way for sure.
There is a video with a very simple example:
For more complex visualizations of music I would look at the work of Stephen Malinowski http://stephenmalinowski.com/ He is a composer and programmer who created software to generate animations based on music.
But even before this, much before computer animation, at the beginning of the 20th century (1920) there were already people thinking on how music would look like, creating animations to visulize both color, fades, movement and form. You should definitely look at the seminal work of Oskar Fischinger https://en.wikipedia.org/wiki/Oskar_Fischinger
I used to use a couple of beginner piano books for kids called 'Through the Rainbow', I seem to remember. Each of the white piano keys was represented by a colour from the rainbow. Are you thinking more along the synaesthesia lines?
