It is well known that musical temperament is the basic of music theory, just as colorimetry is the basic of color theory.
Probably more differences than similarities. I like this question and think about the same thing often from a physics perspective.
Our eyes can barely see an octave in color, just look at the frequencies for visible light. The Violet is not even an octave above the red. Yet our eyes have extrodinary resolution in detail.
We can hear about 10 octaves and perceive notes that are an octave apart as being the same in some sense. That is aural patterns repeat every octave. Our pitch discrimination capabilities are not very good compared to visual discrimination.
I could not even imagine how I'd perceive a color one octave above green (for example). Would it be a higher pitch green?
It seems like a fair comparison if you think of light and sound as being waves. But in reality the disciplines of music and visual art are as much about the eye, ear, and mind (or brain function) as they are about waves. Descriptions of color and perception of color are more about the response of the eye and brain than about wave fields. The same is true of descriptions of sound, pitch, timbre. In short I do not think it is a fair comparison since there are so many differences in how we detect and process color as compared to sound.
Colors are not the same as sounds. Sounds are perceived on a continual scale of low to high, with no qualitative shifts. Colors can be measured on a continual scale of frequencies, but they are perceived as shifts of quality to us, because our eyes evolved that way. There is nothing intrinsically "red" or "blue" about light of the corresponding frequencies; the colors we perceive are just arbitrary codes we have built in.