The Relationship Between Math, Color & Music
I'm admittedly a bit of a music geek and my ear has been shaped by decades of listening to and playing guitar-based rock. Over the years I've gravitated toward technical and complex musical styles and mostly listen to music that's poly-rhythmic, harmonically complex and interesting to me--which I mostly find in progressive fusion and metal. (See Intervals, Animals As Leaders, Corelia, Scale the Summit, Dream Theater, Protest the Hero, Periphery). I'm sure these qualities also exist in some jazz and classical but I don't know these genres well enough to know who to seek out.
I've always been amazed that music had 'theory' and could be expressed numerically. The relationship between math and music has been studied since the 6th century BC when Pythagoras quantified the arithmetical relationships between pitches. While we can't numerically analyze sound just by hearing it, Pythagoras analyzed a vibrating string and found relationships between the length of strings and pitches with simple ratios relating harmonizing tones. The fact that the pitch of A on a guitar can be measured and found to vibrate consistently at 440 hertz is kind of amazing.
Since then, there have been many mathematicians and scientists who have explored how sound is created, measuring pitches based on frequency and harmonics and a great deal more. Point being that our Western 12-tone scale can be accurately represented mathematically and the sounds that are aesthetically pleasing, like the notes that comprise a simple major chord, have a consistent and repeatable relationship up and down the aural spectrum. For example, the intervals between notes that describe a major chord of 1(root)-3-5 work no matter what key or octave you're in. When I was learning music theory for guitar I thought all of this was both strange and a bit magical. It was strange in that there was a numerical representation of what was making my ears happy and magical that it felt like I was learning what felt like a secret code or framework the music was built around. Not that music was less creative per se, but that there were some established themes for the relationships of notes, chords and scales. It felt a bit like seeing edge of the Matrix.
I find music is to the ears what color is to the eyes. These days I listen to music while I think hard about colors and I've always felt that there must be a similar mathematical approach to represent colors and the relationships between them akin to what exists for music. Like music, colors can evoke a range of emotions and also communicate sophistication, simplicity, playfulness, danger, etc. Googling, I found some interesting papers about how colors are measured by wavelength and some papers about relating colors to tones. The ROYGBIV of the visible spectrum seems to be the most obvious parallel to our 12-tone scale, but this doesn't relate colors to each other in a way similar to what exists with music. Tawny Tsang and Karen B. Schloss at UC Berkeley conducted this study between music and color which was published a by Yale that's interesting on the topic. Ian Firth created a site dedicated to the topic at musicandcolour.net that's beyond my knowlege of musical theory. But there doesn't seem to be a consensus about color theory to the same formal and established degree as musical theory, or a consistent relationship between color and music.
Would a set of colors like pastels, while they represent a similar chroma, be akin to a key in music or a scale mode like lydian (since pastels have a 'feel')? Might the popular combination of yellow, green and purple represent a major chord? Perhaps exploring how colors relate mathematically we might more easily generate ideas or discover interesting relationships between colors that we might not have tried otherwise. Perhaps this all exists in a Ph.d dissertation somewhere; I'd love to read it and learn more about a scalar and harmonic relationship for color. Until then, I'll just continue to use my artist brain devoid of 'theory'.