Color to spectrum,
CC: BY-NC-ND Lukas Blersch 25-oktober-2013

This document should be viewed in the sense that it's A: subjective, and B: hypothetical. Nonetheless to my somewhat deviant perception it yields interesting results.

This theory is based on a sinewave and a "spectral synesthetic" perception on generating color by adding harmonics.

To achieve this, this article describes an oscillator. Note two models are possible this is the harmonic oscillator model. Also there's a phase shift model. Which will not be documented in this text. But it's very similar to a "redshift", and has been put to practical use in sound in general.



We have wave A: also known as a sawtooth wave showing all the even harmonics on the positive side in the typical manner. And we have wave B: Also a sawtooth wave where all the harmonics are laid out in an alternating pattern. If we add A to B we get wave C, "a square wave" or odd harmonic spectrum. If we subtract A from B we get wave D a wave that is again a sawtooth, but with slightly different properties. And evades scientific notation. (other than an inverted sawtooth wave at a higher frequency).

Now how would this relate to "color as a spectrum"? Again, I start off by saying it is to my perception, that it's arranged like this. C and D, have both been divided by 2 to normalize the amplitude after summing, and all the sub steps are subject to normalization as well.

A= Red
over orange
A+C=Yellow
over green
C=Blue
over indigo/pinkish
D= violet

Now there are some odd ends, and those are the niche shades like matte orange, lime green, and also purple. Although the former two are in there a light orange can be made by subtracting the fundamental frequency from red, similarly a much more defined green can be made by subtracting the fundamental frequency from blue. Alternatively a much more defined purple can be made by adding the fundamental to pink. To define the altered model we will introduce the fundamental frequency E. Although it boggles my mind it sort of has- has no need to be in there, merely has every right to be. The latter model has a much better tone of purple, But it does tend to show a conflict in the division of energy.

So..The latter model would be equally appropriate.

A=Red
A-E=Orange    | A+A+C
A+C=Yellow
C-E=green   | A+C+C
C=Blue
C+(D±E)=Indigo
C±E=purple
C=Pink

Lighter and darker shades can be made by adding harmonic content, the more harmonics the more defined/satturated the color. The more energy gets over the ideal slope ("Niquist", and bouncing back as odd harmonics) the lighter/whiter the color. So arguably the color white has all the harmonics equally loud thus being an impulse. Or in the practical case white noise.