Does light have timbre? Timbre is a property associated with the shape of a sound wave, that is, the coefficients of the discrete Fourier transform of the corresponding signal. This is why a violin and a piano can each play the same note at the same frequency yet sound completely different. Now for light: if you mix red and blue light, the resulting wave has on average the same frequency as green, but a different shape. Is this why we observe it as magenta instead of green? So can we say light has timbre?
But other colours mixtures don't work! Red+green is yellow, but yellow is a pure colour, so apparently red+green has no unique timbre in this case; the shape of the red+green wave is identical to a pure yellow wave.
 A: Light is almost always considered to be mathematically described by a simple clean sine wave.  If you mix red and blue light, "exactly" 2x different in frequency, unless you do something clever and special, they'll never be exactly 2x but randomly shifting in phase over time.  It would be like two flutes playing notes one octave apart, which might sound sort of like a fundamental and its lowest harmonic, but that's not what your really wanting to get at, is it?
But we can do something clever and special.  There are nonlinear optical materials.  Putting a pure laser beam through one will result in a modified beam with a bit of 2x or 3x the frequency. Put pure red in, get red with a little bit of blue added, and they're steady  in relative phase.  
Physicists and optics engineers have gotten good at applying nonlinear optics.  Frequency multipliers allow the making of high quality coherent light in higher frequencies than can be made with just lasers.   
At the National Ignition Facility (NIF) at LLNL, physicists are trying to make hydrogen fusion practical (or for now, just to get it to happen at all). To get megajoules of laser light at their favorite wavelength, the optical system uses big violet crystals as frequency doublers.  Paper about those crystals: https://e-reports-ext.llnl.gov/pdf/236677.pdf   Doublers and Triplers (and quadruplers) have many more uses in lower energy experiments.
Somewhat related to the idea of harmonics - having equally spaced frequencies with fixed phase relations - is light (usually infrared or THz range) made in frequency combs.  The spacing is less than the fundamental frequency, and may be quite small.  See http://www.laserfocusworld.com/articles/print/volume-48/issue-01/features/frequency-combs-make-their-way-to-the-masses.html for an explanation with colorful illustrations.  
A: Your visual range includes roughly one octave as compared to roughly twelve in your aural range. Further your visual system uses only four types of light sensors
each with limited frequency discrimination, while your hearing has fine frequency discrimination.
So while light spectra could have harmonic structure your visual apparatus is ill equipped to detect it.
