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.