Mixing LED color bins to get high CRI?
This
used to be a strategy used by some D.I.Y. hobbyists. The old white LEDs (and still many cheap 70 CRI Chinese LEDs) used a single phosphor formulation. Depending on the degree of doping in the Ce:YAG microcrystalline structure, the phosphor emission could be more orange-shifted or more green-shifted, but the wavelength distribution was still mostly centered around a narrow range of wavelengths.
Most modern white LEDs use a formulation that combines at least two different types of phosphor, for wider coverage across the spectrum and better CRI. The coverage may still not be great, but it is still better than a single phosphor.
So any potential benefit of combining two different color temperatures of LED are much less when the CRI of each initial LED is already over 80.
Most of these white LEDs around 80 CRI do not actually use a green and red phosphor; more like a yellowish green phosphor and an orange phosphor (both Ce:YAG based). While this results in higher lumen output, it is not the most ideal from the standpoint of CRI. Red phosphors generally tend to have very low efficiency, both because the human eye has a lower sensitivity to longer red wavelengths, and because the red-shifted phosphor emits so much of it's energy in the near-infrared. (There are several strategies to get around these problems, but that is a separate discussion). An orange-centered Ce:YAG phosphor still emits a fair amount of longer red wavelengths, so the color rendering is not so terrible.
Mixing LED color bins to get high CRI?
So my question is this: Does mixing 3 different color temperatures of LED's increase the CRI?
The problem with mixing the light from a high color temperature source with that of a lower color temperature source is that the overall combined light ends up a little magenta-tinted. Remember, as we follow the black body curve on a color coordinate graph, the proportion of blue increases faster than the proportion of green.
There is really no point in using more than 2 different color temperatures. Even with an orange-centered phosphor and a green-centered phosphor, there is still going to be a huge amount of overlap in the yellow wavelength range, in fact it will still have more yellowish-green wavelengths than an ideal blackbody emission should have. So there is no point adding a third color temperature with a phosphor emission centered in the middle.
I researched the spectral graphs, and even if you combined a standard 5000K LED and standard 2700K LED, a high CRI LED (~94 cri) would
still provide better coverage across the spectrum, both in the deep red and cyan.
Also, a single-phosphor LED does not use a truly green-centered phosphor unless the color temperature is
extremely high (~10000K), and that would certainly add much more blue light than you want. I bought some special (cheap chinese-made) "cold green" color LEDs, though, which use phosphor as greenish-shifted as Ce:YAG phosphor can go.