Where CRI comes into play is with pigments or pigment mixtures that reflect colors that are in the light source's deadbands. For example, a pigment that admits light primarily around 520nm would appear much darker relative to a pigment that admits light around 545nm
Your explanation of the peaks in fluorescence are correct except that the color result is reversed. Pigments absorb light not emit it. The color is the area in the spectrum where the pigment doesn't absorb. -- -- -- "Facts do not cease to exist because they are ignored." - Aldous Huxley
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