Basically, ‘white LEDs’ are not really white at all, and those CFL’s come in various ‘flavors’.

Imagine a device where you could compare an LED with the room lighting,

or with sunlight. Where you can put a specific Pantone color swatch into a slot,

and see how it looks different under different lighting. This Comparative Colorimeter

is  what Josef Albers would use if he taught his class on color in the present ‘age of solid state lighting’.

wiki entry for Josef Albers, color theorist

LED color controlled by Arduino, shown here under test with an arcylic light pipe.

Looking into the color comparison light box, showing the nearly white, and purple off-white of two LED arrays.