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Is there a formulaic system to adjust the color of the text on the black background below to compensate for simultaneous contrast and make it be perceived as the same color a the text on the white background?

I'd rather not trust my eyes/monitor and thought maybe there was a standard formula like "reduce saturation by 3% and brightness by 2%" or something like that. Even if there's not a "standard formula" if anyone has any guidelines or tips I'd appreciate it.

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I don't think there is a straight cut answer, because this is a optical illusion (Everyone see's colors a little differently). Depending on what your end medium is I would suggest testing (print it out or test on different monitors/screens - also grab a few friends for their opinions).

Trial and error would be my method starting with 2-3% increments.

Links:

Color in Context

Human Vision and Color Perception

EDIT:

My only other thought, come to me while in the shower is:

You could be to flip it into greyscale, so you see the tonal differences.

Again it is hard to nail anything down to a 100% accuracy because everything is a variable; the medium (print and screen), background color, foreground color, and personally perception on color.

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