Some embodiments include a model builder system that generates a color model to facilitate a color tunable lamp to mix the right amount of light from various color channels to reproduce a target color characteristic of a reference lamp. The model builder system can perform pre-computations that characterize the perceived characteristic of individual color channels and the reference lamp. The model builder system can divide the color channels of the color tunable lamp into floating channels and non-floating channels. Holding the operating points of the non-floating channels constant, the model builder system inverse solves for the necessary flux values of the color channels to reproduce the target color characteristic and to optimize color metrics.