spectroscopy - How to define the light "color" from a given spectral distribution?

The following question may be naive and incomplete in some way I don't know. I'm not a specialist on spectroscopy, colours and light curves, color spaces, etc.

Suppose you have a simple power-law function ; $f(\omega, \alpha) = \omega^{\alpha}$, which describes the spectral distribution of light angular frequencies as this :

$$\tag{1} I = \kappa \int_0^{\omega_{\text{max}}} f(\omega, \alpha) \, d\omega,$$ where the exponent $\alpha$ is a given constant (a characteristic of the spectral distribution) and $\omega_{\text{max}}$ is another constant (the maximal value of the angular frequency allowed). $I$ is the total bolometric intensity of light at the detector's location, in watt/m^2 (the detector is a theoretical ideal device). $\kappa$ is just another arbitrary constant.

Then the question is this :

Assuming that $\omega_{\text{max}}$ is an angular frequency (rad/sec) which is in the visible spectrum or above it (i.e. ultra-violet), how can we define the color of the light described by the $\alpha$ index and the maximal value $\omega_{\text{max}}$ ?

By color, I mean something that could be compared in some way with the perception that we would have of that "$\alpha$-light", in the visible spectrum only.

For example, if $\alpha = 0$, the spectral distribution would be "flat" (i.e. uniform). What would be the color of light if $\omega_{\text{max}}$ corresponds to pure violet light, and $0 \le \omega \le \omega_{\text{max}}$ ? I guess white light !

If $\alpha = 2$, then the distribution would favour the violet and blue frequencies over the orange and red frequencies, so the light would look like blueish in some way, isn't ?

I hope the question is clear enough and doesn't bring me to the all messy/complicated problems of human/eye/brain/psychology perception ! I'm looking for something simple and "physical" only, if it exists ! In other words : is there a simple approximate "trick" to define a "color" from $\alpha$ and $\omega_{\text{max}}$ alone ? I'm just looking for some kind of approximation, to give an idea of what color the light might have.