I don't know if you still need of that but....
Do you want to know how to get a real-time spectral analsys of sound?
1.implement a queue to take a buffer of audio samples
2.take the product of buffer and a proper window function (tipically , Hamming or Hann) calculated by your program as float array
3.do FFT of yelded array: there are may algortihms out there for every language....find the best one for you, use it and take the square module from each output coefficent ( Real_part^2 + Imaginary_part^2 , if FFT returns you algebrical representation of coefficients)
sum coefficients across your bands: to know what coefficient is associated to a frequency you've just got to know that the k-th coefficient is at (SampFrequency/BufferLength)*k Hz.....so it's easy to find band boundaries
if you need to normalize in [0 , 1] interval, you have to do nothing but divide each of 3 yelded bands value for maximum value between the 3
pop your buffer queue by a Shift value that is Shift <= BufferLength and start again
the number of coefficients coming from FFT alg is equal to BufferLength (this is beacause the Discrete Fourier Transform definition) so, the frequency resolution is better when you select a long buffer, but the program goes slower. The light intensity wont' vary after BufferLength audio frames, buf after Shift audio frames.....and high ratio beetwen BufferLength gives you slowly light changes....so you must select parameters that fits your desires, remembering that you have just to turn on & off some light....make your alg fast and lo-fi!
The last thing to do is discover freqeuncy bands from your mixer's eq knobs....i don't remember if this information was on mixers handbooks