Is mean squared error or absolute error on two spectrograms of two different wav files enough to compare how similar they are?
My suggestion would be to partition the spectrum according to the well tempered scale, one frequency band for each half tone. You generate a pattern of 1s and 0s for each chord you want to be able to test, with a maximum of six 1s. 
When a chord is played, just do a FFT of the whole thing, normalize the energy and check each band for a threshold.
Your "fitness" value then could be directly calculated from the correct strings vs. wrong strings in some way.