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I was wondering if any of you could help me with an issue I'm having. I have been using pitch-class sums to represent how dark or light a scale feels. So for example, C major, when you add all of its values together from pitch-class space, would have a sum of 38. C Phrygian, on the other hand, would have a sum of 34. Now I thought this might be because the smaller intervallic distances, when related to the root of the scale, would be causing the sum to be lower in the case of C Phrygian, therefore the scale would be shown to be darker. But the whole process seems rather dubious to me.
So I tried other ways of representing a scale's darkness or lightness by mapping them onto the circle of fifths. C major had most of its intervals on the 'brighter' fifths side whereas C Phrygian had most of its intervals mapped on the 'darker' fourths side. But again it doesn't feel like a strong way to represent it academically.
I think I was going to try a third way of cross-referencing with the harmonic series. The method here was to take a 12-tet approximated harmonic series (sorry JI fans) and make the assumption that intervals that find themselves further away from a fundamental of C have a weaker pull to said fundamental thus making it more dissonant/ dark. For example, the interval b9 would be the 9th interval to appear in this 12-tet approximated harmonic series, whereas a natural 2 would be the 5th interval to appear making it more consonant than the aforementioned b9. This would also make C Phrygian darker than C major as many of its intervals would be further away from the C fundamental than the intervals in the C major scale. But again I'm unsure of this method, mainly because it uses an approximated harmonic series.
So basically what I'm asking is, is there a way you can represent consonance and dissonance/ brightness and darkness in an objective and quantifiable way?
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