While I will not get into the merits (or demerits, as it were) of Whitacre’s compositions, he employs dissonance that is readily accepted by Western culture. Non Pythagorean chords do not create the same effect at all. Think about it this way: what makes a tritone more dissonant than a major 7th?

There are two causes:

First: Overtones/harmonics are structured in such a way that some notes are more closely related to the fundamental than others. For example, a perfect fifth can be found in the second harmonic, so it’s practically the same note. A major 7th above the fundamental is more closely related in the overtones than a tritone is. The same goes for these new scale tones, because they do not exist in the early harmonics.

Second: A tritone is more dissonant because two notes must move to resolve. In these new chords, a simple half step in one direction will not create consonance.

To sum it up, lay off Jimmy. Dude knows what he likes.

Other scales are not Pythagorean and sound much better, like Gamelan music.

I’ll stick to ratio-driven intervals.