Okay, I think I understand what you're after, and I think it's worth looking at, but a couple things to consider. I think the frequency splits would have to be managed as picking a specific frequency would give you different things for different notes, no?
If you set your split at 1000 hz, and split the lo pass left and the hi pass right. You sing C5 @ 523.25 hz, and then sing C6 at 1046.5, the effect on the harmonics and overtones (that Mike pointed out) would be completely different unless you picked a different split point for each note. Otherwise the effect would in effect walk across the stereo field from left to right dependent as the scale increased...which could be cool in and of itself.
If, however, you split at the note center for each note or some interval (OH GOD THE MATHS) up or down, the effect would be uniform.