I agree with 2 things that other posters have said.
1. Using white will add sparkle. In fact, this is something I learned from Alex Anderson in her "neutrals" book - she showed an example of 2 quilts, one with white and one without. The one with white sparkled and the one without white looked muddy and dreary. However, having said that, it's sort of difficult to tell how well it works in your quilt, because your picture is somewhat blurry, I can't see the whole quilt, and the lighting you used may be affecting my perception.
2. I, too, am somewhat confused by what looks like 2 completely different quilts; triangles on top and squares on the bottom. However, as I said before, I can't see the whole quilt, and the finished quilt in your head may be absolutely wonderful.
I think you should go with what YOU determine YOU like best.
