I was running a "clever alchemist" Greatsword on front bar, and sword and shield on back bar.
All the set's items apart from the shield were of gold(legendary) quality.

By hovering over the items with my mouse cursor, I observed that the four piece bonus number on my front bar lied somewhere in the middle of purple and gold numbers. Removing the purple shield from back bar made them show the real gold numbers.

Made the shield gold, and now things are all good.

So I was wondering:
How can items(or perhaps even skills) on your second bar effect your first bar?
How is the quality bonus even calculated?
And should I gold my second set(sword singer) when I don't possess the gold jewelry associated with that set?

Thanks