The other thing you should consider is if it looks good to the human eye. Sure you can just run red and blue led but your tank would look like a rave.
BBA is horrendous though. The other algae are pretty easy to control.
I'm trying to grow green water in a liter bottle outside. I put in pond water and all I have so far is a small amount of dust algae. I'm trying to figure out what nutrients triggers these diatoms. I just put in a pinch of micronutrients to see if this is the trigger. If not, next would be the macronutrients.
You should look at diatoms under the microscope. They're beautiful.