The relationship being 1.732 from the phase to phase voltage to the phase to neutral voltage we get:
240/1.732 = 138.56 AKA 139
It's all about the windings. I have no idea of why they would do this.
I don't either.. really. I am working at a small remote site that has a hydro generator producing 3 phase 480. Almost everything except the housing units is on 208Y/120 transformers which seem to work very well. I think the idea behind the 480-240Y/139 transformer was to balance the legs on the hydro a little better while providing 240, but the thing is only 1/10th the KVa's of the hydro so not much help in my opinion. The transformer is a really nice looking stainless steel 30KVa unit. Really pretty to look at but probably would have been better using 3 smaller individual 480-240/120 transformers to balance the hydro. The owner was a little confused when I told him we had to install yet another transformer to get 120 in the building. I figure the best way to go about this is to run the heat and lights off 240 so I can install a smallish 2-3KVa transformer for a couple of outlets. This is just for a storage building with no occupancy, appliances etc. Just heat, lights, and a 240 volt air compressor.
All that said, I don't think I technically have to follow any code since the building is floating and not connected to a utility, however I believe following the NEC is the best way to ensure I don't run into any issues or create a potential safety/liability issue for someone in the future. Can of worms?