Sorry, thought I was clear. The premise that the physical location of the voltage reference must also coincide with the physical location of the other voltage is the fundamental fault. That is not the case and anyone who has ever made a phasor diagram should know this. It might also be worth mentioning, as I have in the past, that a phasor diagram and circuit diagram are not the same thing either so you should see the disconnect between the physical layout and the related physical angles vs the voltage phasors with the related phasor angles.
See here:
Photobucket is blocked here so no picture.
Okay, those statements are clear. However... The reference frame I suggested is not a voltage reference, nor a phasor diagram, nor a circuit diagram. It's a phase reference frame. And the frame was chosen for two specific reasons: 1) It minimizes measurement errors ; 2) It's inclusive.
Without seeing it, I suspect you have an application specific phasor diagram. It'll happily work for all your intended purposes. An issue I thought we had previously resolved. If all you care about is your intended purpose then what you have is more than enough. All the results will be usable.
But the bottom line of what we are really looking at (as opposed to how we can manipulate it) is that we have a 240Vac Single-phase voltage divided circuit with a mid-point reference. So it's called single-phase because that's what it is.
The typical argument in this thread has been: Because I can hook up like this, see it like this, use it like this, mathematically describe it like this, then it isn't anything else but this.
Except, yes it is something else. Something else with properties that allow you to do what you want to do. To the best of my knowledge, barring a few typographical errors, I don't know of anyone that has made any false postings.
It can be displayed on an oscilloscope in numerous different ways. Just because we ground the neutral, which makes it the most logical and convenient place to reference, doesn't make that the definitive reference. All the other reference points are just as valid. All the other reference points show graphs that are just as real, just as accurate, just as correct. And most of those graphs show sections of the secondary coil to have <0 or <180 depending on whether your hot probe is left or right of the reference probe. A fact that ought to intuitively tell you that the direction you place your probe matters to the display and not the circuit. And yet...