Isn't this what you don't want me to do, define the number of phases by counting line-line voltages? And now, when it is convenient you are moving your reference point when you measure your voltages.
What I said was using ONLY line-line voltages was incorrect. Line-neutral voltages can also be phases.
The only difference between a corner grounded open delta load, an open wye load, and a center tapped single winding load, is the angle between the voltages.
The difference has to do with the magnitude and phase angle. Since a phase is a voltage, the number of equal-magnitude voltages with unique phase angles is what determines the number of physical phases. Some systems can supply more than one system of voltages. For example the 3-wire 120/208 wye: a one (1) single-phase 208v system, one (1) 2-phase 120v system, two (2) single-phase 120v systems.
So 3-phase suddenly becomes 2-phase as soon as the angle becomes different than 60??
Now that really is funny. How about: "So 3-wire 2-phase suddenly becomes 1-phase as soon as the angle becomes different than 90??". Given the historic names we use, the conventional name might change, but the physical system still has two phases.
In the delta case, when the angle suddenly becomes different, one of the voltages suddenly no longer has the same magnitude and can't be counted in the system of voltages (remember: equal-magnitude but different phase angles). Physically, that leaves us with two phases (voltages) in the system.
In the common-conductor case, the magnitude stays the same but the angle changes. So that voltage is still is part of the phase count (unless it suddenly matches a different voltage that has already been counted).
If you remove one 'phase conductor' from a 3-wire delta, you only have single phase (1 line-line voltage) even though you still have 2 'phase conductors'.
I agree with that and have said the same. But when counting phases in a system, we are counting voltages as phases, not counting wires.
You claim that 2-phase is a common term in the utility industry, it may very well be among line workers. But it clearly is not common in the rest of the world. I state definitively it is not commonly used by electrical equipment manufacturers except as an adjective.
You have to be able to distinguish between a conventional name and the physical system. The conventional name is derived from the system and may not represent the system's complete physical make-up. That is why some names appear to conflict between different systems. Just using common sense, it should be easy to see that if you have two phases then it is a 2-phase system (with a phase in this context being a voltage, not a piece of wire).
"Used as an adjective" is just your opinion. Because you refuse to see things from a different perspective, when I showed you an example of where it was used differently, you concluded that it must have been "used as an adjective". After that, I clearly showed you where the author meant two phases as in two voltages or emfs. Because of your refusal to be able to see a different perspective, you then concluded that the author must be some non-industry-standard anomaly.
I do not see it commonly used in the IEEE color book series.
Why quote standards as the definitive answer if you only agree with them when they match your own viewpoint?
Utilities like Commonwealth Edison and Xcel Energies do not use it in their service rates books and metering manuals.
We already have conventional names for service drops. What makes you think they would stop using them? The idea is to understand the relationship between the names being used and the physical system.
The NEC only uses it to describe what you derisively call the 'historic' system.
Derisively? You are way off base. Where have I scoffed at this system? My use of the term "historic" for the quarter-phase system was to try to distinguish between the different systems I was discussing.
If you have been reading my posts with that notion, maybe that is why you are not hearing me. Perhaps you would better understand what I am trying to say if you get rid of the idea that I am attempting to make fun of the existing system.
How about you consider that I am trying to to make a serious effort to explain the relationship between the names we use and the physical systems we have and then re-read my posts?
It is a simple fact that the conventional names we use are not completely descriptive of the physical systems we have. That is why the names appear to be in conflict. If you can step back and look at why the names work for what we are doing, you can understand why they are applicable even if they don't always exactly match the physical system.