This entire thread is about definitions, and the constraints placed on those definitions.
And I think that is what is causing some problems. Because of past definitions, some cannot tie to a general definition. I have been using a general definition of uniformly spaced phases. You have given examples of a general definition covering non-uniformly spaced phases. I don't think either of us have a problem when these definitions cross each other. Others just can't seem to make the connection. Perhaps some time spent in the audio world would broaden their minds.
The 90-degree system originally labeled as 2-phase was two single phase systems with a distinct relationship. This system could also be considered part of a 4-phase system. Some of those having problems broadening their mind could probably walk the path from the historic 2-phase system to a 4-phase system (and would almost be forced to).
But at what point do you take the 4-phase system with four 90-degree relationships and turn them into two 180 degree relationships and call it 2-phase? It appears that is what some say you have to do by saying that even-numbered systems can't exist.
I like your example of walking the degree circle that illustrates that at some point you might run into your definition.
I guess if we in the U.S. electric world generally deem 2-phase as having a 90-degree phase displacement, the rest of the electric world, audio world, circuit world, and other disciplines need to fall in line. :roll:
I'm all for using standard terminology, but we should not lose sight of the bigger picture. Many want to use a historic label as an all-encompassing definition. Most definitions are not that absolute.