Andy - regarding your last paragraph on the 3.7 charts. Those charts would indeed FAIL my definitions of both "time coincidence" and "phase coherence". BUT I don't buy the charts. Note they are taken at 50" and on the tweeter axis, both of which meet Stereophile's MO, but are illegitimate for the system under test. At 100" and 35" ear height, those measurements actually yield clean triangles without those false anomalies.
I am really not the guy to try to explain this stuff. It's pretty deep and complicated by real and imagined factors, and my knowledge is real, but not fluent. Here is what I can say: Jim was an engineer's engineer, and an honest mathematician and physicist. He pursued the problems to their root causes and engineered thorough solutions. I have only conversational knowledge of what he knew to his bones. That said, I was in the lab every day for 20 years and helped devise and implement the test set-ups and cross-checks. For frequencies lower than our chamber could reliably measure (100 Hz±) we had a roof system (100'x 500' flat roof) which we correlated with both straight and ground-plane techniques. It is germane that our test system included impulses for step responses at 1/3 octave intervals from 10Hz to 30kHz. Thiel speakers pass those pulses from bottom to top, including through the crossover regions. I don't know of a more stringent test for coherence, and to my knowledge, all speakers from the 03 in 1977 meet that requirement.
I am really not the guy to try to explain this stuff. It's pretty deep and complicated by real and imagined factors, and my knowledge is real, but not fluent. Here is what I can say: Jim was an engineer's engineer, and an honest mathematician and physicist. He pursued the problems to their root causes and engineered thorough solutions. I have only conversational knowledge of what he knew to his bones. That said, I was in the lab every day for 20 years and helped devise and implement the test set-ups and cross-checks. For frequencies lower than our chamber could reliably measure (100 Hz±) we had a roof system (100'x 500' flat roof) which we correlated with both straight and ground-plane techniques. It is germane that our test system included impulses for step responses at 1/3 octave intervals from 10Hz to 30kHz. Thiel speakers pass those pulses from bottom to top, including through the crossover regions. I don't know of a more stringent test for coherence, and to my knowledge, all speakers from the 03 in 1977 meet that requirement.