"First an admission: I've been lazy. I haven't kept up with the latest tuning developments. Secondly, I'll reveal my ignorance with a "stupid" question. Is there a succinct description of the resultant aural benchmarks of pure 12th tuning?"
Define succinct. 8^)
The following are targets; one tries to get each as close to the target rate as one can while at the same time trying to get each of the other targets as close as possible.
12ths are clean.
Fifths and octaves are tempered the same; a fifth will beat the same as the octave above the upper note of the 5th. That is, C4-G4 = G4-G5.
Fourths are faster than fifths, but beyond that, in the 4th-5th test of the 4:2 octave, the fourth beats twice as fast as the fifth. C4-F4 beats twice that of F4-C5. (This doesn't explicitly answer how much faster to make the 10th over the 3rd, but it is a very clear, if indirect, answer, all the same. Tune the 3rd-10th so that the fourth is twice that of the fifth.)
Fourths and double octaves are tempered the same. C4-F4 = C4-C6. (This answers how to tune the 3rd-17th, so that the fourth and the double-octave beat the same.)
These targets may seem "circular" at first, but there is only one solution to make all of the above true - pure 12th equal temperament.
"You explain that the various ETD makers achieve pure 12th curves in various ways. What about us aural tuning guys?"
There are two aural methods that I know of for tuning pure 12th ET: one is my Every Which Way for Pure 12th ET which is a beat-counting method. And Bernhard himself tunes clean 12ths and tunes a 3rd note in between to make the 5th-octave intervals or the octave-fifth intervals into a clean 3-note chord. It works; I've listened to him do it.
"The piano tuners compromise always started by stating that the initial 4:2 temperament octave had to be widened "slightly", making the 10th slightly faster that the Major 3rd and pushing 5ths purer without making 4th too busy. So for decades we all tried to define what "slightly" meant and the results varied between technicians according to their preferences."
See above. "Slightly" is defined for the compound 3rds by carefully controlling the slow-beating 4ths, 5ths, octaves, 12ths, and double-octaves.
"Does pure 12 take care of this "slightly" question? By striving for pure 12th will we automatically get the stretch "right?" No more guessing about how much stretch is enough. I imagine there are wide double octave."
Yes to all these.
"Does pure 12 stretch get extreme enough in the top octave to allow for pure triple octaves without unduly wide single octaves?"
The answer here is counter-intuituve. But stay with me. In the math model of pure 12th ET, the octave is tempered 1.23 cents wide, the double-octave is 2.47 cents wide, and the triple octave is 3.70 cents wide. But because of increasing inharmonicity when ascending the partial series of the lower note, the triple octave comes out tempered wide, but less than the 3.70 cents. Octaves, double-octaves, and triple-octaves, then can all come out close to clean. (Preferences in the top octave are still hopelessly personal; some add a bit of extra stretch, even in pure 12th ET. That's OK.)
"In a related question, why was Stopper so secretive and proprietary initially about his work? Is his "philosophy" readily available for all to study and apply now? Was he the one who really created the interest in pure 12 tuning?"
Yes, I learned of pure 12th ET directly from Bernhard. And by the way, Bernhard has embraced the fact that the ETD's are adopting pure 12th ET. Adoption of pure 12th ET is good for everyone, and certainly good for Bernhard and his OnlyPure.
"And, from a historical perspective, do you put Virgil Smith's philosophy giving an essentially pure 12th result even though the way he tried to describe it was not the best?"
I revere Virgil, and consider him to be an important part of tuning history.
"Finally, although I don't subscribe to David Pinnegar's tuning preferences, I agree to the extent that the wider we set the initial temperament octaves, the wilder the thirds will be across the middle of the piano. There are those that will say, so what. Customers don't hear thirds. Even professional tuners struggle hearing thirds. Why bother? As David rightly points out, those wide thirds can be obnoxious, especially heard as 10ths and 17ths in the tenor areas. My tendency is to sacrifice a bit of stretch in the middle and make up for it with more stretch in the top octave and a half."
Pure 12th ET is a slightly (there's that word again!) stretched piano tuning that consistently controls the M3rds and protects them from getting wider than necessary. The overall effect of consistent stretch is a coherent, consonant effect. I have heard this over and over!
"Thanks, Kent for all your work and research in all of this. If we've come to a place of agreement on what now constitutes "slightly" then that is a huge step forward in our profession."
I appreciate your interest very much.