John – there is lots of sense in what you say. I even came up with some idea after giving harmonic slurs more thought.
If nothing else they could probably serve as a measure of one’s capabilities to navigate the instrument range effortlessly or otherwise.
I now for instance understand that my limited range is not just that but it’s an indication of strained playing in the middle register.
I can do Low C – middle G slur quite easily but only after finding the adjustments needed. That is I have to recreate the feeling each time I play that slur and I’ve been learning to play trumpet for 10 years! My poor slurring technique is a clear indication that I still need to do lots of work for acquiring the feel for these ‘minute changes’ in the shape which define pitch.
Perhaps those who develop on trumpet quickly have a talent for feeling these fine changes (along with a good sense of pitch!) and also have the ability to ingrain that feeling quickly.