Yes

Just kidding 😁. I believe it’s both. Not much tongue arch is needed for smaller intervals, but more helpful with larger intervals, IMHO/experience, etc.

I had the same issue! I did not want to do harmonic slur practice because I didn’t know if I was doing it right.

Stick with the process.

Focus on the feeling of the singing c exercises. As you progress through the course, your slurs will be done with less and less effort. I can’t tell you exactly how to do slurs because that won’t help you. You won’t discover it by knowing exactly what to do; you’ll discover it by reinforcing the feeling of correct playing. When that feeling bleeds into your playing, your slurs will be effortless.

Keep practicing the WIHSC!

Great answers, thanks guys!

Nevertheless, I think it doesn’t hurt to know what to do exactly to promote good slurring technique and not solely rely on the method that should indirectly improve the slurs. I mean it’s in a way put up side down. Aren’t we doing slurs to improve our playing abilities?

I understand from Greg’s Largo stage material that slurs should only be thought as a result of changing SHAPE. That means we have our ‘Uhhh’ embouchure formation with already activated Aperture Corners and then we should do some work with the Aperture Corners to make the harmonic slur happen.

What I’m not quite sure of is what the action of Aperture Corners should be to result in most efficient slurring and still have enough potential to go high enough in the harmonic series without too much strain.
I see there are 3 possible ways to make the aperture opening smaller (isn’t that our goal here?):

1. Stretching the middle part of the lips outward from the center(No! Not smiling which is no longer considered a valid embouchure technique). I’m talking about stretching the inner middle part within the fixed embouchure.
2. Pursing – working from the mouth corners inward (and forward?).
3. Two above actions combined. That’s what I’ve actually seen being recommended elsewhere on the Brass playing resources and it was described as a commonly accepted method.

However – it’s easier said then done especially when you have to consciously engage a set of different muscles.
Maybe Greg could clarify this ambiguity.

I’m sure Greg can, but the act of harmonic slurs, I believe, is how we refine the movements we need to make based up in our own physiology, equipment, etc.

Experimenting with minute changes in our embouchure, tongue level, etc. (Shape changes), and observing how those changes help our speed or sound while doing harmonic slurs, helps us to learn what, specifically, we need to do to improve.

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.