That is not how I understand it.

The “short” version of my understanding:

“Centered sound” is all about sound quality – basically the amount of overtones you produce, the “richness” of your tone.

The pitch is only about the base frequency of the (hopefully resonant sounding) note you are playing. If you are sounding too sharp or too flat, you have basically two options to correct this:

1- adjust the tuning slide of your instrument.
2- lip the note up/down as needed – at the risk of loosing sound quality if you have to overdo it.

I’m afraid I cant give you a dictionary like answer or set of definitions.

I think it’s also in one of Greg’s many videos: go listen to as much live performances as you can (if conditions permit these days). Don’t forget to have fun and enjoy the performance – but also really listen. What aspects of the sound do you like, what aspects can you find back in your own playing …

As I see it, we all develop our own understanding of what a “good sound” is. It is also very personal and also depending on the kind of music your’re playing. A lead trumpet in a bigband sounds very different from the trumpets in a symphonic orchestra. The keyword here is “different”, it is not as in better or worse.

Probably raising yet more questions than giving answers …

Great question, I think there are many aspects to a centered sound or a great, resonant sound.

If I recall correctly, I believe Greg describes in one of the videos that resonance is the optimum balance of Air and Shape / optimum efficiency–it’s when things feel and sound the best. Since it’s the optimum efficiency, it’s when playing is the easiest. I like this concept–that the most efficient is the best sounding; I believe that makes logical sense.

I don’t know about you, but I don’t get that sound everyday…I have good days, bad days and ok days…

Lately, it has occurred to me that I’ve stopped aiming for resonance–having the best sound / feeling, optimum efficiency…I’ve been more “results oriented” lately. Things have been going relatively good, so I kind of have been getting away with that… But, at the end of the day, we’re playing a musical instrument–that’s what it’s all about (music), not high notes, etc.