Here's something I think you'll find helpful. I gleaned it from Mark Van Cleave
Efficiency through Resonant Intonation:
What is Resonant Intonation?Intonation is the player's ability to match the pitch of his/her instrument to the pitch of the instruments around them. Resonance refers to the acoustical phenomenon that occurs when the resonant frequency of an object or space (in this case: the volume of air inside the instrument) is stimulated. Resonant Intonation refers to the act of playing in tune with your instruments resonant frequency. Matching the pitch you produce with the pitch that the instrument wants to produce (because of where you have it tuned.) I like to call this the Shower Effect.
Now that you have an Idea about what I'm talking about .....what does this have to do with brass playing? When a player tunes his/her instrument, that's exactly what is being tuned. Just the instrument! Playing in tune is not a given, just because your horn has been tuned properly (A-440). You can play in tune (A-440) with your instrument tuned correctly or incorrectly! You can bend the pitch almost a full half step either direction without touching the tuning slide. Good intonation is a result of learning to hear when you are in tune and when you are not.
The problems arise when your horn is tuned to, let's say, A-436. You now have to bend the pitch sharp in order to match the A-440 tuning of the ensemble. You are in tune with the other players but you are no longer playing in tune with your instrument. Your instrument wants to resonate the A-436, but you force it to produce the A-440 by over tightening the embouchure or whatever. This is not only less efficient physically, but also less efficient from the resonance standpoint of the instrument. You do not get the instrument to work with you as a team. You are now fighting the acoustical properties of the instrument. You have set the instrument═s tuning to resonate at A-436, but you produce A-440. This new pitch (A-440) will not generate as much resonance as A-436 will. Playing this way will not result in the Shower Effect!
You can check the horn's tuning by popping the mouthpiece with your hand. You will notice that you get a pitch. This is the pitch that the horn wants to produce. This is the pitch that should be matched to the ensemble. This is the pitch that (if matched by the player) will produce the most resonance and result in a bigger and easier to produce sound.
So, to sum all of this up: You can tune your instrument, you can tune your ears, and you can tune your ears to your instrument. When you are producing the pitch that your instrument has been tuned for, you gain resonance as well as ease of operation or efficiency. Playing in tune with your instrument is what I'm talking about. You should tune your horn to the ensemble and yourself to the horn