Here are some exercises that help me a great deal with intonation work.
A note about the vibrato (“vib.”):
A good way to increase embouchure strength is to pitch bend within the partial to find out how far you can ‘stretch’.
Not only does this build strength and control, but allows you to find you maximum pitch control for intonation without relying solely on the right hand or slide adjustment, i.e. you have to adjust on the fly or are playing stopped horn/muted where right hand adjustments aren’t possible and you are sharp/flat in the moment.
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Exercise #1 - simple pitch bends
I personally do these every single day as the first thing I play after breathing and free buzzing (sometimes even before that).
The idea is to connect one note to the next with as little embouchure or air disruption as possible. If one note “bleeds” into the next, then you’re doing it right.
How to do it?
Play the first partial centered before blowing as flat as you can. Don’t merely relax the corners, in fact, keep them supported.
Pretend you’re aiming a water hose down at the ground on the “jet” setting as opposed to turning the water off as the stream dissipates. Keep the air strong.
The more flat your pitch is before the next partial sounds, the better, breathing as necessary.
Exercise #2 Overtone Strengthening
This is an excellent exercise I picked up along the way and adapted into something that works for me.
Much like the exercise above, this one requires air and control. There is no pitch bending between as many of the partials are close together.
The goal is smooth and even triplets, and eventually speed.
Try slurred and repeat articulated.
