"In your opinion, which embouchure will help a player reach double high C fast assuming a player has no embouchure, air support and pressure
problems?"

I studied and played 4 embouchures. I've had students ask that question during a lesson. I then play a double c on each embouchure.

They all have a different approach to get there. And there is some specialization.

But if you are looking for an embouchure just to play a note then I'm the wrong one to ask.

Carlton will say the Maggio, Jerry will say Superchops, .......

The truth is that no embouchure is right for everyone. There are physical differences that help some embouchures and hurt others.

If I have a student looking for a new embouchure I make them work on breathing, support, relaxing and buzzing first. This makes a HUGE difference in their playing.

So far I've not had a student who couldn't improve in each of those areas. (My students are ALL adults. And most have degrees in music.)

After those areas were straightened out it was easier to fit them to the right embouchure for them.

If you try to find an embouchure first then when the breathing.... is corrected the embouchure may not be the most natural for that player. We tend to compensate for what ever problems we encounter. All of those compensations add up to inefficient playing.

There is a best embouchure for each person but not a best embouchure per say.

Information about my trumpet & embouchure books.
http://www.BbTrumpet.com

Best wishes
Clint 'Pops' McLaughlin