Pops, I have divided my answer to your question into several sections. First I look at the definition of the word embouchure, then I list some important aspects of what defines a good embouchure, then I discuss how to develop a good embouchure and finally I list some very good embouchure methods.

The word "embouchure" - a definition
Let's look in a dictionary:

Em · bou · chure

1. The mouth of a river.
2. Music.
a. The mouthpiece of a woodwind or brass instrument.
b. The manner in which the lips and tongue are applied to such a mouthpiece.

[French, from emboucher, to put or go into the mouth, from Old French : en-, in; see en-1 + bouche, mouth (from Latin bucca, cheek).]
Source: The American Heritage® Dictionary of the English Language

When we talk about embouchure, what we are really referring to is the way that you form your mouth around the mouthpiece of the saxophone.

The embouchure is the "whole system"
Some books and methods describe the embouchure as the way we set our lips to play. This is too narrow a definition. To me the "embouchure" is the whole system that makes playing possible. Not only the lip setting, but the teeth aperture, the oral cavity, the mouthpiece rim, the throat, all the facial muscles that are in use when playing. People have very different physical makeup, some have big lips, some have small, etc. Every person has his / her own unique embouchure. This whole embouchure system is indeed very complex.

Embouchure and "settings"
Some have classified embouchures after players:

• The Farkas embouchure,
• The Stevens/Costello embouchure,
• The Superchops or Callet embochure,
• The Maggio embouchure

The brass embouchure and our vocal chords
The action that takes place between a brass mouthpiece and the lips when a sound is produced can be compared to the action of the vocal chords when we talk or sing. We are all born with vocal chords, but the "brass chords" (embouchure) are artificial or "man made". Few people, if any, can pick up a trumpet and play with a good embouchure. Some few lucky ones, the "naturals" can play with good sound from a very early time. Maybe they have an intuitive ability to transform the lips to "vocal chords" - they are able to use their musicality to "sing" on the instrument. But the majority of brass players, especially those who choose trumpet and horn, struggle to find a good embouchure. Some lack range, others both range and endurance. A lot of players have a bad sound.

What defines a good embouchure?

1. good tone (or sound)
2. good endurance
3. good range

1. The muscles around our lips are those, which bring our lips to an extreme pucker, such as would be used to whistle.
2. The cheek muscles group, are those which bring our lips to a smile.

When the "sweet spot" (optimal placement) is found, the beginner can start to develop his playing. The main goal now is to find the balance between air & vibration.

The vocal approach
Some people with embouchure problems try to analyze what the muscles do. Knowledge about anatomy is good - but to think about oris orbicularis and the buccinators etc. when developing the embouchure is to ask for trouble. It leads you into "paralysis by analysis".

Like a good singer, we must focus on sound and let that activate our mind and body to "self-correct". The greatest brass teacher in the last century, Arnold Jacobs, called this approach: Song & Wind:

"When we combine Song and Wind, the musical message, song, is the principal element comprising 85 percent of the consciousness. The remaining 15 percent is the application of the breath, wind, to fuel the vibration of the lips."

Here are some books that are very good for developing an efficient embouchure. They all share some common things like breath attacks, long tones with crescendo and decrescendo and lip slurs. They all have simple but powerful exercises with the necessary instruction text:

Carmine Caruso: "Musical Calistenics for Brass"
James Thompson: "Buzzing Basics"
Jeff Smiley: "The Balanced Embouchure"

Thanks to some of Carmine Caruso's long time students, it is now possible to take full advantage of the book "Musical Calistenics for Brass". Trumpet player Charly Raymond and trombone player Sam Burtis have explained how to use the Caruso exercises in an efficient way. Burtis has also written a book, "The American Trombone" where he describes the basic Caruso exercises. Some of this writing can also be found on the Internet at the "Online Trombone Journal". Raymond is the moderator of the "Caruso Forum" on the website "Trumpet Herald".

A crucial point in the Caruso exercises is, as Burtis says, to "listen to the foot" - tapping the foot while mentally subdividing the beat into 16^th notes. About the breath attack Caruso says the following:

The Breath Attack is used in this initial exercise because it is the quickest way to get the lips in focus, to get them touching. Repetition of the Breath Attack brings the lips into the best position. I call this balance; others may call it embouchure.

The essence of an even, sonorous sound is the balance between embouchure tension and air flow.

I developed exercises designed to exaggerate the normal lips range of motion, thereby increasing the lip's ability to form more complex combinations of opposing motions (shapes) which more effectively promote a continuous state of balance within the context of dynamic activity.

In other words, through the repetition of relatively simple exercise targets, the lips become more intelligent, more able to move far enough and morph into more complex shapes to match the task at hand.

Pops, your books and your "cyber teaching" have also been a great help to me.

Good luck with this new project!

Ole