Lip tension, tongue arch and air speed are great for changing pitch in a particular register. But lip compression is needed inorder to change registers. Jeanne has already pointed out that arching the back of the tongue causes headaches and blackouts. So please remember to use a forward arch.
A combination of 6 things are NEEDED to play trumpet well. Close lip setting (aperture) + mouthpiece pressure (just enough to make a seal) + lip compression + lip tension + tongue arch (forward) & Air (speed and support).
These 6 points control the range of the instrument. There are many variations available in how these can be added together to play any one note.
It is possible to play a double high c with a close setting and compression only. Stevens’ static exercises are played that way. Adding some mpc pressure to that can flesh out the notes yet these can be done with almost no tension.
On the other hand lots of people play high c with an open lip setting lots of lip tension and mouthpiece pressure. With the lips pinned open there is no compression. This is tiring because of muscle fatigue from the tension and impaired bloodflow through the lips caused by mouthpiece pressure.
Inorder to move from the open setting to a closed setting the player has to learn to relax the tension and back off on the mouthpiece pressure. Compression works far better than tension so both range and endurance improve.
Now to obtain a big full sound you need a balance of lip setting, compression, tension, mpc pressure, tongue arch and air usage. This balance changes by register. For example the low register needs more air mass to fill the bigger aperture but less air speed or pressure. The lips require little tension or compression. I have found that people can put the close setting to real use quicker by learning to relax the chops.
Trust me we all put some tension back in as we ascend. I have to constantly remind people (in the upper register) to relax some and take the workload off of the lips.
There is natural muscle tone (tension), there is loose and flabby, and there are stages of tightness (tension). You have certain levels or amounts of tension that you rely on for each register. (Some change tension every note, others by the difference in the harmonic series and still others by octaves.)
The dependence on tension, where and how much you change is based on how you use the other playing factors. Lip compression (lip against lip not facial or corner tension), lip setting (how close they are before the airstream starts), mouthpiece pressure (this can easily seal off the aperture an open setting needs 5 X as much as a close setting). Added to this is the way you use your air. In my case because of a close lip setting I use the normal resting facial tension on the entire 1st set of notes in the harmonic series (Low F# to low C). The next set (low C# to second line G) uses a little tension but far less than open aperture players do on low F#. In fact the 3rd set (second line G# to middle C) uses less tension than lots of people start with on Low F#.
Tension is tiring. It also adds stiffness to the lips and prevents a free vibration. Added stiffness is how tension helps to play higher notes but it restricts and limits the ease of tone production of the mid and low register.
One way to judge your tension level is to see how much of the face is involved. Under high C it should be completely limited to the lips and corners (1/2 ” away from the lips). I see a great many players who are tense in the cheeks (this robs you of endurance) and neck (this hurts your tone). Over high C I have tension in the area around the lips going out in all directions about 2 inches or so. My cheeks and neck never get tense.
Lip compression is the act of 1 lip pressing against the other. Like pinching the thumb and forefinger together. Inorder to do this with your hand the thumb must be touching the finger (there can be no air space between them), It works the same way with the lips.
There are 5 main ways that this lip compression is obtained.
1. The entire chop setting is drawn toward the center. Corners pulled in and top and bottom lip pulled together. Like the drawstring example in the Farkas book or the making a fist in Jacoby’s book or the diagram in Callet’s book. Three different embouchures that all use the same method of lip compression.
2. Using the muscles of the chin to push the lower lip into the top lip. This creates a knot of muscle at the chin and it moves the center portion of the lower lip.
3. Using the muscles of a frown to compress the lips together. The Roy Roman bulldog face. A frown will pull the top lip down slightly as it pushes the center part of the bottom lip upward.
4. Using the jaw to assist register changes. This is the way Roy Stevens taught. He started with a very open jaw (tooth) position. That way he could bring the lips in toward each other in more compression by moving the jaw upward. (This is fine if you make sure to keep the teeth apart at all times.)
The interesting part is these techniques work with more than 1 embouchure setting. (The lips do have to touch.) I gave examples of 3 different embouchure settings for #1 but that applies for all 4 types of compression above.
5. Is done by use of a pucker. The compression is partially created by the lips in their pucker and partly by the mouthpiece holding them in place. This can only be used in 2 of the 4 main embouchure systems.
Using Lip Compression is described in several books
Stevens (out of print), The Art of Brass Playing,Jakes’ Method, Brass Playing Mechanism and Technic, The Encyclopedia of the Pivot System, Super Chops (only 2 pages of the book), New Approach to Trumpet Playing, Trumpet Isometrics (about 2 pages), Sail the 7 C’s (a page or 2 of text but has good exercises), The Psychology of Cornet and Trumpet Playing,
The No Nonsense Trumpet From A-Z & Trumpet FAQ’s (my books) (They are different from other books in that they are 90% text explanations and 10% exercises.