I remember my dad always practicing long tones growing up, telling me to do them, and telling his other students the same. I know he has found them to be super effective in building endurance and stamina in the embouchure.
I found this “extreme” long tone exercise from Cat Anderson (jazz trumpeter with Duke Ellington) on the website http://brassmusician.com/
Cat Anderson was known for his huge range (5 octaves) and credited his “20 Minute G” Exercise for that fact. See below for the exercise as explained by Jon Gorrie.
“20 Minute G” Exercise
Like a whisper
In his method book from 1973, Cat Anderson instructs the student to play a 2nd line G (concert F) “like a whisper” for 20 minutes. The student is allowed to breathe when necessary, and is also allowed to take the mouthpiece off the lips when doing so.
More than just a high note exercise
Many ‘high-note’ players, including Anderson himself, have claimed that the “20 minute G” is the secret to their upper register. Although practised correctly, this exercise can be much more than an upper register exercise. Played with relaxed breathing and a suitable rest period afterwards, the “20 minute G in a whisper” may aid in overcoming excessive mouthpiece pressure, building endurance, aid control and articulation, and, as Anderson mentions, improve upper register playing.
The thought behind this is that whilst carrying out this one simple exercise, your mind is free to focus on areas of your body where you are holding tension. Where tension is found, it can then be gradually resolved, leading to a more efficient overall physical ‘setup’.
How to get started
To get started with the “20 minute G”, one suggestion is to begin with the “30 second G”, increasing the duration of the exercise over several days to 1 minute, 2 minutes, 5 minutes, 10 minutes, and so on.