My favorite exercise in my book is called Attacks\Long Tones. The attacks part of this exercise works on this very subject: Hitting the right note the first time.
We take a note in a given register, the higher registers for more advanced students. The first phase starts on F#, first space. (Later phases start on the C# above, and then eventually the F# on top of the staff.) Play that note with a breath attack, VERY SOFTLY. Play one short note only, and remove the mouthpiece. Replace the mouthpiece and do it again. Repeat the above procedure at least three times, removing the mouthpiece each time. Finally, play the note, sustain it, and bend the pitch down a half-step and back, with your air, not your valves. Concentrate on the quality of attack, trying to give the note a definate start without a sound of air preceeding the tone. This is tough, especially at a soft level.
Now repeat the whole exercise, the individual attacks and then the sustained note with the pitch bend, but do them with a light tongued attack. Maintain the very soft volume. The tongued note should have exactly the same breath exhalation as the breath attacks. We add the tongue to the breath attack, we don't replace it. Arnold Jacobs describes this approach as a 'tHOO' attack. This doesn't mean TH as in THE, but that the sound is started and maintained from the lungs, whether tongued or not.
Finally, re-attack the note once more softly, and extend it into a sustained long tone, with crescendo and decrescendo.
All of the above is repeated on seven different starting notes, moving upwards chromatically from the first one. This coordinates nicely and can be combined with a flexibility exercise in each of seven keys/valve combinations.
The most crucial aspect of this exercise is the soft volume level. Half as loud is twice as hard. If you master soft attacks, your confidence level on louder attacks will soar. Also very important is the removal of the mouthpiece between attacks. Even a 'kacked' note starts the lips vibrating and makes the re-attack much easier. We want to learn to start the note without the initial kack or exploration.
I use visualization with this exercise, picturing a conductor's downbeat to bring in a very soft, exposed trumpet solo that begins with the note I am playing. I try to conjure up the most terrifying scenario possible, and focus on the delivery of the breath and the tone of the note to follow, not on the attack itself.
Done properly, this exercise does wonders for your attacks, confidence, and lip response. It provides a real work-out for the mouth corners, without pounding the lips. When I finish, I need a rest, but my lips will feel great upon returning. On paper it doesn't look like much, but I consider it my single most valuable exercise. It shows that a G on top of the staff, played pianissimo after 174 bars rest, is much more difficult than the G an octave above at the end of a big band shout chorus.
This is a humbling exercise which separates the women from the girls. But a little humility is good for a person. Perhaps especially so for trumpet players.
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