Lip trills differ from lip "shakes", both in sound and in the technique of execution. When I speak of a shake, I am referring to that technique that is primarily used in jazz music, a slurred figure in the upper register similar to a trill but usually alternating between notes whose interval is usually greater than a major second - that is, an interval wider than just a single scalewise step. The interval is often a third, and by some trumpeters it is even wider - for example in many of the older recordings of Maynard Ferguson. In my experience with playing shakes, I have a feeling of controlling the pitches primarily with my air, assisted by an up-down jaw motion. I concentrate on using very strong air support, and using considerably more air to go to the upper note.
Lip trills, by contrast, are always stepwise - the alternation between two pitches of a major second. The speed of the lip trill is usually faster than that of the shake and it should sound as smooth as a normal, fingered trill. Because the notes must occur between overtones that are a step apart, the lowest lip trill possible is between E and F-sharp at the top of the staff (fingered 1-2-3).
The feeling I have when playing a lip trill is totally different than when I play a shake. Although I do use good, steady, adequate air support on a trill, the quantity of air is usually much less than that of a shake. The most important thing, I feel, is to have a feeling of focusing very "far forward" - I would say clear out on the front tip of the lip, whereas with the shake I feel that the motion is further back in the oral cavity. Try whistling a high note, then whistle a trill - that little fluttering quiver is approximately the same sensation as a lip trill. You can bully yourself through a shake by using your strength and power (and probably should do so, to get the right style), but a lip trill must be performed with flexibility and finesse. With a shake I feel that my airstream is a fat column of air, but with a trill I feel that it is fast, intense, but small ribbon of air.
Following is an exercise which I wrote for the purpose of working on lip trills. Start with this 1-2-3 fingering and work your way up chromatically after you are comfortable with each successive pitch level. Start at a tempo of about quarter-note = 126 and try to work up to 184 or faster.
Remember to play lightly, with finesse, and to feel yourself focusing your tone "far forward".
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