Bear Woodson wrote:
How LOW can I write Half-Step and Whole- Step Trills, and get CLEAR,
FAST Trills in good intonation?

For half-step trills: As low as you want, as long as the fingering for the trill involves nothing more than wiggling the second finger. That means the following trills in the 2 octaves below middle C are less desirable: Bb-Cb, G-Ab, F-Gb, C-Db.

For whole-step trills, I'd stick with the same principle and use the ones where you can wiggle the first finger. 1-0, 12-2, 13-3 (on F and Bb horns).

Greg

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