Overtone (harmonics) studies were a big part of my teacher's regimen and I started on them when I was 12. But overtones really became ingrained when I changed my embouchure in my young 20's.
So it should be no surprise that I jumped into a discussion on the On Line Trombone Journal (OTJ Forum) with what I know about the subject. There are some very learned educators and monster players (sometimes one in the same). So to bolster my side of the discussion I made this video.
The goal is to play throughout the range of the instrument with out having to use any appreciable movement (from either tilting the horn up and down or sliding the mouthpiece higher or lower) or opening or closing the jaw.
This is an example of playing up and down the overtones, one breath, from low Bb to the altissimo F. The horn is a 9 year old Bach 36 and the mouthpiece is a 30 year old 6 1/2 AL.