Finger a note in the lower register, then, without moving any fingers or using the octave key, you should be able to adjust your embouchure and breath support to sound various higher notes, these are called the harmonic (or overtone) series consist of the same notes relative to each basic note (fundamental): You should eventually be able to continue through the harmonic series to get at least eight notes (two octaves):
“ There is a lot of confusion between the terms harmonics and overtones. Very simply, the basic note you start from is called the 1st harmonic or fundamental. The next note (ie one octave higher) is called the 2nd harmonic, but the 1st overtone. The next note (octave and a fifth) is the 3rd harmonic but 2nd overtone.”
You may find that the 3rd note of the series (octave and a fifth above the fundamental) is easier to get than the 2nd note (octave above the fundamental). The following exercise is based on the bottom Bb, but should be tried on all notes of the lower register. As you get higher the harmonics become more difficult. You will probably need to alter your embouchure to get the harmonics to sound, experiment with putting more mouthpiece in your mouth and changing the position of your tongue. Try to imagine the note you are trying to play so that you can hear it in your head.
This takes a long time to master, but is an extremely useful exercise for general tone but also useful for developing altissimo range and alternate fingerings.
This next exercise is a particularly useful one. It can be adapted to have a wider or narrow range. You could instead use just the fundamental and 1st overtone, or you could include more overtones. This is the one I like to warm up on when practising harmonics.