Overtones are the natural harmonics that are present in a note. The lower the note, the more overtones it has. Since a bugle doesn’t have any keys, the player produces the different pitches using overtones. The saxophone is able to produce overtones as well. If fact, you can play any bugle tune by fingering a low B or a Bb and using your embouchure to produce the overtone. Overtones are a great way to strengthen your embouchure. I found a You Tube video that talks about strengthening the embouchure that I like from Earspasm. We naturally have a bite, so overtones help develop the muscles on the side of our mouths. We want to have equal pressure all the way around the mouthpiece.
A great book for overtones is Sigurd Rascher’s Top Tones for Saxophone.
Overtones can be challenging to start with. Here is a simple exercise that is easy and can get you started. It starts with the first overtone, the octave.
Start with a D major scale. ( D E F# G A B C# D )
Start with the second octave, with the octave key. Play the first note D and hold it out as long as you can, a couple of seconds after you start, release the octave key but still hold the pitch. Easy right! You have just played the first overtone in the series. Now try the E, then the F# and G etc. going up the scale. Start the note with the octave key then drop it. Remember to hold the notes out as long as you can. You will notice that the first couple of notes are easy, but as you go up the scale, it gets harder. You should also feel the sides of your mouth tire. You are making progress.
Overtone exercises are not fun and they don’t sound that great when you play them, but the rewards that you get from consistent practice of them is worth it. I am convinced that the way to a great tone is with overtone exercises.