I've recently been thinking more about the importance of proper breathing and abdominal support when playing sax. One thing I've observed is that no matter how much you develop your voicing, if you don't have proper air support than voicing doesn't have as big of an effect. One extreme version of this view was given by Lenny Pickett recently in a Vandoren article. Pickett denied that voicing (tongue position) plays a significant role in playing altissimo, which frankly, is mistaken according to a study by Lawrence University (the site includes video of what players' tongues and other oral-cavity-shaping muscles are doing when playing altissimo, multiphonics, etc.). Pickett's position is understandable considering many saxophonists are generally unaware of the muscle movements that shape voicing, and that is likely one of the factors contributing to the long practice hours it takes on average to hone saxophone voicing. However, what Pickett offers instead provides some awesome insight into saxophone playing.
Pickett talks about how he understands breath support or "control" to be the most important factor in producing altissimo, and I can't disagree with him there. I find breath support to be the most important factor in playing the saxophone in any register, particularly in the more difficult to execute registers (e.i. low and high). If my breath support is weak and anemic, I can still squeeze out some altissimo notes, but they sound pretty terrible, I don't have as much control, and I can't play as high.
So, what's going on here? According to basic saxophone acoustics, in order for a player to attain the next higher harmonic, so either a higher overtone or an altissimo partial on a given fingering, the pressure in their oral cavity has to overcome the pressure in the mouthpiece. It's a fairly simple equation that feels much more complicated to execute than to talk about. That means that every tactic that increases pressure in your oral cavity plays a role in producing altissimo. In terms of voicing, your tongue is used to decrease space in your oral cavity and act as a baffle, increasing the air speed, and other muscles help with these acrobatics too. Meanwhile, breath support provides the underlying pressure that your voicing then increases. When you breathe in properly, filling the lower part of your lungs and expanding your diaphragm, you create a pressurized system that your abdominal muscles can now push up against and increase the pressure further. Trying to play the saxophone in any register without this support is tone and technique suicide.
This means that breathing in well is the first step. There are lots of different ways that people promote proper breathing. Common tips include not letting your shoulders rise or make sure your belly expands. Those may be signs that you're breathing well, but they are not proof. What's the proof? When you breath in you should feel pressure build up in your lower abdominal area. That's it.
When you're sitting down, the building pressure is very easy to feel. When you breath in deeply, you feel the diaphragm pushing down against your abdominal muscles and the pressure quickly builds as you're breathing in. If you feel the pressure build up, you're doing it correctly. If you don't... you get the idea.
Another helpful tip, though not directly related to breath support, is to breathe without taking your bottom lip off of the reed. This helps keep your embouchure position and formation consistent.
Support: Blowing Out
The act of engaging your abdominal muscles to blow out is a somewhat subtle technique that needs to be developed. Sorry for the frankness, but it's similar to bearing down to use the bathroom (and that's why you can't play saxophone as well when you need to use the restroom!). Pickett suggests working on long tones at various dynamics to help strengthen your abdominal muscles. Playing softly with a good tone certainly requires really good air support. Another good exercise is to play low notes, starting them with only air attacks (no tongue).
One of my favorite exercise for strengthening and engaging abdominal muscles consists of strongly pulsing your abdominal muscles while playing long tones. I described this exercise in detail in an earlier post.
I hope you've come away with an understanding of how diaphragmatic breathing is foundational to saxophone playing (any wind instrument really) and particularly important for the altissimo register. Honestly, no matter how many chops you've already got together, you're playing will benefit by improving your breathing and air support technique. Sometimes more advanced players think they've already worked on breathing and don't need to worry about it, but until you can play altissimo like Lenny Pickett (or Chris Potter, Mark Turner, Ben Wendel, etc.), you've got some work to do.