Posture
One thing that helps tons, and tones the core muscles is playing tenor in a position so that I am in perfect posture.
I sustain proper posture on tenor by using a Codera, AND a pair of leather shoes that I have had the heal lowered so that I naturally stand straight with the saxophone. On days (without the tenor) where the muscles are tight, the tendency is to lean forward, the shoes correct the posture. On days where the posture is straight,(without the tenor) the shoes tendency is to pull me backwards slightly.
There is a slight pull back my balance the weight of my Buffet Dynaction (heavy sax) counterbalances. On days where I am leaning forward naturally and play the sax, thus a double pull forward, it still corrects the playing posture. It also positions the jaw for optimum open throat. The pay off to this position is that it becomes natural after awhile. I have gained alot more power because of the right muscles relaxing. My alto playing I have to watch as the increased internal wind pressure can bother a disc in my lower back. I have being playing alto recently using a 4 vandoren Blue box reed on a meyer 5 mouthpiece. I will not play that resistant setup alot but its nice to know I still can for that really dense tone. On the tenor I went up to a Zonda 4 on a Link STM NY 5* from a Zonda 3.5. I'm still toying with that. It is alot easier to play the 3.5, a singing quality has emerged like the Morgans have, but with the Link tone.
I have a board set up with a milk crate, a small rubbermaid stool and some cut 2x4 wood and stretch in the zero gravity position for about half and hour a day. I also sleep with my legs raised about two inches, with a board under my mattress by my feet.
I am looking for ways to keep proper posture as long as I can day and night, thats the goal. On the computer I use the giant exercise ball as a chair, that way I am in constant motion. I do stretch over it and sometimes with the weight balls. For walks, I take a 3 or 5 pound weight ball with me and toss it up as I walk. It builds core because as it comes down its more like 3-20 pounds depending how high you throw it, and how much arm is extended whn catching it.
For walking shoes I use Garmont Nagevi XCR.
www.garmontusa.com/light-hiking.html
They somehow level in the heel, so if you step on a small stone, the shoe adjusts and or rolls slightly, because the sole is slightly rounded. The hips stay level and take pressure off the disc and muscles are not overtaxed if they get tired. They are designed for hiking over uneven terain. They work fine on almost any surface except and level poured concrete floors. Floors in a house are almost never level. The hiking shoes tendency is to keep you standing straight. I find on tenor they do not work as well as the leather shoes. I can hear it first in the tone and ease of playing.
Check out Ben Webster playing when he was younger. Thats the posture I'm going for. His left shoulder is raised a bit though. In theroy if he had a codera he could play with even better posture.