Re: Altissimo in depth
As everyone above said, playing the overtone series based on low Bb, B, C and C# is essential not only for learning altissimo, but also for developing your tone on the sax. Don't bite! Use breath support (use your diaphragm), tongue position and keep your embouchure in an O shape (try to do the overtones with as little change to your embouchure as possible). It's natural to squeeze the embouchure as you get higher in tone, but this is a bad habit. Of course getting a good private teach helps. The Teal book is good in lots of ways, but very few can develop an embouchure suggested in that book without biting. Most jazz players use their chin muscles to support their lower lip to keep from biting (this is said to be BAD in the Teal book). While this may be recommended against by classical teachers, learning how to do this totally changed my sound for the better and I'll never go back. This was something I had to learn after years of trying the other way...years after going to schools like North Texas State University. (Some people out there may hit me over the head for suggesting this, but what can I say, it really changed everything for me.)
Back to the point, there are a lot of great jazz players that never played much altissimo at all. It's much more important to develop tone and facility in the natural range of the instrument. Altissimo fingerings are different for alto and tenor. And, in spite of what many have found, I learned most of the fingerings I use from books and they have worked great. Variations come later. Soprano altissimo required more personal fingerings for me. Admittedly, I personally didn't find the fingerings in Top Tones for Saxophone particularly helpful, but the rudimentary exercises in that book are very important. I seem to recall using a book about high harmonics by Ted Nash that I think was good for tenor fingerings. I learned some good alto fingerings from some book called Jazz Styles and Analysis...a "comprehensive" book of transcribed alto solos from about a hundred different alto players.
Sorry for the long post...my day job is sort of slow right now....hope this helps!