There is an entire universe of saxophone multiphonics and alternate fingerings out there. John Gross, one of Portland's own heavy-hitters, wrote about the most comprehensive book on the subject called "185 Multiphonics for the Saxophone, A Practical Guide"( published by Advance Music). You can hear John put some of these to use on his recording with drummer Billy Minz called Beautiful You.
Bert Wilson is another NW saxophonist who is crazy about multiphonics. Bert is one of the few cats that only uses multiphonics that make functional chords. Bert plays chord progressions with multiphonics. I must admit that to my ear most multiphonics sound pretty harsh and raw, whether they are harmonically functional or not. I might use one now and then when playing free music, but like altisimo, I find that it's best to limit them. I most often use them not for the multi-note effect but as barks. By a bark I mean a note that pops out louder and with a different timbre, used for dramatic effect. The most widely used barks are simply overtones. Check out Lester Young on Jazz at the Philharmonic, you'll hear him use this technique on the A sections on Rhythm changes. Every time he does it the crowd goes totally nuts. He plays repeated middle C eighth notes, alternating between regular fingering and the 1st overtone of low C. Since the overtone C has most of the keys down the sound comes out of the bell rather than the upper stack. When a mic is right in the bell this makes the overtones explosively pop out. This same technique can also be used from middle F up to G# with the second overtones of low Bb to C#. The overtone notes are bigger and darker since more of the tube is being used.
The two other barks that I use are mulitphonic fingerings without the extra notes.
- The first one is a bluesy Bb: Finger a Eb with the octave key and without your G key. Relax and tighten your embouchure slowly as you blow, actually it's more of a dropping of the jaw. You'll notice that you'll hear a Bb alternating with the G below it. By rapidly and drastically tightening and loosening your chops a minor third shake can be created. Start very slow at first and then faster as you get the hang of it. Phil Woods uses this one a lot, it has a very distinctive bluesy sound. You can use just the top note (Bb) without the shake also, this gives an extra low pitch that woofs. It's great for a Blue seventh or third (the extra flatted 7th really comes from the 7th overtone).
- The second one is a bluesy G: This one is the same idea as the last one but on a different note. Finger a low C plus the octave key and without the F key (index finger of the right hand). Try the same thing with your chops as above. You can also get a nice multiphonic with this fingering in the lower octave. Take off the octave key and just relax and blow, a full three note multiphonic should come out.