For many years I have often used “multi-phonic” fingerings on the saxophone, which produce two or three tones simultaneously in a dense cluster. Though these note clusters are invariably dissonant, when played properly they create a rather beautiful “fog” of sound, and thus every creative saxophonist should be familiar with them. But in the past (lonnnggg before the Internet) I had to dig through a lot of books to cobble together a set of multi-phonics that I knew worked on every saxophone (tenor,alto, soprano, and baritone), and eventually compiled the full set set pictured below (upon arriving in Japan and beginning what would be a major avant-garde phase of my career).
Be forewarned, they initially sound like ‘yelling’… all scratchy and scream-y when you first begin to try them. Once you learn to hold them steady with a consistent air stream, you will hear what they are capable of as complex, expressive phenomena. The multi-phonics shown above are two of the nicer sounding ones a person can choose. The top one should come out sounding like a bit like a diesel engine idling, while the lower one should come out sounding like a low pitched electric razor. It takes a bit of practice playing multiphonics, as you have to direct the air through the mouthpiece at a specific speed, and at a slightly different angle from a normal note. These are micro-adjustments, and eventually your mouth and mind will naturally work out the right position.
[I gave them all names to remind me of what they sound like to me, but if you hear them differently I suggest you transcribe and rename them yourself to help your memory.]