semi virtual sax

Digital musical instruments tend to be very limited in expressiveness compared to real physical ones. This is because only a few control signals are used, like key on/off, as opposed to the continuum of ways that a musician can interact with a real instrument - like guitars, violins, brass. On the other hand acoustic instrument design is very much limited by practical issues that don't exist in the digital world. I propose a new kind of instrument where the main resonating body itself is composed of real and virtual parts.

Imagine a saxophone where most of the body is cut off and replaced with a system of electroacoustic transducers (microphones and actuators), such that it behaves identically to a real saxophone body. This should be possible in theory because that behavior can be described as a linear time-invariant (LTI) system, which is almost trivial to implement in DSP.

There are a few big problems to solve. In the following, "incoming" means from the mouthpiece towards the end, and "outgoing" the opposite.

1.) The natural reflection from the end of the tube must be eliminated so that it can be replaced with a virtual reflection.

2.) Any pressure or velocity signal measured along the length of the tube is a mixture of both incoming and outgoing waves. These must be separated, as only the incoming wave should be fed to the DSP. Otherwise the system would just self-oscillate.

3.) The incoming wave has a significant "DC component". Air is not simply vibrating, but there's the more or less steady flow. This must be let through without too much resistance.

There's an alternative way to simulate the body, which might be easier to make but sounds dubious in theory. Instead of creating a "virtual" reflection wave, just pick up the incoming one, and feed the outgoing signal directly to the reed via some setup of magnets. The reed itself could be ferromagnetic, and a strong solenoid with a permanent magnet core needs to be embedded in the mouthpiece. At the very least this should create a controllable feedback loop, but I'm worried that mouth resonances which are important in playing especially high notes and bends might not work if the reflected wave isn't fed into the player's mouth through the mouthpiece.