Do the parameters in these harmonic systems compress better? Instead of needing to hold individual parameters for each oscillator, could groupings of oscillators be instead be described with its output over a given time and then just reverse that output to get the original parameters (I’m thinking the output is like an FFT of the oscillators which is a single value, then do an inverse FFT to get the original oscillator parameters etc)
You mean describing the core of the system via its normal mode or similar or even performing normal mode analysis to recover it from a waveform? I have no idea how that performs as a lossy compression method versus other options such as quantization but regardless I'm fairly certain it would be computationally infeasible given the application.