If I understand correctly (as a non-mathematician) Hilbert space filling curves only map N dimensions to 1.

However, I'm looking for a similar concept, that maps N dimensions to X dimensions. (My choice of how many).

And ideally has the same nice properties as Hilbert space filling curves (good locality preservation).

Is there some generalization of Hilbert space filling curves?

This would give greater granularity over the traversal of the state space / degrees of freedom / dimensions.

It would allow compression of 100 dimensions down to 50, or 25, etc.

Why am I interested in this? I want to create a tool to allow me to traverse the state space of all possible "sounds" continuously, but with the chosen level of granularity. I want to choose the level of compression.

So 44,100 dimensions -> 20,000 dimensions -> 5,000 dimensions -> 1,000 dimensions -> 500 dimensions -> 100 dimensions -> 50 dimensions (this is where I might start to add some knobs to control the output) -> 25 dimensions -> And so on.

Why no data? I don't want to use an autoencoder, nor "bias" the state space. I'm not looking to traverse the state space of all sounds in my dataset. I'm looking to traverse the entire state space of all possible sounds.

Someone shared this with me: https://ieeexplore.ieee.org/document/4288125

But the issue is it stops at surfaces. I'm really searching for a generalization of Hilbert space filling curves that goes beyond 1 or 2, converts it to N dimensions

Or any concept you feel would help my goal really