It seems to be easy to implement digitally, but it really isn't, because a lot of the nuances and non-linearities that add weight and colour to synthesis with real electronics aren't present in simple digital emulations.
For pure DSP the choice is more or less between open additive, modal (which is a kind of constrained additive), AI-constrained additive, which is what Google have been playing with, and physical modelling, which is digital modelling of strings and bows.
If you want to "enforce a physically correct relationship" between etc you're going to want AI-constrained additive or physical modelling.
The aesthetics of all of this are a different topic altogether.
I was thinking of relationships like these:
1) Decay time of nth partial falls as a certain formula of n.
2) Frequency of nth partial is slightly different from n * fundamental, by a factor which is a formula of n.
3) Spectrum of nth partial isn't a delta function, but a hump whose width is a formula of n.
All these ideas come from physical effects, but you can use them to generate sounds directly, without any physical modeling or AI. My hunch is that could be more such ideas and they could play together nicely.