Even in this case, they're choosing the easy path (plucked, pizzicato), but the human/instrument interface is still audibly oversimplified while the resonant body has an unnecessary amount of "realism". The sound of pizzicato has a distinct character because the player's finger/skin slides a bit on the string as they're plucking, among other factors, which sounds like it's missing here. This can be tricky to implement because it's not necessarily a one-way impulse. The string is already vibrating and affects the finger, hence "interface".

This applies 10x more with bowed strings.

I suppose this is the innovative part. They're not simulating just the string, but also the fluid it's immersed in, which is a computationally hard problem.

I made a vibrating string simulator in college for our Numerical Methods course and for quite a while I couldn't understand why it sounded so bad.

Turns out rounding errors in floating point operations can propagate to a point where they produce this distinct, "metallic" sound.

They're incredibly small, but if your system of differential equations is large enough, they'll become noticeable. Switching to an algorithm with better numerical stability would probably mitigate this issue, but I didn't get that far with my project.

Julius Smith wrote pretty comprehensive textbook on the subject of building physical models of musical instruments, available online. Here, for example, is a chapter on modeling bowed string sounds: https://ccrma.stanford.edu/~jos/pasp/Bowed_Strings.html

https://www.youtube.com/watch?v=RKT-sKtR970

Ouch: this is completely inaccurate. Physical modeling has its roots in the 80s and Stefan Bilbao has been doing FDM based methods for over 20 years. I think he discusses fem in numerical sound sysnthesis

My father is a luthier, and while he definitely needs to wait until the instrument is finished to hear the full sound, he also uses multiple techniques on parts of an unfinished violin to hear *some* sound. For example, he knocks on the top or back plate and listens to the sound it makes.

I don’t know how much of it is just voodoo, but he’s been doing it for 50 years, so I’m sure he noticed some correlation to the final sound by now. :) I'll have to ask him.

https://youtu.be/ODR6eQOjm9w

https://github.com/Qzping/ELGAR

It's just fun to see solutions to problems you didn't even know to exist.

"Show HN: Anyma V, a hybrid physical modelling virtual instrument" 01-aug-2024 https://news.ycombinator.com/item?id=41132104 29 comments

"Show HN: I built a synthesizer based on 3D physics" 02-may-2025 https://news.ycombinator.com/item?id=43873074 123 comments

It's much more difficult to use, though - you have to control lots of aspects of the simulation (using automation in DAW or MIDI controllers) to make it sound actually realistic.

OK I guess it seems like this is more of a tool for luthiers than for composers or music producers.

[1] https://audiomodeling.com/

That's not how building a violin works, it is not a physics problem, it is material matter, it is a taste matter, it is a matter of adapting to material what you have, ...

[1] https://www.youtube.com/watch?v=UB-5uPcWVVE

Looking it up just now, it turns out that, "Modern physics research shows that the f-shape allows the instrument to push much more air than a traditional round hole, resulting in greater acoustic power and projection."

Just wanted to share in case someone else had that same bit of false knowledge in their head.

I have no doubt there's been analytical/semi-analytical models around for decades. I mean a program that can take an arbitrary geometry or class thereof with specific materials and simulate the high frequency vibrations and model interactions with the body with high fidelity (not through ad-hoc models) is probably still out of scope of real time simulation.

My point is really that there's often families of models that deal with one thing, from semi-analytical first coded in Fortran in the 80s that can run in milliseconds but is only valid in certain configurations with a low degree of accuracy, to "first principles" simulations that may well require a supercomputer to produce results to a useful degree of accuracy (and not in real time). So, just because you see someone claim they can "simulate X", and then another makes the same claim 40 years later, that doesn't mean they're doing the same thing.

For instance, aeronautics has XFOIL. It's a semi-analytical model first devised in the 80s that computes aeronautics coefficients for a certain class of airfoils (NACA). My understanding is it's a very clever, and industrially significant, piece of code, but ultimately it works in a narrow regime with some heavy simplifications. You can now get results from this in real time on a webpage. A proper CFD calculation to a NACA wing will take in the order of minutes to hours on a workstation (depending on requested precision and settings, e.g. speed of air), and while closer to first principles, it's still using physical simplifications (RANS). So yeah, although nominally people have been "simulating airfoils" for 40 years, the techniques have refined considerably, and will continue to do so (practical LES and, someday, DNS). It might be another century that people are still "simulating airfoils" in ever more accurate (nailing down within the constraints), high fidelity (lifting constraints) and generic ways.

Back to instruments, this is a difficult coupled problem, in fairly high frequencies (high frequencies = more expensive), with possible fluid-structure interactions, not to mention the geometries are fairly complex (to even get a workable mesh to begin with). My uneducated guess is we're still at either semi-analytical, or at the "considerably simplified first principles" stage for this type of problems. Just like DNS, I'm sure you could "just resolve the scales and run it through a simulation with a really tiny time step", and this is liable to be similarly expensive as DNS (million dollar single simulation). Additionally, they have to deal with the human ear, which is perhaps more unforgiving than an error plot on drag or lift. So I wouldn't dismiss news of instrument simulation as stale just because someone made something that produced similar artifacts in the past, as the methods will continue to evolve considerably.