Reverbs: "best sounding" vs "most accurate in physical model sense"?

[soundmodel]

Reverbs: "best sounding" vs "most accurate in a physical model sense"?

I was reading on using 3D wave equation for doing reverb and it's presented in some papers as if it's the "most accurate", but unusable for most cases due to full computation requiring massive amounts of computational resources.

But then I also thought, is 3D wave equation-based reverberation necessarily the best sounding? Since in musical DSP physical accuracy may not translate to "best sounding".

But then I wondered if "best sounding" is not based on the 3D wave equation, then what is it based on?

Note: I'm not asking for trade secrets here, but I'd like to understand how "good sounding" relates to the well-known modeling techniques.

[DaveClark]

But then I also thought, is 3D wave equation-based reverberation necessarily the best sounding?

If the solution to the 3-D wave equation is accurate, then the sound will be as good or as bad as it would be for the environment that is being modelled. The main advantage of solving the 3-D wave equation mathematically is that you don't have to build the physical venue. It's important to choose the appropriate venue to model, and this includes taking into account the source material and other considerations.

On computational resources: The Green's function method allows one to create IRs that represent solutions for a source at a particular location and a receiver (mic) at another location. These represent the geometrical part of the solution to the wave equation. If you have several of these, you have a virtual studio or concert hall, etc. You can use these over and over again for various sources. The computational burden can be as low as for a cab simulation in a guitar amp sim, but it can also be two or three times higher (for example) for a long reverb time. If you have control over volumes and decays, then you can use these to simulate modifications of the virtual studio, such as modification of absorption by using different materials on the walls. A disadvantage of the Green's function method is that the Green's function is often not known. Many studios and concert halls have oddball shapes, and for good reason. Regular geometries can have degenerate modes which emphasize certain frequencies.

I'd love to have an affordable finite-difference simulator that could model, in real time, an entire concert hall with moving walls, moving reflectors and absorbers, as well as moving, rotating, and pulsating sound sources, but that would certainly qualify as a "challenge" problem, i.e. challenging to the best resources available at this time.

IMHO good-sounding reverb is an art, not a science. It can, however, be a science-guided art.

I also think that there is no "best-sounding" reverb, but there are certainly more and less popular ones.

[soundmodel]

But then I also thought, is 3D wave equation-based reverberation necessarily the best sounding?

If the solution to the 3-D wave equation is accurate, then the sound will be as good or as bad as it would be for the environment that is being modeled.

I wonder what is a 3D wave equation based reverb that's also from a good room?

[DaveClark]

I wonder what is a 3D wave equation based reverb that's also from a good room?

Given that this is a developer's forum, I'd rather give an example of worse compared to better --- in other words avoid specific products and write about principles.

Worse would be to solve the 3-D wave equation for a square box where length, width, and height are all the same. Better would be to solve the 3-D wave equation for dimensions of a room that corresponded to the so-called "Golden Ratio." The reason for this is that the square box produces degenerate room modes whereas the latter does not because the ratios of the various dimensions are irrational numbers. For the latter, the room modes aligned with the primary axes of the room are not all the same, nor are they related in a simple manner such as would be the case if the room dimensions were all integer multiples of each other.

Given a room, the location of a source, and the location of a receiver (e.g. microphone), it would generally be better to solve the 3-D wave equation with absorbers and reflectors placed to optimize the sound. For example, if the microphone was a coincident stereo mic, then one might want to compensate for a nearby wall. If the same thing was done for the simulation, it should also improve the results.

In general, there are many rooms out there which have received praise from audiophiles, musicians, recording engineers, etc. Any such room that has been simulated by solving the 3-D wave equation, and assuming that this was done competently, should receive equal praise. The principles of designing good rooms, if applied to simulations of rooms that were only virtual, should result in improved results compared to ignoring these principles.