More wood please!

I completely agree with this.

I am sure it is not going to be easy.   Maybe even impossible.

But that is the final step.

What do we mean by "wood" ?
I suspect that it may be resonances from;
a) The case
b) The lid
c) On uprights the "flat" panels.
d) something else.

I see a lot of discussion in a lot of places about soundboards and
I can agree that its resonant frequency/frequencies matter(s) a great deal.
I haven't read anything about any such resonances in the lid or other "panels".
The cavity of a physical piano would also have some resonant frequency or frequencies,
at least I know that it is significant in other string instrument design.

So, I doubt that we will see the equations used for  these factors, but it would be nice if a developer could chime in with a description of how these are considered and whether or not they relate to "woodiness".

In old tech; delay lines do that.
Is the math just a simulated delay line with feedback and (notch) filters ?

Here's an idea. Pianoteq 4 already supports convolution reverbs through IR (impulse responses). How about getting impulse responses from real grand piano soundboards such as Steinway, Bosendorfer, Yamaha, Fazioli, etc. and then use the already perfect hammer-string model of Pianoteq to run it through those soundboard IR-s? Pianoteq developers will have to bypass their own soundboard model and instead use the convolution ones. That's not cheating, it's not a sampling. And it would add the real "wood" to the sound I presume.

That would give you only one particular case of soundboard behavior. You know that soundboard behaves differently depending on which notes you play... so only one IR sample would definitely not be enough. It would have to be dynamic...

BTW, it IS sampling, in a way. Convolution is a sample-based process...

Still, convolution is a linear operation. We need nonlinear here, exactly because of different microphone placements.

I understand the mathematics behind convolution - I had a few courses on DSP on my college

I think EvilDragon's point about needing different IR for each note is correct, not because of the frequencies in the note itself, but because the sound is transmitted into the soundboard at a different point. It's rather like hammering the string at a different position: the harmonic content is different. The advantage of modelling is that you can derive an impulse response for coupling to any point.

Also, I agree that the mathematics of computing convolutions efficiently is complicated, but conceptually, the idea is quite simple. It's just like playing many copies of the same "response" sample on top of each other, one for each sample point in the input waveform, where each copy starts at the time-offset of the sample point and has an amplitude given by the sample value (which may be negative). So, if the response lasts for a few seconds, that's equivalent to playing more than 100 thousand samples simultaneously! That's why you need some clever math tricks.

If the wood question was that simple, as a convolution effect, Modartt would already solved it 100%.

Modartt, to my point of view, wants weverything in the modelled universe. If they want to add extra woodness, will try to find a way that this will interact with all other elements.  They want a living machine.

I'm sure they can run a test, to get just the pure sound of wood for each hey strike, and could add it as sampled sound over the modelled sound, in the same way the hammer noise, but it would lost some of the living aspect of pianoteq.

Ahhh, until a negative proof is established I shall continue to believe that the undefined variable "Woody Sound"  can be achieved, EVENTUALY.

I haven't got into it, I suspect that it is some interaction of cabinet and cavity resonances - along with harp, soundboard, etc.

Somewhere I vaguely remember that a particular guitar, when analyzed, was found to have a resonant frequency of the cavity that was a perfect fifth from the resonant frequency of the spruce top - the top of a guitar being the soundboard of a guitar.

Dondascher, I am not sure to what degree your posts are being sarcastic but I'll try to answer you anyway. A real piano is made of metal and wood. Everybody knows when something sounds "metallic" (No, I am not talking about Metallica and heavy metal music ). So, when you try to emulate a real piano and the result sounds metallic, then you logically think there's not enough "wood" in the sound. Pianoteq used to contain a lot of "metallic" notes. Now, it managed to decrease the "metal" in it and add more "wood". But there is still not enough of it.

So, Pianoteq managed to emulate the characteristics of metallic materials in a piano, judging by how metallic the sound used to be (and to some degree still is). In order to add more wood, they need to better emulate the characteristics of wood materials, their response to vibration, etc. This may not be that easy but I believe it is not impossible.

P.S. English is not my native language and I apologize if what I write is incomprehensible or confusing.

One solution could lie in post effect processing.  When the wood body vibrates it, in turn, imparts vibrations back into the strings and "distorts" the original wave form, probably more noticeably in the harmonics as the fundamental is so much stronger and it's initial attack sound happens so fast.  There are outboard effects available for guitarists which have controls for specifically adding more guitar body wood.  Fishman makes some, so does Roland.  It would be interesting to try one of these pedals on the output of Pianoteq.  What type of processing they are doing, I don't know -maybe some type of random, multi-tap delays on the early reflections, some EQ, some mild third harmonic distortion.  I don't own any of these specific effect pedals, but I'd like to hear and try more experiments with post processing and VST effects that fall into these categories.  Even though you can impart VST effects into your DAW or host after Pianoteq, I've often hinted at the convenience of Pianoteq (standalone & VSTi) being able to host a VST effect chain post or pre microphone output.
(...and yes, I've harped on this solution many times in the past, so forgive me)

I am able to anticipate a result before I can "clearly see a way to (the bottom of) it".
Someone used to call it Imagineering - I still believe in it.

Alternatively, perhaps what we refer to as "wood" is what wood adds to the sound by subtracting (absorbing) some frequencies.
Thick heavy planks of wood ABSORB sound very well, thin tone woods in violin plates"sing".

I see a lot written asking for "more wood" and "less metallic", often in the same sentence.

I wonder if these are the antithesis of each other, i.e. if one were to add filters to take away the frequencies that wood absorbs - does that lead to less "metallic" and more "wood" ?

Not that subtractive synthesis is new :-D

There are also some interesting discussions in other forums on carbon fiber soundboards, thinner and lighter lids, ABS plastic cases, etc.