If this stuff interests you have a look at Pianoteq. They take this to a whole new level, through physical modelling they get extremely close to being able to generate realistically sounding pianos.
Interesting one! For the time I played piano, I ended up buying myself 2 ADAM A7X monitors and played with Ableton's Grand Piano. I also downloaded a supposedly other library that allowed me to use sampled grand piano sounds which was supposed to improve sound quality.
It, however, never ended up sounding quite as good as my brothers's simple 300€ Yamaha keyboard.
Even after having trained my ears for many months, I still don't know why the piano sounds from my speakers just weren't as pleasing as what by bro's Yamaha produced.
The modern Yamaha keyboards use samples from real pianos. In mine there is both a Yamaha and a Bosendorfer and both sound quite good. But being sample based they are essentially just playing back recorded sounds.
Pianoteq generates the sounds using nothing but a bit of software and it is really most impressive.
I've never been able to work out if Pianoteq uses physical modelling - modelling the strings and soundboard as the solutions of differential equations - or spectral modelling - overtone resynthesis, which is rooted in sampling but reassembles the harmonics in samples dynamically instead of playing back a fixed sample series at different rates.
I suspect it's the latter, because there's a hint of detail missing in the way the overtones move.
The wikipedia article[1] says it's "Fourier construction" but without reference (that I can find) and without elaboration. At their website[2] they list some of their staff; I looked up research by one of their researchers and found a paper "Modeling and simulation of a grand piano"[3] which looks quite heavy on the physical modeling of strings and soundboard. I'd expect that to work better than spectral modeling because I think the latter would introduce (too much?) latency via needing to collect an entire spectral window (plus extra computation to compute the phases, and even then I don't think it could sound good enough?). Whereas physical modeling works directly in the time domain and there's a wealth of literature around it. See e.g. J. O. Smith III's waveguide synthesis work[4].
This problem is similar to the one faced by photographers. Why do in-camera shots look so much better in one camera vs another? A big reason these days is the camera's default software post-processing matches your taste. I bet with a little fiddling (particular with things like eq, compression, reverb, maybe resonance - all of which Live has in abundance!) you could find a great sound. It's just easier because Yamaha has great taste in sound. (One day I swear I will get a C5!)
The other thing that affects your experience, and that doesn't have anything to do with timbre, is latency. Ableton through a USB audio interface into monitors is going to take (much) longer than the onboard sound generation + speakers on a digital piano. It's going to add at least 20ms plus whatever time is required to compute the sound. Meanwhile any cheap digital piano is going to do better than that.
I agree that unchecked latency (no matter how imperceptible) can sour or perception of an instrument's playability. That said, latency of 3ms is very attainable so long as your interface isn't a decade old. That's a very usable speed.
Software instruments are usually about as quick as you'd ever need them to be (no latency). So just make sure your audio buffer is set low (32 - 128 samples) and that you're not doing any heavy DSP processing that's going to add extra latency.
It takes some vigilance to do and it can be a pain in the ass to manage when you're trying to play the instrument in a CPU intensive session, but if you do it right you'll only get latency at the output stage (3ms).
I have Live 11 on macOS 11.2.3 on an Intel 2.3GHz MBP and Live states output latency as 13ms for a 64 sample buffer at 44.1KHz sample rate. Apparently latency is reported by the audio interface driver itself, rather then measured, because live has a parameter to override that latency, including with negative values (using time travel?) It's something I should fiddle with, for sure. It would be nice to have playable virtual instruments!
Negative values typically offset for instance midi output to a point prior to the point where they normally would be output. So this only works for items that have a timestamp. But a soft-synth for instance could be driven that way to anticipate a longer delay further down the chain to end up with a more neutral delay once the whole chain has been traversed.
I guess the yamaha has dedicated DSP, it might also have some analog circuitry as part of the signal path. Both of these will change the quality of the sound coming out, potentially for the better. Also for some reason sometimes downsampling to 12bit gives a pleasing character as can be heard on some of the hardware samplers from the 90s. As for the sounds actually on the keyboard, its possible they were recorded from a different piano, with different mic placement and a different mic pre amp to the ableton sounds, all of which could potentially lead to a nicer sound being heard.
I haven't used their product, but the examples of all the effects they model impressed me quite a bit.
Unfortunately it is not possible to link to the examples page directly. To see what I mean, click on the Fine details of sound tab here:
https://www.modartt.com/pianoteq#acoustic
Pianoteq is great, and they have some really classic keyboards in their collection.
I really wish there were more open source physical modeling synths out there. I'd love to play with physical modeling code, but it's just not that common.
