Physical modelling of piano's: Page 2

QuasiUnaFantasia · 2022-11-18T16:27:56+00:00

With the new version 8 of Pianoteq, and some on-going discussions about modelling of acoustic piano's (here, and on PW) I have been thinking about how to cre...

Physical modelling of piano's

dore_m

QuasiUnaFantasia Here's some further interesting stuff: Yamaha does physical modelling also (and even producing sound from their model):

https://www.yamaha.com/en/about/research/technologies/piano-simulation/

That looks like finite element analysis (FEA), which is a way to analyze behavior and optimize a piano design, but not a way to make realtime calculations that affect the way a DP or VST sounds. As I said, they probably change parameters (using a real piano, or a modeled instrument - FEA) to observe the behavior of a longer string, or different material. Using these observations on how the physical characteristics affect the sound, they try to optimize their sound engine to change with these parameters.

QuasiUnaFantasia

Del Vento If you want to get to the results that are shown on the Yamaha website, yes you absolutely do.

Yes, but that was obviously not implied by the guy who wrote that paper back in the 1980's. He wouldn't even have dreamed about using PDE's for sound generation.

Del Vento sorry this is really close to my expertise, my Ph.D. and my job, so I tend to be quite picky, nothing personal

Fair enough, I did my postdoc in it, so I'm a bit picky myself.

But, the heart of the matter of our disagreement seems to be your insistence that physical modelling must base itself on differential equations, whereas I maintain that this is not a requirement.

What I think is the quintessential difference between the PDE approach (which we both agree Pianoteq is not essentially based on) and "method 4" of that original paper, involves only the mathematics used. Both approaches are fundamentally approximations to sound generation, one operating at a higher level of detail, the other on a lower level.

The true difference between both of these approaches and modern versions of "method 1" is that nowadays machine learning methods would be used for method 1, and there would be absolutely no trace of physical meaning to any parameters involved. (Incidentally, this is exactly what I want to do).

Del Vento

QuasiUnaFantasia Fair enough, I did my postdoc in it, so I'm a bit picky myself.

👍️

QuasiUnaFantasia But, the heart of the matter of our disagreement seems to be your insistence that physical modelling must base itself on differential equations, whereas I maintain that this is not a requirement.

Well, I guess my insistence is my interpretation of the word physical. I understand the other point of view and I relaxed that insistence by distinguishing between "physical model of the instrument" vs "physical model of the sound". To me, physical means based on the existence in the physical world and hence somewhat requiring to have a model of the physical object that is modeled. Hence only a PDE-based cuts that for "the instrument" (via FEA, but also other methods are possible, @dore_m finite difference being another popular one). The "sound" itself has physical existence, and one could make a model for that itself, regardless (or at least partially regardless) of how the instrument generates it. If we can agree that you don't care about making a physical model of the instrument but only of its sound then I think it's fine to do that without solving the PDEs of the instrument, and there is no disagreement. I still think this approach is closer to 1 than it is closer to a full-fledged model of the instrument but I am okay to stop insisting on this since it feels like an argument about one shade of orange being closer to yellow or red -- and often different viewers disagree (regardless of what the RGB analysis objectively says).

QuasiUnaFantasia What I think is the quintessential difference between the PDE approach (which we both agree Pianoteq is not essentially based on) and "method 4" of that original paper, involves only the mathematics used. Both approaches are fundamentally approximations to sound generation, one operating at a higher level of detail, the other on a lower level.

We totally agree here

QuasiUnaFantasia The true difference between both of these approaches and modern versions of "method 1" is that nowadays machine learning methods would be used for method 1, and there would be absolutely no trace of physical meaning to any parameters involved. (Incidentally, this is exactly what I want to do).

Fair enough. Keep us posted.

QuasiUnaFantasia

Del Vento I still think this approach is closer to 1 than it is closer to a full-fledged model of the instrument but I am okay to stop insisting on this since it feels like an argument about one shade of orange being closer to yellow or red -- and often different viewers disagree (regardless of what the RGB analysis objectively says).

Yes, I think we have been nitpicking over words themselves, whereas we seem to agree quite well on the deeper meanings behind them. 😆 Well, it keeps us off the streets. 😄

CyberGene

I think Del Vento pretty well describes my understanding of Pianoteq: it doesn’t try to model the piano through a geometric and physical representations of the piano parts and their mechanical interactions and properties, thus simulating the actual movement of hammer and string vibrating from that strike and then sound waves radiating through soundboard, etc. This is impossible to do in real-time even with precalculated portions of the differential equations involved. Instead, they try to approach the recorded sound of a real piano. Yes, you can change stuff like hammer hardness, string length, etc but I bet that’s more of a clever observation of how to change that sound approximation strategy rather than any real physical modeling. Just as an example, many digital pianos “model” the degree to which the piano lid is open by EQ-ing the sound. Apparently an open piano is brighter. But is that physical modeling? So, it’s down to what we understand by physical modeling.

And it’s the only problem I have with Pianoteq and more precisely the fans of Pianoteq. I listen to how PT sounds and it leaves me cold. I don’t care how it makes that. But I have all reasons to believe that some people don’t listen as much to the sound but rather try to convince themselves that “physical modeling” is so much better than sampling, PT must then be so much better than sampled pianos. And I would argue (without facts, just by a wild speculation) that many of these people believe PT has PDE-solving (largely synonymous with finite element analysis in this case) stuff which is why it must be so great. I don’t reject how realistically PT behaves in terms of pedaling and resonances but I’m not convinced by its sound and for me that’s where my personal taste about piano is.

kapelli

So, any of you know which methid Roland and Physis Piano are using?

AND… if there would be Grand Pianoteq… so without reference to any actual existing pianos do you think that metod 4 would still being big advancement over the currently used method 1?

So their own piano, with their own digitally designed scale, type of wood used, frame shape and so on.. oh..yes… do I want too much?

And also, the fact that they are using method one, for me is a clear because all of their pianos have some common sound signature…

And I feel disappointed, because I was truly convinced that Moddart is doing, is exactly measuring strings, tensions, vibrations, calculating surfaces, lid opening… and now O thin that probably lack of that is responsible for its synthetic and unresonant sound.

Del Vento

kapelli So their own piano, with their own digitally designed scale, type of wood used, frame shape and so on.. oh..yes… do I want too much?

According the video that @QuasiUnaFantasia posted earlier in this thread, Yamaha is doing that… but to design their acoustic pianos. I suspect that if the model was able to produce good sound in a practical way (i.e. without having to wait for three hours to get 1sec of sound) they will consider incorporating those in their instrument. I say "suspect" rather than "I am sure" because Yamaha is a big corporation and I don't know how balkanized it is. If a motorcycle engineer has a great idea for piano, do they have a process to get that feedback to the right people? I have no idea!

MacMacMac If the piano does so by having mice run on treadmills, that's fine with me.

As long as I don't have to feed them and clean their poop, that would be fine with me too. But I guess we'll soon enter into an argument about mandatory hantavirus vaccines 🤣

MacMacMac I don't care how the sound is produced. I just care about the sound.

Jokes asides, I believe everybody agrees with this, with one modifier: playability. I am sure some people (and perhaps even you) would accept an inferior sound if it responds better to the player, for example for pedaling, including half-pedaling and re-pedaling.

Before you say "sounds is king, I don't care about the elusive playability", let me make an extreme example. Consider a perfect recording of a piano, wonderfully made, but totally unplayable: single layer and no editing of the sound. When playing, no change in dynamics whatsoever (not even adjusting the volume of that single layer) and not even noticing you releasing the note, but keeping it sounding for the duration of the sample, rather than the duration of the note being held. Total polyphony: 1. This is quite simple to get it right and "perfect" sound-wise! You have to "only" record it correctly! But it's obviously useless. Modifications to the sound are needed, an easy one is adjusting the volume, and using multiple layers doing cross fading among them. This is probably easy to get right, so let's make another example: deciding how to "interrupt" the sound when you release the key. Not super difficult, but not simply "stopping the sound" otherwise that would be like an audible click. Perhaps hide that click by playing a noise release sample? A possibility, but is it the best? How about sympathetic resonances? Things get tricky with any of these, as I am sure @dore_m can explain to us. So while nobody would accept my "perfectly sounding, not playable" extreme example, different people may accept a different trade-off between "perfect sound" and "perfect playability", assuming that increases in playbility reduce the quality in sound. To me this assumption looks like a reasonable thing to happen because you cannot record every single possible duration and dynamics and combinatorial possibility of notes playing at the same time, so you have to do some sort of "live editing" of the recorded sound. And with any of such changes, the possibility of unwanted artifacts and decreased "closeness" to the original "perfect" sound becomes more likely.

MacMacMac

I'm with CG on this. I don't care how the sound is produced. I just care about the sound.

If the piano creates good sound, then it's good, regardless of the techno-crud.

If the piano does so by having mice run on treadmills, that's fine with me.
(I guess that would count as physical modeling, eh?)

QuasiUnaFantasia

Funny observation: I am studying a short sample of a chord (played using the Steinway B piano from Ivory II, not that it matters), and it turns out that the single frequency with greatest importance is 12.29 Hz. The lowest key, however, has a base frequency of 27.5 Hz ...

Why is stuff never simple? 😅

Del Vento

QuasiUnaFantasia Funny observation: I am studying a short sample of a chord (played using the Steinway B piano from Ivory II, not that it matters), and it turns out that the single frequency with greatest importance is 12.29 Hz. The lowest key, however, has a base frequency of 27.5 Hz ...

Perhaps that's a beat, rather than a partial?

dore_m Yes. Many times the fundamental is not the loudest partial.

This is always the case for the lowest range of the piano, where the second or third harmonic is louder than the fundamental. But what @QuasiUnaFantasia is reporting here is more dramatic: a frequency lower than the lowest possible fundamental for any note.

The only explanation I can think of at the moment (2 minutes after reading it and without thinking it hard) is that it's a beat.

QuasiUnaFantasia Why is stuff never simple? 😅

Because those who came before us did all the simple stuff and left us with the hard things….. it's gonna be even harder for our greatgrandkids….

dore_m

Yes. Many times the fundamental is not the loudest partial.

QuasiUnaFantasia

I'll have to look on something simpler than a chord, because it gets too complicated with more than one note sounding at the same time. Maybe that will indeed reduce the importance of frequencies below the lowest fundamental.

Del Vento Perhaps that's a beat, rather than a partial?

Thanks for alerting me to that!

dore_m

QuasiUnaFantasia I'll have to look on something simpler than a chord, because it gets too complicated with more than one note sounding at the same time

Interesting. I'm always looking at single notes and only recently analyzed pairs because only pairs create cross resonance. Much easier to only look at one note at one velocity.

Del Vento But what @QuasiUnaFantasia is reporting here is more dramatic: a frequency lower than the lowest possible fundamental for any note.

Got it

Pianissimo

A beat? From IvoryII ?? It would be more interesting to compare a chord from an acoustic grand vs the sampled chord from the digital vst of the same grand.

QuasiUnaFantasia

The problem with the chord is that you get frequency responses from each of the notes played, but in addition to this you also get interference tones from the differences of the notes played. So with two notes played, you get three tones sounding (one probably much lower than the two others). With three notes in a chord, you get the three tones themselves, and then up to three intererference tones (could be just two, but three is likely - especially if the piano tuning is stretched).

Joannchr

dore_m According to the article submitted to HAL in 2018

https://hal.inria.fr/hal-01894219

Juliette Chabassier ( from Modarrt) talks about the evolution of the various methods used to reproduce piano sound and says "In parallel, a modal-based software piano, Pianoteq, was introduced by Modartt2 in 2006" So I would assume that PTQ is still based on Modal Synthesis which is explained in more details in the document.

Del Vento

Joannchr Very interesting and very detailed, thanks for posting.

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