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Out of a NI Noire thread I read that Noire has resonance but it's modelled, not sampled; the same I read about another piano, UAD ravel, whatever.

But it started me thinking. I don't think is ever possible to sample resonance or is it ?

I mean resonance (without pedal) is the effect that striking one note has on the other notes being held. Very complicated. Still every different chord combination would have its own resonance effect; and each one would be different although slightly but definitely different. Now how many 6 notes chords are there on an 88 keys instruments. I'll save you the math, it's 500 millions. And you have 2/3/4/5 notes chords. 3 notes chords possible are 100.000. Even worst for 7 or 8 notes chords. I know, not all of them will be practical, musical, sensible but I feel you would nevertheless looking at several 100,000s. Sampling those ? I don't think so. So it's got to be modelled. You hit a key and a modelling engine decides what nearby keys are already pressed and how much of an overtone for those should be generated.

Is that right ? Anyone knowledgeable about piano sound design would like to shed some light on this ?

Thanks,

M.

For resonance occurring at audio frequencies, and if there's enough energy for the oscillations at the resonant frequency to be of a substantial amplitude to be audible to a person ----- then sure, the frequency (for frequencies) of oscillation is expected to be detectable by a suitable sort of microphone. If detectable, then it is recordable, which also means able to be sampled.

Although - with modelling. For sure, one could expect it to be challenging to produce a real-time model of an actual system with lots of strings. But people are clever and crafty. With fast enough computing systems, and enough memory, and clever processing techniques/algorithms, they can obviously get some nice workable approximation.

Also - maybe have to keep in mind that while resonance in unstruck strings is just what happens in acoustic pianos --- it doesn't always necessarily mean that it is 'ideal' or fantastic. So physical modeling could actually help with addressing certain 'unwanted' effects that might inherently exist in acoustic pianos. Not meaning eliminating all resonances --- just limiting the amount.

It is easy to record a bunch of notes with their resonances, but you can’t easily isolate the resonance from the interaction of two notes (sympathetic resonance) and can’t record all combinations of notes.

Then a usual way is to have some sinus signal added with frequencies and amplitude computed from the intervals of the note. (Octava, fifths, thirds have different sympathetic resonance amplitudes).

Some libraries have resonance samples, but I don’t know how they are made.

Yep, exactly what I was wondering

Even that took a long time to be implemented in mainstream DP's!

"Pairwise" sampling (each pair of strings gets two samples -- (1) A is down, B is struck, versus (2) B is down, A is struck) is likely to be impractical, with current limits on CPU's and storage. As you point out, 88**2 is a big number.

What save the resonance models (I think) is that most pairs of strings have weak resonances -- so the modellers can ignore them. You can try out various DP's, and see that some implement "string resonance" better than others.

It's not only "nearby keys" that have to be considered. The bass strings are very rich in harmonics, and (on an acoustic piano) can be excited by notes (and excite notes) well into the midrange. Try holding down CDEFG in the lowest octave, and striking middle C, sharply. Then release the bass notes, and listen to the resonances go silent.

Having done a little (ok, alot) of postprocessing of samples, this thread has to me thinking:

I already record pedal down (all strings can be sympathetically be moved) and pedal up (all dampers down except for the note being played). Definitely there is a difference in spectral analysis between the two. Wonder if I could somehow subtract one from the other and thus have an isolated resonance sample (?)

Well when you play a note on a piano, the other strings vibrate sympathetically and that is picked up in the recording. So when you play a note or chords, those resonances in the background of the sample can still be heard.

Obviously, it wouldn’t be as robust, rich, or loud as the real thing or the modeled versions, but there’s some there. And I’d wonder if what really matters is the resonances that are evident to the ear immediately, not the ones so quiet or undetectable.

So, I would argue that samples would have *some* level of resonance within them.

As good as the modeled version or the ones created by a separate algorithm/script/plug-in, definitely not.

That won't work. It will give you a resonance sample between the note struck, _and the undamped harp_.

But what you need, for "string resonance", is a resonance that's the difference between:

. . . (a) striking middle C with dampers down, and

. . . (b) striking middle C with dampers down, _except_ the damper on <pick any string>.

You'd need to sample the resonances "pair-wise", between every pair of strings -- an "N-squared" job, where N=88.

. . . . IMHO, sampling is not a good way to handle this emulation problem.

Most of the resonances are weak, but there are enough strong ones to affect the sound of music, as it's played. There's even -- on some acoustics -- resonance between a note, and the note adjacent on the keyboard (e.g. C and C#). That's not accounted for by "harmonic resonance" -- it's something else.

When I got my PX-350, my first impression was that it sounded "clean" -- devoid of all sounds, except for the notes being played. Acoustic pianos, though, don't sound like that. Some of the difference is inter-string resonance.

Some virtual pianos have a sound recorded pedal down. Then there is no need to have samples with only the full 87 notes resonating with a 88th.

The point is mainly when while press C4, you hit C3 briefly. The C3 will interact with the C4 and produce sympathetic resonance. Recording each 87x88 pair of cross resonance can be and important task and will likely use too much space.

how does pianoteq do it ?

typo -- 'or'

And adding - which is why - very good samples acquired through maybe some 'painstaking' work (or aka a heap of effort by the recording/tech audio crew) sounds realistic when played back with good gear - as the audible resonances are recorded too. And implementing extra goodies - such as resonance-adding algorithms ------ things really come to impressive life.

I am not sure I understand all the outcomes of the Modartt patent.https://patents.google.com/patent/US7915515B2/en Modartt can also apply the patent partially.

The modelling goes as far as to include a finite elements simulation, but in a pre synthesis module. I don’t think it run in real time, but I guess it can compute the 87x88 mutual influences and record them as a bunch of partials.

(Note: With the Bechstein Digital Grand, the model is the Kontakt library, not the actual piano. Then, I guess the finite elements simulation doesn’t apply).

Are you sure of the need for pairwise samples? I assume that sympathetic resonances are essentially harmonic and thus each string will always produce the same spectrum of resonance regardless of which other key(s) did energise it... So you would only need 88 samples, and some table of how much a given free string will resonate following different keystrokes. But maybe you simoly ballpark it to "low, mid and high"...

Thus, maybe you just need a sample of a pedal up keystroke that is good at inducing resonance, and the sample of the SAME exact keystroke (not so easy without a robotic arm) also with pedal up BUT now with key X pressed down in advance. The subtraction of the two samples should give the sympathetic resonance of X that will be played whenever the strings of key X are undampened and other keys are struck.

Maybe not the same spectrum of the resonance - but simply the same spectrum we get when one key is pressed, which is pretty much the idea behind sample playback, even though we know that samples are relatively short. This isn't referring to physical modeling obviously. So then they have to think about what sounds should be coming out when the velocity is relatively low, medium, high etc (ie. or more defined levels). So a particular sample is used depending on the velocity and/or other quantities (eg. acceleration even - if workable). Any audible resonance is going to be in there anyway - because that's what the 'real' instrument did ----- during recording. The other fancy stuff they could do - and did (right?) is to add some clever/fancy algorithms, to make it 'look' (or sound) as if the instrument doesn't produce the exact/same/identical audio spectrum for exactly the same input condition (for each key press). Very similar - or even extremely similar, but not 'exactly' the same, to prevent the lightning striking in the same spot repeatedly scenario ------ upping the 'liveliness' of the instrument/sounds.

Now - as for what actually happens when striking multiple keys on an acoustic piano ----- where the time of striking each particular key (for a particular combination) is going involve time dependence in the waveforms --- we can sort of see the challenge in modeling. How the strings vibrate each other from the interactions has time dependence involved. We can see the complexity.

But once again, I wouldn't be surprised that the 'sympathetic' resonance is something that designers of 'real' pianos wanted to have some control over ----- as too much of a good thing (or too much of something) can be no good. And this is where physical modeling ------ taken to the very highest level of technology and technique can be something really significant. The progress made up to now has been leaps and bounds for sure. And they're just going to get better and better - just like in the movies how they even started making forests, jungles, oceans, and animals (computer generated) fool people. And that is just going to get better and better. Ok .... not 'fool'. Let's just say making people really think that it is real. Although, when it comes to audio. Audio is real. So that's fine.

That is - can see the complexity associated with modeling - as a single string that is influenced by a different string (where that different string is struck at a particular time), and another different string struck at some other time, or even at the same time, is a case where regular linear operations such as involving superposition isn't going to be workable, because the physical activity occurring in a single string isn't going to be the simple 'sum' of individual influences from other strings.

Your premise is false, unfortunately:

. . . The spectrum of resonance, produced by an open string, depends _very much_ on how it is energized.

Find an acoustic piano.

Hold down C4 (middle C), let the sound die out. That's our "open string".

. . . Strike G4 (G, a fifth higher) staccato -- you'll hear G5 ring, the third harmonic of C4.

. . . Strike C5 staccato -- you'll hear C5 continue to sound, because it excites the second harmonic of C4.

. . . Strike E5 staccato -- you'll hear E6, the fifth harmonic of C4.

A string, when it's struck by a hammer, doesn't give a _thud_ like a drum. It gives a sound where most of the energy is at the fundamental and harmonics of its fundamental pitch:

. . . its those frequencies, and _only_ those frequencies, that excite, and get sustained by, an open string.

This one of those situations which is genuinely, irreducibly complex. It's one reason why it's so hard to build a DP that "sounds just like an acoustic piano".

Kawaii’s system triggers the sustain portion of their samples for sympathetic resonance.

@Charles: in that case, I stand corrected (although I was right on the harmonics part). But according to your explanation, maybe there is no need for a pairwise ser of samples, but maybe only a pairwaise table of resonant harmonics, and a limited number of samples...

It is/was hard. Although, these days, in my own opinion, they have created DPs (and we have them and use them now) that not only sound like an acoustic piano. But also sounds 'better' than any acoustic piano, or at least sounds just as good as ANY acoustic piano. And not just the sound. The key mechanism (action) behaviour these days is as good as - or even better.

There was a mention from somebody in past discussions about certain digital pianos can/do sound 'clearer' than acoustic pianos. And somebody replied - 'clearer/cleaner' is not necessarily 'better'. But - in my opinion - clearer/cleaner can certainly be better. But for sure - in any case - just choose whatever one is satisfied with. Choose them all - if one can (or wants).

In the DP space, there sure are ultra clever and crafty engineers, physics/science/math/programmer/techs etc out there ----- that give us this awesome technology. Hats on and off to them. Nice work. The evolution of the DP is impressive. It also covers the evolution of the piano. Because a DP is pretty much an evolved acoustic piano.

Yes, that is indeed devilishly complex. You can sympathetically excite upper harmonics of any open string. I had to actually try this to understand it. I did as suggested, and indeed heard G5, which was not coming from the G5 string, it was coming from the C4 string as an upper harmonic.

I don't see any way of simulating this with a sampled instrument. you could only model this, I think.