Sympathetic Resonance

dore_m · 2022-06-19T15:57:09+00:00

So I've been playing around with sympathetic resonance in Garritan and Noire to see how it's handled. I was trying to see how I might be able to implement i...

vagfilm

Del Vento by coincidence, I just found a very old Scientific American article about the science of the sound of the piano

Can you share it? I remember one about the physics of singing in the shower and it was a gem...

Del Vento

vagfilm Can you share it? I remember one about the physics of singing in the shower and it was a gem...

Unfortunately I have the paper version of the Italian edition of such article. If you care about it, I think pictures fall under fair use of US copyright.

Otherwise, see https://www.scientificamerican.com/article/the-coupled-motions-of-piano-string/ (but don't forget https://scottaaronson.blog/?p=6202 )

@CyberGene how do I disable URL's preview? I don't like it in this context!

dore_m

After noodling about this a little more, I think situation 1 above (where the open string gets excited by energy from staccato note) is probably unnecessary to re-create/simulate. I'm showing an artificial situation, where the velocity of the open string is 0, but in reality, when you're playing, you'd hold a chord with your left hand and play a staccato note in your right hand. The chord in your left hand would already be ringing out, and not at a 0 velocity. Sure the strings might get excited with more energy from the staccato note, but it's negligible, and the real change in sound would come from the overlapping/resonant harmonics that are simulated by the sine waves.

vagfilm

Hi,

I run a simple resonance test using the VSTs at hand (VSL Steinway, Pianoteq Steinway, Noire, ModernU, Garritan CFX). I have also tested others, but the results were mediocre or not significantly different. This is not to be exaustive, but to give an idea of what is out there.

Since my experience with acoustic grands is limited, I don't know how well implemented the resonances are, but Pianoteq and Noire stand out as the best ones. Noire is really good and the scripting is open for dissection and ideas...

This test was suggested by Charles Cohen in a PianoWorld post #3216573
https://forum.pianoworld.com/ubbthreads.php/topics/3216444/resonance-modelled-resonance-sampled.html

Each WAV file contains 2 sets of 4 notes.

First set (resonance of hold C4):

no silent note + C5 played staccato (midi vel=127, ticks duration=30)
C4 silent + C5 staccato: C5 should continue to sound, as the second harmonic of the open C4 string.
C4 silent + E5 staccato: E6 should be heard, as the fifth harmonic of the open C4 string.
C4 silent + G4 staccato: G5 should be heard, as the third harmonic of the open C4 string.

Second set (resonance of hold C maj inv chord instead of C4 - C4/E4/G3)

no silent notes + C5 played staccato
C chord silent + C5 staccato
C chord silent + E5 staccato
C chord silent + G4 staccato

https://we.tl/t-pYUn91hETR

Drew-r

Asking as a lay pianist/enthusiast, it is difficult for me to get my head around the purpose of comparing or otherwise analyzing sampled resonances (former) versus modeled resonances (latter). My head is sort of reconciled with a Yamaha or Kawai at least being qualified to simulate modeled resonances of their APs, but still wondering how Roland is legitimately qualified.

If the former are produced from recordings of one or more given specific branded models of what actual AP/GPs do sound like, and the latter based on one or more given scientists’ computer algorithms producing an amalgamation of what any hypothetical genetic AP might sound like, is it realistic to expect there is a place the twain may some how meet as apples & apples?

dore_m

That's really helpful. I do like how the harmonics are pretty obvious in Noire's representation, but like the beating effect that happens in Garritan and Pianoteq.

When you hold the C chord, of course the spectrogram gets muddy. My hope is that I can just simulate the resonant harmonics with the sine waves, and when multiple notes are open the script will just trigger more sine waves and end up with the same result roughly as your tests. My son is coding up the harmonic frequency pairs right now (woohoo! Summer Python challenge!) I can share the python with you if you like, although I'm sure you could code it yourself.

Drew-r is it realistic to expect there is a realistic place the twain may some how meet as apples & apples?

Based on my recent research and experimentation in this, I don't think there is much of a hybrid approach. VSL probably uses samples, which creates incredibly large libraries, and Noire uses modeling - which is what I'm attempting more or less. The overlap is in my idea of using a low velocity sample to simulate the open string fundamental harmonics where I wrote:

dore_m I've been noodling about this, and here's my strategy: I mocked up the garritan resonances by doing three things:

I use a low velocity sample of the open string to simulate some of the harmonics of that string (I think these are the frequencies that make Garritan "muddy")
When there are overlapping frequencies between the struck note and the open string, I use sampled sine waves to ala Pianoteq to reinforce those frequencies. I basically made a Kontakt group of sine waves and trigger them by Midi note number according to resonant frequencies. Note, getting the stereo image right is a chore because I have to phase change the L and R channels to match the microphone character. Also, getting the ADSR envelope right also is challenging, but I can get close enough to be encouraged.
EQ filtering - for 1, the primary frequency seems to be too strong, so I EQ'd out the fundamental so the sound is more "ethereal". For 2, I used the LFO to simulate the beating effect.

Otherwise, I can't think of another hybrid way to achieve the resonances.

vagfilm

dore_m VSL probably uses samples

As far as I remember, the number of active voices reported in the VSL GUI is not altered by the onset of symp resonance; that suggests that it is modelled not samples.

dore_m

No kidding. I'm still guessing that sympathetic resonance would take an immense amount of recordings if they did. Wow, they fake it too then…

dore_m

@vagfilm Say, did you use the room mics or close mics to capture the VSL sympathetic resonances? Because I'd expect the mics further away would tend to pic up less of the resonance, which might explain why they are more muted than the others in your recordings.

vagfilm

The VSL recording uses only the condenser close mic; the symp resonance knob is set at maximum value of several dB.

The VSL resonance is indeed less complex than others and of significantly shorter duration. If that is more or less realistic, I have no idea.

dore_m

vagfilm The VSL resonance is indeed less complex than others and of significantly shorter duration. If that is more or less realistic, I have no idea.

Not realistic at all. Unless my piano sustains sympathetic resonances better than a concert grand. I tried your condition 2, and even at a staccato mf, I can get at least 10 seconds of harmonic resonance.

Del Vento

dore_m vagfilm The VSL resonance is indeed less complex than others and of significantly shorter duration. If that is more or less realistic, I have no idea.

Not realistic at all. Unless my piano sustains sympathetic resonances better than a concert grand. I tried your condition 2, and even at a staccato mf, I can get at least 10 seconds of harmonic resonance.

From the acoustic pianos I owned, I second this

CyberGene

Del Vento how do I disable URL's preview? I don't like it in this context!

I believe the author of the post should be able to disable the link preview by clicking on a X button in the preview. However this disables all the previews within that post, not just one of them. And you can’t restore previews in that post once disabled. Let me know if that works. Mods can also do it, but let me know if you can do that too, as author.

vagfilm

Del Vento Unfortunately I have the paper version of the Italian edition of such article. If you care about it, I think pictures fall under fair use of US copyright.

Completely OT, but I will keep it brief. Thanks for title of the article: I downloaded it through my institutional account. It looks daunting! I was hoping the article was from Jearl Walker's "amateur scientist" easy-read section at the last pages of each issue. Always great reads.
Scientific American lost his footing a LONG time ago, and the demise was caused by poor selection of invitations and becoming more pseudo-technical rather than sticking to the basic sciences. There was a wonderful french magazine from the same period called Jeux et Stratégie, that suffered the same slow decline.

Drew-r

@vagfilm

In the forum editor, click the chain-link icon, insert the url with a title and optionally a description and when the post appears, the title text is the hyperlink.

Del Vento

CyberGene I believe the author of the post should be able to disable the link preview by clicking on a X button in the preview.

I don't see any X button in the preview.

Drew-r In the forum editor, click the chain-link icon, insert the url with a title and optionally a description and when the post appears, the title text is the hyperlink.

That works only if the text you specify is not the URL itself. If you specify the same URL for the text, the preview appears. I guess that's not a big deal, and I should stop being nostalgic for a gone-by text-only ASCII-art past

CyberGene

Del Vento maybe you should do in the edit period. I’ve removed them for you. Next time check if you have those controls or possibly an option in the menu or something like that.

dore_m

Getting back on topic, my son did write a quick python script to automatically tell me which overlapping harmonics to simulate using sine waves. I asked him to number the harmonics so i could figure out how to use that information to choose the respective harmonic gain as I will just be triggering midi notes (samples of the sine waves). **so proud of my 12 year old! So now I have the ingredients: the resonant frequencies, the number of the harmonics that overlap, and the velocity of the note that induces the resonance. Ahhhh.. now I have to figure out an algorithm that takes those inputs and automatically calculates the harmonic gains…. Maybe a screenshot of the output from C4 (Midi note 60) and C5 (Midi note 72) will spur an idea from some contributors….

Del Vento

dore_m Getting back on topic, my son did write a quick python script to automatically tell me which overlapping harmonics to simulate using sine waves.

Just curious on what this is. Can you please define "overlapping"? And assuming what temperament?

dore_m

Del Vento ust curious on what this is. Can you please define "overlapping"? And assuming what temperament?

So here's how I understand it. For each note, the strings vibrate at the primary frequency (eg A4 = 440 Hz), and then also vibrate at the higher harmonics. These higher harmonics all follow the same interval pattern relative to the induced note. So A4 on a piano is actually many frequencies, 440hz, 880hz, 1318 hz etc…. (aka the fundamental frequencies of A4, A5, E6, etc.; AKA midi note numbers 69, 81, 88 )

This interval pattern of harmonics comes down to these known intervals (translated into midi note number intervals): 0, 12, 19, 24, 28, 31, 34, 36, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 51, 52. When given 2 midi note numbers, you can just make arrays of the harmonics for each note and compare the "overlapping" ones - the harmonics that are in common between the two notes. Anything overlapping is a sympathetic resonance.

So, for C4, and C5, which are midi notes 60 and 72 (see picture), the common overtones are midi notes 72, 84, 91, 96, 100, 103, 106. These are the frequencies to simulate sympathetic resonance using sine waves.

Now, I haven't fully considered the temperament as I'm mainly working in the center of the piano. I know (think) that the harmonics are pure physics and math (equal temperament), but pianos I work with are stretch tuned. So that means that if I induce a harmonic of a low string, which is stretched flat, the sine waves I'm working with will not be exactly the right frequencies. I haven't figured this out yet - but maybe like my half pedaling scripts - better to have something that is 90% there than nothing given my coding skills and limitations of Kontakt.

Its good to get my thoughts on this down somewhere for reference and as a reality check that others can read/comment. I did study vibrations in college, and went on to intern at a defense company studying how to dampen vibrations in missile airframes. But that was a long time ago, I've forgotten many of the details, and those vibrations were highly non-linear. I think I realize why no one has directed me on the relative power between the harmonics now after writing this - its because

each piano has different damping characteristics
because the distance between the strings matters in how much power is transferred from the struck string to the open string.
The mass of the string
Stretch tuning vs equal temperament mucks up the power induced since the frequencies don't overlap perfectly

And maybe some other contributing factors. I just need to do as was recommended. Record some and figure out a close-enough correlation.

Del Vento

dore_m @Del Vento Thanks! that was the type of response I was hoping for. I

You are most welcome!

vagfilm Thanks for title of the article: I downloaded it through my institutional account. It looks daunting!

It looks daunting at first, but it's not when you read it. It basically talks about what modern piano technicians call "bloom", the fact the the decay does not stop as quickly as expected and in some circumstances the volume even increases. Interesting read, but besides the first plot/graph and the one before last, not much relevant for this conversation or for digital anyway.

dore_m In some respects, I think I already have a competitor to Pianoteq 😛

But I meant seriously and professionally, not as an artisan and free option as you currently are.

Del Vento

dore_m So here's how I understand it.

This is a good start but there are a few things missing. I mention them only for you to know what you are neglecting, as you say your approach may be good enough.

The harmonics might be inharmonic and not exact integer multiple -- the famous inharmonicity of the strings
Temperament is a totally separate issue from octave stretching. So let's start with stretching. As you say, the stretching is mostly relevant at the extreme range of the piano, not the middle. The stretching is done basically to make sure that octaves match the second harmonic, and thus is closely related to inharmonicy (note from the formula of the link above that you can pick only one harmonic frequency to get a perfect match)
Temperament has nothing to do with stretching or inharmonicity, and all to do with music sounds. We like sounds that are pure, say a sine wave. Add a second harmonic, and that is still good, because in two periods of the higher frequency, one period is made of the fundamental. If the frequency is a bit off, it will beat, as you probably know well (and can easily try generating sine waves). The (musical) fifth (which is not the fifth harmonic, in fact it is the third) correspond to a frequency which is 3/2 of the fundamental, i.e. after 3 periods of the fifth, the fundamental has made 2 periods and it is again in phase. Again, an imperfect match will cause beats. The problem is, if you do the whole circle of fifth, you raise the frequency by 3/2 at each step, and then divide by 2 each time you need to lower the octave to stay in the same middle range. Since the division and multiplication can be done in any order and the result is the same, it's easier to do all the multiplications first, and the divisions later. The total multiplicative factor of raising a fifth for 12 times is (3/2)¹² in total. That can never be a multiple of two! Hence the "true" circle of fifth is not a circle but a spiral. Even using more notes (like they do in the Eastern tradition) it does not change this fact: (3/2) multiplied by itself any number of times will never be a multiple of 2. So you need temperament, which basically is "making some or all of the fifths different from 3/2, so that the octave does not beats". Equal temperament is the mathematically easy "all the fifths are identical broken", whereas Pure Major temperament is the one which preserves the vast majority of intervals (not corresponding to a black key in C major) as pure as possible, and "screws" as much as necessary the subsequent ones, again to keep the octave pure (assuming no stretching, then with stretching we break the octave too).

For these three reasons, there is never exact sympathetic matching of the frequencies. However, even without a perfect match, there will be sympathetic resonance, as somewhat described here.

Hope this helps, at least understanding these complexity. Your kid can probably parametrize the equations described in the references above, and in a few years you guys will release a competitor of pianoteq 🤣

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