Sympathetic Resonance

dore_m

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 in future libraries (or retroactively to completed libraries). I thought I'd bring it up to some of you Physics majors - as I recall, there are many here. You might find it interesting.

I first made a midi file playing:

C4 at medium velocity, to see the waveform

C3 short at medium velocity, to see the waveform, then C3 (zero velocity) and C4 staccato at nearly same time

D3 short at med velocity, then D3 (zero velocity) and C4 staccato

Etc with E3, F3, G3, A3, A#3

This is all to see how the sympathetic harmonics are excited, and what they look like.

(Note on reading the pictures: Graph is Frequency vs Time, and the brighter the yellow, the louder the frequency.

Garritan CFX:

Noire:

To corroborate my intuition, I see that the open string harmonics are excited by the staccato note, and the ones that overlap are brighter. This is seen by the relatively continuous and brighter horizontal lines, and the darker lines that don't line up with the staccato note impulse.

First thing I noticed is that Garritan's harmonics have a periodic decrease in volume (you can see dashed lines). I simulated these overtones with sinewaves, and it definitely sounds more like pianoteq - Garritan is simulating (by recordings of overtones or possibly sinewaves with an LFO?) the "beating" effect -cool!

Anyway, I thought this was cool, and am now trying to break this down into samples and sinewaves to accentuate the resonant harmonics. If you're interested, I'll post some sound comparisons. Since this is a feasibility study, I have to decide if its a good enough mockup to code.

vagfilm

Hi. As coincidences go, I am also running some tests on resonance, triggered by a PW discussion about the claimed lack of sympathetic resonance in the VSL pianos. So, I doing some midi testing on my VSTs (which is messy, because I lack disk space in my laptop, and I have to keep deleting and reinstalling libraries; maybe I will split the test between 2 computers...). I have yet to test ModernU.

My preliminary findings are:

spectrograms give too much information... There is one main harmonic that dominates the weaker harmonics, but in the spectrograms they all look alike and it is difficult to tell the tree from the forest;
it seems that not all galaxy instruments use the same resonance engine: Grandeur seems to be much more simpler than Noire;
Each resonance engine is very different, with some being quite muddy (Garritan) and other very pristine (Pianoteq); Noire and VSL are middle ground;
VSL does have resonance and it does resonate differently on single vs multiple open strings (I don't think that Grandeur does that...), but it is a fact that it does not have silent key (???).
As the spectrograms reveal, the harmonic space is already quite populated. My intuition tells me that triggering realistic resonances for each key stroke will easily result in overall muddiness. This is a perceptional effect: it is important to understand not the realism of the total note complexity, but what are the conditions in which the LACK of resonance is perceived, and trigger a few harmonic samples only on those conditions. I hope it may be simpler than it looks.

I am still tweaking my midi test file, but will post it here when ready. I am using a test "protocol" suggested by Charles Cohen at PW.

@dore_m Since you have both the mics, the MH, and the expertise, it would be interesting to have a real world resonance test done and recorded in an acoustic. Are you up for that?

Drew-r

vagfilm

Not to muddy up this conversation, but for you guys - @vagfilm , @dore_m etc. - analyzing spectrograms of digital / midi / VI piano resonance sounds, do you use ( do they even exist / available for the DIY public?) specimen / benchmark spectrograms (or similar waveform snapshots) from actual APs/GPs that you compare, or is the digital sound arena its own separate beast for which such comparisons are not applicable or relevant?

dore_m

Drew-r analyzing spectrograms of digital / midi / VI piano resonance sounds, do you use ( do they even exist / available for the DIY public?) specimen / benchmark spectrograms (or similar waveform snapshots) from actual APs/GPs that you compare, or is the digital sound arena its own separate beast for which such comparisons are not applicable or relevant?

They don't exist - you really have to own the library, and render a MIDI file of specific keys or key combinations into a wave file and then analyze. Rendering a midi file is basically the same as recording with microphones, it yields a wave file to inspect. We have to rely on community, and each other to compare each VST we own, which makes it difficult for one person to analyze without really owning many VST's unfortunately. Luckily VSL has a 30day evaluation period, and the Pianoteq demo can be used.

CyberGene Most probably a well-crafted generic LFO beating would be enough to sound like string resonance without being exactly the same.

That's exactly what I spent this weekend doing. It has promise, even if I didn't tune the beating to exactly the correct beating frequencies.

vagfilm @dore_m Since you have both the mics, the MH, and the expertise, it would be interesting to have a real world resonance test done and recorded in an acoustic. Are you up for that?

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.

I know this is a long answer, but in doing 1, 2, 3, I think I can simulate any piano's sympathetic resonance with some recordings used as example. I just need analyze the spectrum in the recordings and simulate the relative energy with 2, and adjust 1 according to how much of the open string adds to the sound.

I'm currently negotiating/planning to sample three instruments hopefully before the end of the year. But coordinating this activity has fallen through many times in the past, which is why I'm coordinating 3 at the same time. I'm trying to figure out what sympathetic resonance conditions I should record on THEIR pianos as one of them might come up pretty quickly (I have a few friends with Steinways that I saw at a party on Saturday).

I may get to OPP (other people's pianos) first. Recording my own piano would mean tuning it again. I'll be doing that, but its not my priority right now since I might have to tune OPP soon. Gearing up to sample someone else's piano means I have to do the mic setups on my own piano and pre calibrate before I go. It's more efficient to get the mic settings, cables and stands angles pre-setup so I can be more efficient in the target piano's home. 12 mics is no small number.

So the short answer is yes, I can do it on my own piano if OPP falls through.

(sorry to be so wordy and detailed - I'm using this post as a change log in case I have to put down the testing for whatever reason)

CyberGene

I'm not sure if I can add anything useful to the discussion, as @dore_m has already made quite a good analysis. The beating is probably caused by both the usage of equal temperament, hence partials do not overlap exactly but have some difference causing beating, and similarly the inharmonicity and the offset of partials from the ideal equal temperament value. However I'm not sure for such a subtle effect one needs to do the exact calculation of partial to partial match and exact beating, etc. Most probably a well-crafted generic LFO beating would be enough to sound like string resonance without being exactly the same.

BTW, I usually turn off string resonance emulations since I often find myself scratching my head about what exactly is wrong with a software or digital piano, muddying the tone and ultimately realizing it's the string resonance which I turn off and it gets better.

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.

dore_m

Here's where others can help @CyberGene @Del Vento @vagfilm ,etc.

I did this sine wave simulation work manually in a DAW triggering Sine waves by midi note number and velocity chosen by ear/spectrogram.

For me the missing link is the theoretical power equations for the overlapping frequencies. Probably these will all be different depending on what instrument I sample, but I know there is an equation or simplification of the equation that can get me the relative power of the harmonics so I can start out in the correct ballpark without having to re-create every combination manually.

Any physics majors point me in the right direction without having re-take my college courses?

vagfilm

dore_m Any physics majors

@CyberGene, @Del Vento : no excuses... 😊

Del Vento

dore_m Here's where others can help @CyberGene @Del Vento @vagfilm ,etc.

dore_m Any physics majors point me in the right direction without having re-take my college courses?

Let's see.

dore_m For me the missing link is the theoretical power equations for the overlapping frequencies. Probably these will all be different depending on what instrument I sample, but I know there is an equation or simplification of the equation that can get me the relative power of the harmonics so I can start out in the correct ballpark without having to re-create every combination manually.

I am not sure I understand your question. The simplified theoretical treatment of sympathetic resonance tells that in the "quiet" string only the harmonics of exact frequencies existing in the "loud" note are excited. Uninteresting. In practice other frequencies are excited too, as your beatings demonstrate (I know, it's a simulation). Which frequencies? Hard to tell and in the extreme case simply everything (just push the damper pedal and hear the "ocean in the seashell" sound).

My suggestion is the same as @vagfilm : record what the acoustic does, comparing a single note with a single note when the damper of another silent one is lifted and check the difference. Not by eye as you are doing in this post, but by actually computing the difference, so you sidestep @vagfilm 's objection of spectrograms hiding the interesting information. Also try the difference between two as-identical-as-possible recordings of the same note, just to get an idea of what is normal recording-to-recording variability.

This is not much, I know, but that's all I can contribute for now (by coincidence, I just found a very old Scientific American article about the science of the sound of the piano which I was already planning to read in the coming days and might provide some insight)

dore_m

If no other way, I was just going to measure the differences in relative harmonics and use it as a guide with some lookup table or something.

But @vagfilm your comment about muddiness in some VST's makes me want to control the open string/struck string volumes with separate sliders. It's the struck string relative harmonic gains that will give each piano it's specific character and the open string harmonics that, I think create the muddiness. Not sure, just a conjecture.

dore_m

comparison-test.mp3

Just put some work in progress here. What you'll hear is the progression that I referred to in the first post, but you'll hear two versions of each note combination: Garritan sympathetic resonance (as the waveforms in the first post), then my re-creation using samples of Garritan and sine waves. Not the same, but maybe good enough?

CyberGene

I wouldn’t advertise myself as Physics major although on paper I have the degree… BTW my degree is in engineering physics and as such I’d just recommend measuring your piano for the actual relative power of partials and use that as hard-coded coefficients 😀

dore_m

CyberGene I’d just recommend measuring your piano for the actual relative power of partials and use that as hard-coded coefficients

Yeah, that was what I was planning for my next sampling project - but someone else's piano. just trying to decide which sympathetic conditions to record.

n-player

The people I would ping are: Jeff Hurchalla, bsntn99, karvala at PianoWorld. The first two have been on PianoWorld this spring, but karvala's profile indicates he has not been to PianoWord for a couple of years.

All three had great analysis and insight on VI noise floors in the PW threads. Jeff was the lead developer for Garritan although he changed careers a few years ago.

I would make a post at PW and/or PM the three.

CyberGene

n-player I recently invited Jeff and he said he might join but I guess he’s been busy.

HZPiano

Hello,

Broken-record me says he loves Modern U, in particular for the resonances that are said to be sampled (as opposed to modeled/synthetically generated) and come across as very natural, musical and hugely pleasant.

Apart from this, I'm afraid I cannot contribute much to the daredevil deep-digging analyses by y'all in this thread!

Cheers and happy musical resonances,

dore_m

Del Vento Not by eye as you are doing in this post, but by actually computing the difference, so you sidestep @vagfilm 's objection of spectrograms hiding the interesting information.

So I create the sympathetic resonance situation by rendering MIDI/Garritan. I have those waveforms. I then use Garritan without the sympathetic resonances and create the harmonics using sine waves in Kontakt, and I get the results in the sound file. Yes, I'm doing it by "sight" using the graphs that I've attached, but I also am using the spectrum analyzer plots where I can measure the difference in amplitude for each partial's frequency. I'm not confused by the spectrogram and spectrum analyzer plots at all. I can see where all of the frequencies are coming from - either open string, or overlapping harmonics between open string and staccato note.

But yes, I need to record a piano in different situations to re-create the partial's amplitudes definitely. It's just a real pain to re-create these with sine waves for each combination unless I had an equation or something to get me close. I can code something to find all of the overlapping harmonics -that seems easy. But guessing the loudness of each resonant frequency and/or matching a recording is very time consuming.

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?