Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Simultaneous partials in a string: reality or myth?

Thank you for the link to that paper, Prout. My point was that you don't have to wade through all the math in detail, though it helps to see how the authors built their model. The last two sections describe their results and conclusions.

The quote says that the sound of a piano is more than just the sum of the partials produced by its strings and, as you'll know, it goes on to talk about soundboard resonances excited by the initial transients.

I was particularly interested in the initial longitudinal wave and its effect on soundboard displacement downward which was consequently 'pulled up' by the the arrival of the transverse wave.

Indeed, but at no point does it say that the partials in a real piano are not real. The model is an attempt to explain the real partials that are actually present - these are not abstractions, they are really there.

Paul.

Prout,
Thanks for linking the paper. I am reading it but it will take some time to fully grok it.

Discussing competing models can reach the absurdity of "number of angels on the head of a pin" at times. All models contain approximations and simplifications. I hope our fellow PW posters realize that. The real test is how useful a model is for making predictions.

I would like a better explanation of the mechanisms creating "Phantom Partials". Conklins work on I find very muddy. It could be my weak math abilities are the hindering point.

Precisely. Choose a model, or develop one, that is suitable for the purpose. One may work for tuning, another for "improving" tone.

Interestingly, the authors of the paper consider their model as a crude skeleton of the instrument, but they go on to say:

However, even in its imperfect form, we believe that the model could be used as a companion tool for piano making. In this context, investigating the influence of soundboard modifications on the radiation of sound and on string-bridge coupling appear as potentially fruitful examples.

And that, Ian, was all this thread was about.

"Q.E.D."

I guess I may have missed the obvious point of the thread. For me, the behaviour of the vibrating string must contain all the information needed for us to hear what we hear. Even resultant tones, which supposedly are constructed in our brains, still require the base pitches necessary. My point has always been that, at any moment in time, there is only one thing that can be measured, and that is the amplitude of something. Somehow our brains reconstruct the variations in amplitude and allow us to hear all the noise, partials, whatever, that actually exist, if you will, in the vibrating string, and the mathematics of a quantized sample, can also simulate with some fidelity, that vibrating string and allow us to appreciate its complexity.

Yes. See Fig 12 in the paper: actual and simulated hammer acceleration, string displacement, bridge acceleration at string end, soundboard acceleration, sound pressure. As a simple minded exercise compare the plots of string displacement with those of sound pressure.

All,

This thread has been somewhat confused by mingling different issues, e.g.
* actual string motion (as a sum of actual, real partials),
* decomposing a sound into partials and reconstituting it from them
* modelling these things mathematically
* the difference between the string's vibrational modes (partial envelope) and the actual sound generated by the soundboard (soundboard anisotropy, coupling at the bridge, etc.)

All I really wanted to find out is whether it's possible for a string to make a motion consisting of several simultaneous and real partials - preferably without the need to "disassemble".

Kees, I did read what you wrote, but I didn't necessarily understand its pertinence to the topic. (That may well be my shortcoming, not yours!)

For example:


And yet, notes on a piano, in spite of being time dependent, all exhibit rather well-defined frequencies, at each partial. I mean, we've been talking about these exact pitches in the temperament threads for ages. So what did you aim for with the above statement?

Or this one:



It might be "old" and "well-known" to you. At least to me and Paul, non-analysable vibrations are a novelty. Also, you posted the above in a thread on string motion (not sound). Are we to understand that the mechanical motion of a real string cannot be fully described by partial analysis either? If so, I'd really like to understand this better.

Anyhow, I don't want to belabor any points, nor cause you too much trouble. I've had some partial answers , so for my part, this thread can go into decay.

Mark,

The fact that if you remove the "partials" from the piano sound you do not get silence, demonstrates the presense of non-periodic components in the piano sound. I don't really know what to say about "a string by itself". The strings I have in my closet do not vibrate at all, know what I mean?

I don't want come over as a smart-ass know-it-all, but it is a technical topic with a large scientific literature that I am somewhat familiar with as that was my trade in the past. I think a physics forum is the place to discuss it. You can ask questions on http://www.physicsforums.com/: there are certified "experts" there that are extremely helpful for understanding at all levels.

Kees

Kees, I really think it would be better if you came across as a "smart-ass-know-it-all" than how you are currently coming across. I've read every post you've made on this matter and the one thing that is consistent is your refusal to back your position with detailed arguments. It's all shrouded in riddles, obfuscations and statements about how much you know about the subject, and how all answers can be found elsewhere. I don't consider this to be a healthy style of discussion. It's essentially holding yourself at arm's length from the discussion so you can't be properly challenged. I would much rather see a substantive justification of your opinion than worry about issues of modesty. So how about it? This is the place to discuss it. It is being discussed right here, right now.

No thanks.

Kees

In one sense I think BDB is right.

Of course a piano tone contains a summation of many frequencies above the fundamental. I'm not sure partial is the best term, but eigenvector while more precise is less understandable.

But the minute we talk about a wave we're talking about a visual representation, not of the sound, but of a mathematical equation.

For example. A limp string vibrating at low amplitude would produce something close to a sine wave. What does that really mean? Can you see a sine wave with a stroboscope? No, what it means is that if you took one point on that string, and measured the displacement over time, and produced a graph of the displacement over time, THE GRAPH would look like a sine wave. Not the string.

A square wave could theoretically be produced by summing the sine waves from several strings. But nowhere would a strobe show anything square looking.

Hi Y'all,

At the risk of dumbing down the conversation, I am posting a link to a video I made describing, in my own way, the harmonic series. As Kees said, it is defined by humans, for humans. And since I am a human teaching humans how to tune, I thought I would create this video to speed things up.

Some of it you might find it interesting, although it doesn't really move this conversation forward. Only to say that, as a practical application, I don't see the benefit of answering the question, although it is still interesting.

My video on the harmonic series, from the perspective of teaching a beginning piano tuning student so they may understand other aural tuning concepts that are built upon this subject, e.g. coincidental partials, etc.

http://youtu.be/dCmy6N3DnV8

Comments welcomed.

P.S. go right to the last section to hear me singing the harmonic series on one pitch.

Good explanation, Mark.

A question; when tuning and listening for, say, the second partial do you filter out its "coincident" partials - the fourth, sixth, eighth, and so on?

In other words do you listen to it as a pure tone (second partial only) or a composite tone (even numbered partials together)?

And what about the fundamental and other partials?

A single audio speaker, producing a sound containing multiple partials, would have its piston moving slowly in and out at f1, and imposed on that motion is a simultaneous motion at the higher partials. This can, in fact, create a Doppler frequency shift on the higher partials as the large scale motion of the piston at f1 occurs. One more reason to use multiple drivers. Can one assume that this same phenomenon occurs on a string? Looking at an analogue waveform of the sensed vibrations clearly shows this type of amplitude variation.

Hi Ian,

Thanks for the compliment, and for watching.

Have you heard about that crazy thing I did with my voice before? Not sure what it is called. I thought I discovered it myself (yes, I know, arrogant) but my nephew, who is an actor, said it is some kind of native thing. Not sure which natives though.

I'm not sure I understand your questions. When individual notes or intervals are played, all the partials can be heard, if your ear is trained well enough to focus on them, but it takes lots of time and practice.

So, no, it is not a figment of the imagination. I.e. there are scientific ways that we can separate the partials and look at them individually, but they are there in the whole tone. I am able to isolate specific partial frequencies when listening to a single note or interval, and then that frequency appears more prominent in my ear.

I'm sure I am not the only one, and anyone with a musical ear, who has done any transcribing or lifting of arrangements from recordings, should be able to isolate partials from a single string, especially if trying to isolate the third partial from a bass string. IME, that is the easiest to hear.

To answer your question, no, I do not think anyone can claim to hear only a pure sine wave when listening to a complete musical tone. We can only perceive the isolated partial more prominently, which helps to identify and hear beats better, for the purpose of comparing with other beats, and refining pitches on the piano.

Hope that answers your questions.

Cheers

Prout,
I am having a difficult time seeing how Doppler frequency shift could occur in the string medium. Doesn't a Doppler frequency shift only occur between the steady state wave source that is in motion relative to the sensing point? So the piano and listener would have to be moving in space, (space with atmosphere for sound), relative to each other for a Doppler shift to be created.

The first good, succinct, easy-to-understand video on the subject that I've seen anywhere to date. Bravo!

Kees could do a better job of explaining I think, but, at the fundamental pitch, a single maximum amplitude displacement would occur at the centre of the string. Imposed on this displacement would be simultaneous multiple nodes occurring at the various partial frequencies. Those partials would be on a moving string, hence exhibiting a doppler shift with reference to the listener.

Edit: In the case of the speaker, and, if I am correct, a string, when it moves toward the listener the higher order partials will be frequency shifted up, and when the speaker cone or string move away from the listener, it will be shifted lower. This effect of a speaker has been measured. I don't know if this is something I could detect with FFT analysis.