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#2222951 - 01/30/14 05:41 AM Simultaneous partials in a string: reality or myth?
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1958
Loc: Pretoria, South Africa
In the P12 thread there was a side discussion on partials.

BDB stated the notion that a string would have to "disassemble itself to vibrate at a variety of different sine waves".

Kees agreed [Edit: in principle], stating that "decomposing a sound into partials is a (often useful) approximation invented by humans, no more, no less".

Pyropaul, on the other hand, wrote that "The string has many different modes of vibration and they all occur simultaneously - it doesn't have to "disassemble" itself."

Essentially, BDB says that observing partials is only an artefact of a stroboscope: "You are describing an effect of the strobe, not of the vibration of the string. It is statistical, rather than physical, sampling the position of the string at specific moments."

Jeff, OP of the P12 thread, asked for a new topic to be started, which is what I'd like to do here, in response (rebuttal, really) to BDB and Kees.

Originally Posted By: BDB
We watched a vibrating string in real time, without stroboscopic effects.


As did we.

If your demonstration delved into partials (which it should have, if it was any good), you should have seen something like this (again, these are taken without any stroboscopic effects, they are blurred long-time exposures):
(taken from metasynthesis.com)
(taken from physicsthebook.com)
Partials are no approximation. They are real, and they can be excited simultaneously. The resultant string movement is simply the sum of the partials at each point in space and time. For example:
(taken from projects.kmi.open.ac.uk)
And an animation showing the sum of partials 1, 2 and 3:
(taken from scratch.mit.edu)

What pyropaul wrote, is therefore true: any periodic oscillation can be expressed/reconstructed as a sum of sine and cosine waves (with individual frequencies and amplitudes). This is the gist of Fourier transforms, and the frequency spectra that Kees himself has been posting here lately.

This page also describes it rather well:
http://www.acs.psu.edu/drussell/Demos/string/Fixed.html

Partials are no "invented approximation", and there is no need for strings to "disassemble" themselves in order to vibrate simultaneously at different frequencies. What the strobe captures, is no statistical artefact, but a snapshot of a real vibration at the strobe's frequency.


Edited by Mark R. (01/30/14 05:43 AM)
Edit Reason: given in post.
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2222970 - 01/30/14 07:08 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Mark,

thank you very much for posting this. I don't understand why some people were so vehemently opposed to the idea. Piano tuners, of all people, are the most aware of partials in a vibrating string.

Don't forget, also, the discussions previously about longitudinal and transverse waves. These are also just as real as the partials we hear.

As you state, the position of a vibrating string in time is described by the superposition of multiple modes of oscillation with different amplitudes, frequencies and phases. And, as I mentioned earlier, inharmonicity is due to the stiffness of the string making for an effectively shorter string for the higher modes of vibration.

Paul.

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#2222977 - 01/30/14 07:41 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4912
Loc: Bradford County, PA
To look at it another way, "If a tree falls in a forest and there is no one around to hear it, does it make an noise?"

Those little "hairs" in you inner ear is the interface between what is happening with the air that is being moved by the string and what you percieve. It could be argued that those little hairs is what breaks the string into little pieces that vibrate at different frequencies. Each little "hair" has it's own resonate frequency.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2222980 - 01/30/14 07:46 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
bkw58 Offline

Silver Supporter until December 19, 2014


Registered: 03/14/09
Posts: 1672
Loc: Conway, AR USA
Piano Tuning 101.

"A vibrating wire subdivides itself into many
simultaneously vibrating fractions. Each fraction
produces an audible pitch of its own, called a partial."

- A. Reblitz
(See his illustration, 1993 ed., 6-2, p204)
_________________________
Bob W.
Retired piano technician
Piano Technicę

"Never argue with a fool, people may not be able to tell you apart." - author unknown

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#2222981 - 01/30/14 07:57 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
ando Offline
3000 Post Club Member

Registered: 11/23/10
Posts: 3546
Loc: Melbourne, Australia
I would have thought this is an absolute no-brainer. It staggers me that BDB would claim what he did. Not only are they measurable, but the human ear can selectively focus on many different partials as separate tones - provided they have good listening skills and know what they are listening for. I mean, you tuners are talking about hearing these things every darn day - surely you can't claim them to be mythical when you are using and hearing them in your tunings and inharmonicity judgements? As a guitarist, I am intensely aware of these partials and how they can be exploited. They are certainly real. Moreover, it's the relative strengths of different partials that help us to distinguish one instrument from another (coupled with attack/sustain/decay envelope).

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#2222986 - 01/30/14 08:19 AM Re: Simultaneous partials in a string: reality or myth? [Re: UnrightTooner]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: UnrightTooner
To look at it another way, "If a tree falls in a forest and there is no one around to hear it, does it make an noise?"

Those little "hairs" in you inner ear is the interface between what is happening with the air that is being moved by the string and what you percieve. It could be argued that those little hairs is what breaks the string into little pieces that vibrate at different frequencies. Each little "hair" has it's own resonate frequency.


It's not as simple as that. The hairs in your ear don't cover the 10 octaves we can hear - there's no way you have a hair long enough to resonate at C0, for example. The string's motion is described by the superposition of all of its harmonics, same for the motion of the air molecules that convey the energy from the string to your ear. Microphones don't have resonant hairs but they also faithfully reproduce the harmonics when the sound is converted into an electrical signal. The change of voltage is also perfectly described by superposition of sine waves too.

Paul.

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#2222997 - 01/30/14 08:35 AM Re: Simultaneous partials in a string: reality or myth? [Re: UnrightTooner]
bkw58 Offline

Silver Supporter until December 19, 2014


Registered: 03/14/09
Posts: 1672
Loc: Conway, AR USA
Originally Posted By: UnrightTooner
To look at it another way, "If a tree falls in a forest and there is no one around to hear it, does it make an noise?"

Those little "hairs" in you inner ear is the interface between what is happening with the air that is being moved by the string and what you percieve. It could be argued that those little hairs is what breaks the string into little pieces that vibrate at different frequencies. Each little "hair" has it's own resonate frequency.


It's probably more simple than QP. The little hairs detect, though I may be splitting hairs.
_________________________
Bob W.
Retired piano technician
Piano Technicę

"Never argue with a fool, people may not be able to tell you apart." - author unknown

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#2223006 - 01/30/14 09:00 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4912
Loc: Bradford County, PA
If the guy that wrote This Thesis was still around, he might be able to explain it. (Yeah, that's my Dad! smile )
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2223014 - 01/30/14 09:07 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1958
Loc: Pretoria, South Africa
It's not the hairs that resonate. It's the basilar membrane between the two cochlear channels. Pitch is not recognised by hair length, but by the point of maximum vibration of the basilar membrane. The highest frequencies are sensed right at the point of entry (oval window), where the basilar membrane is stiffest, while progressively lower frequencies cause the basilar membrane to vibrate progressively deeper into the cochlea, where it becomes progressively more supple.

Stiff bodies have high resonant frequencies, supple ones have low resonant frequencies.

http://en.wikipedia.org/wiki/Cochlea#Detailed_events
http://bio1152.nicerweb.com/Locked/media/ch50/pitch.html

So, the cochlea does cover the 10 octaves we can hear, but without the need for 10 octaves (2^10 = 1024) of hair lengths. It's the stiffness gradient of the basilar membrane that differentiates pitch.


Edited by Mark R. (01/30/14 09:09 AM)
Edit Reason: Addressed post to all, not only Paul.
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2223021 - 01/30/14 09:36 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4912
Loc: Bradford County, PA
OK, Mark, but the question remains, and I think it is the point that BDB is making in an argumentum ad absurdum, do the partials exist outside of observing them? Like does the sun rise or does the earth turn?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2223025 - 01/30/14 09:50 AM Re: Simultaneous partials in a string: reality or myth? [Re: UnrightTooner]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: UnrightTooner
OK, Mark, but the question remains, and I think it is the point that BDB is making in an argumentum ad absurdum, do the partials exist outside of observing them? Like does the sun rise or does the earth turn?


Yes of course they do, unless we want to go down a rat-hole of talking about quantum reality. But otherwise, partials are real, they are not an artifact of our hearing system. I find it quite surprising that so many seem to doubt this.

Would anyone argue there is such a thing as white light? At one time, yes, but Newton showed the more interesting reality. It's essentially the same argument with sound - all sound is composed of sine waves of various frequencies and intensities. There is no "piano wave" or "trumpet wave" anymore than there is a "white ray".

Paul.

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#2223034 - 01/30/14 10:11 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1696
Loc: Vancouver, Canada
Piano-sound vibrations are not periodic.

Kees

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#2223035 - 01/30/14 10:12 AM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4912
Loc: Bradford County, PA
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner
OK, Mark, but the question remains, and I think it is the point that BDB is making in an argumentum ad absurdum, do the partials exist outside of observing them? Like does the sun rise or does the earth turn?


Yes of course they do, unless we want to go down a rat-hole of talking about quantum reality. But otherwise, partials are real, they are not an artifact of our hearing system. I find it quite surprising that so many seem to doubt this.

Would anyone argue there is such a thing as white light? At one time, yes, but Newton showed the more interesting reality. It's essentially the same argument with sound - all sound is composed of sine waves of various frequencies and intensities. There is no "piano wave" or "trumpet wave" anymore than there is a "white ray".

Paul.


Are there square waves, triangle waves and saw tooth waves, or just superimposed sine waves?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2223041 - 01/30/14 10:21 AM Re: Simultaneous partials in a string: reality or myth? [Re: UnrightTooner]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: UnrightTooner
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner
OK, Mark, but the question remains, and I think it is the point that BDB is making in an argumentum ad absurdum, do the partials exist outside of observing them? Like does the sun rise or does the earth turn?


Yes of course they do, unless we want to go down a rat-hole of talking about quantum reality. But otherwise, partials are real, they are not an artifact of our hearing system. I find it quite surprising that so many seem to doubt this.

Would anyone argue there is such a thing as white light? At one time, yes, but Newton showed the more interesting reality. It's essentially the same argument with sound - all sound is composed of sine waves of various frequencies and intensities. There is no "piano wave" or "trumpet wave" anymore than there is a "white ray".

Paul.


Are there square waves, triangle waves and saw tooth waves, or just superimposed sine waves?


Just the latter - it is the superimposition that creates the waveshapes we see as square, triangle or sawtooth on an oscilloscope. Try it with an analog synthesiser and see what you get when you add sine waves of the right frequencies and amplitudes.

Paul.

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#2223043 - 01/30/14 10:25 AM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: DoelKees
Piano-sound vibrations are not periodic.

Kees


So? What is it your harmonic analysis of beat rates is showing, if not the partials that make up the sound? Of course the amplitudes and frequencies may vary in time, but the resultant waveform can still be perfectly described by the appropriate sum of sines at the right frequencies, amplitudes and phases. Everything goes back to the basic physics of simple harmonic motion - motion that cannot be decomposed any further. This may also be the reason that we hear sinewaves as "pure".

Paul.

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#2223049 - 01/30/14 10:35 AM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: DoelKees
Piano-sound vibrations are not periodic.

Kees


How about bells? You even have a nice java applet that generates the sound of bells.

Kees Bell Generator

The write up even states: "The bell has 50 modal frequencies"

So if a bell can be composed of 50 frequencies, why do you think a piano note cannot be similarly composed?

Paul.

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#2223052 - 01/30/14 10:39 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1958
Loc: Pretoria, South Africa
Jeff,

I don't think BDB's comment was a re-phrasing of the (in)famous philosophical question, "does the act of observation make it any more or less real". Read my opening post again. BDB was questioning the very presence of actual partials in a vibrating string, and the fact that a strobe makes them visible, he called a statistical artefact.

If you first strike a note on the piano and then touch the speaking length exactly halfway, the second (and fourth, sixth etc.) partial will continue to ring for a while. The same goes for the other partials. Now the act of touching cannot generate any partials, as it doesn't impart any energy to the string. This means that all those partials were already physically present in the string before you touched it.

The movement of the string is the sum, no more, no less, of all the partials physically present, each with its own frequency, amplitude and phase. Granted, as soon as more than two or three partials are combined in one string, the resulting shape of the string at any given moment will be incredibly complex. Nevertheless, the partials are all there, each one of them very much physical and real.

Whether the string vibration is observed
a) in the time domain (overall string motion vs. time), or
b) in the frequency domain (individual partials resolved by cochlea or by stroboscope), or
c) both, or
d) neither,
doesn't change the vibration [Edit: being a sum of sines[/i] one bit.

In other words, the information that's carried in both domains is exactly the same, and a transformation from time domain to frequency domain or vice versa doesn't add or remove any information from the signal.


Edited by Mark R. (01/30/14 10:44 AM)
Edit Reason: given in post.
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

Top
#2223054 - 01/30/14 10:43 AM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1696
Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: DoelKees
Piano-sound vibrations are not periodic.

Kees


So? What is it your harmonic analysis of beat rates is showing, if not the partials that make up the sound? Of course the amplitudes and frequencies may vary in time, but the resultant waveform can still be perfectly described by the appropriate sum of sines at the right frequencies, amplitudes and phases. Everything goes back to the basic physics of simple harmonic motion - motion that cannot be decomposed any further. This may also be the reason that we hear sinewaves as "pure".

Paul.

A "sine wave" with a time dependent amplitude is not a sine wave. It does not even have a well-defined frequency.

In fact my "partials" represent the best approximation by a sum of non-sine wavelets, where each wavelets is the product of an exponential and a sinusoid. That is also a matter of choice, there are arguments the exponential envelope is better modeled by the product of a power function and an exponential. For the case of hand, it makes little difference for the approximately harmonic partials that are of interest here.

I assure you if you reassemble all the partials and resynthesize the sound you do not get the original sound back: just the part that is well approximated as a sum of partials.

This is really all old well-known stuff, investigated in depth in the literature. For example there is a sound synthesis method from the '80-ies by Rodet where you explicitly split the sound into something that is modeled by partials + a residual that can't be modeled like that.

No offense, but a little knowledge is a dangerous thing.

Kees

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#2223056 - 01/30/14 10:48 AM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Kees,

I'm well aware of the approximations introduced by considering band-limited signals. Do you believe that a vibrating string simultaneously contains multiple modes of vibration? I think we're getting to the point where we're effectively arguing about the number of angels on the head of a pin. Harmonics are a real phenomenon and are used daily by piano tuners.

Paul.

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#2223061 - 01/30/14 10:55 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1958
Loc: Pretoria, South Africa
So, Kees, if there are no real partials present, as BDB maintains, what gets the soundboard vibrating at those frequencies - as you've kept showing us in your spectrograms? What creates those (periodic!) beats when tuning an interval?

By the way, I would have thought it rather obvious that we're not considering the decay envelopes at this stage. We're considering constituent frequencies, and for such purposes, a slowly damped sine wave can still be considered a sine wave, I would submit.

[Edit: but perhaps, nothing is obvious. I'm not a physicist or signal processing expert... Just battled through two years of university physics.]


Edited by Mark R. (01/30/14 10:58 AM)
Edit Reason: given in post.
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

Top
#2223067 - 01/30/14 11:05 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1696
Loc: Vancouver, Canada
I have no intention of guessing what BDB meant, why don't you ask him?

Kees

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#2223089 - 01/30/14 11:32 AM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: DoelKees
I have no intention of guessing what BDB meant, why don't you ask him?

Kees


I asked you this question:

Do you believe that a vibrating string simultaneously contains multiple modes of vibration?

Given the area of your PhD research (and your impressive set of publications), I'm genuinely interested in your answer.

Paul.

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#2223091 - 01/30/14 11:36 AM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1696
Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: DoelKees
I have no intention of guessing what BDB meant, why don't you ask him?

Kees


I asked you this question:

Do you believe that a vibrating string simultaneously contains multiple modes of vibration?

Given the area of your PhD research (and your impressive set of publications), I'm genuinely interested in your answer.

Paul.

To repeat:
Originally Posted By: DoelKees
Decomposing a sound into partials is a (often useful) approximation invented by humans, no more no less.

Kees

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#2223094 - 01/30/14 11:40 AM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: DoelKees
I have no intention of guessing what BDB meant, why don't you ask him?

Kees


I asked you this question:

Do you believe that a vibrating string simultaneously contains multiple modes of vibration?

Given the area of your PhD research (and your impressive set of publications), I'm genuinely interested in your answer.

Paul.

To repeat:
Originally Posted By: DoelKees
Decomposing a sound into partials is a (often useful) approximation invented by humans, no more no less.

Kees


I'm not asking you about the decomposition. I'm asking you about the vibration of an actual string. Can it contain more than one mode of vibration at once?

Paul.

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#2223099 - 01/30/14 11:45 AM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4912
Loc: Bradford County, PA
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner
OK, Mark, but the question remains, and I think it is the point that BDB is making in an argumentum ad absurdum, do the partials exist outside of observing them? Like does the sun rise or does the earth turn?


Yes of course they do, unless we want to go down a rat-hole of talking about quantum reality. But otherwise, partials are real, they are not an artifact of our hearing system. I find it quite surprising that so many seem to doubt this.

Would anyone argue there is such a thing as white light? At one time, yes, but Newton showed the more interesting reality. It's essentially the same argument with sound - all sound is composed of sine waves of various frequencies and intensities. There is no "piano wave" or "trumpet wave" anymore than there is a "white ray".

Paul.


Are there square waves, triangle waves and saw tooth waves, or just superimposed sine waves?


Just the latter - it is the superimposition that creates the waveshapes we see as square, triangle or sawtooth on an oscilloscope. Try it with an analog synthesiser and see what you get when you add sine waves of the right frequencies and amplitudes.

Paul.


It is an easy thing to create an electronic square wave generator, and there is no need to superimpose an infinite number of sine waves at exact intregal frequencies (partials) and at exactly the same amplitude to do so.

Do you see my point?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2223102 - 01/30/14 11:47 AM Re: Simultaneous partials in a string: reality or myth? [Re: ando]
bkw58 Offline

Silver Supporter until December 19, 2014


Registered: 03/14/09
Posts: 1672
Loc: Conway, AR USA
Originally Posted By: ando
...I mean, you tuners are talking about hearing these things every darn day - surely you can't claim them to be mythical when you are using and hearing them in your tunings and inharmonicity judgements?


I understand. Take heart. It may not be quite that bad. I would venture 99.9% of full time professional piano technicians do not post here. And so, what we see first hand is only a miniscule part of the whole. I wouldn't even call it a microcosm. Some remarks are based in fact and reality. But much is theory and has nothing whatsoever to do with what happens on the job. Another day, it might. At the moment, it's just postulation. Often there is misunderstanding; at other times statements are just flat out wrong.
_________________________
Bob W.
Retired piano technician
Piano Technicę

"Never argue with a fool, people may not be able to tell you apart." - author unknown

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#2223103 - 01/30/14 11:50 AM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1696
Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: DoelKees
I have no intention of guessing what BDB meant, why don't you ask him?

Kees


I asked you this question:

Do you believe that a vibrating string simultaneously contains multiple modes of vibration?

Given the area of your PhD research (and your impressive set of publications), I'm genuinely interested in your answer.

Paul.

To repeat:
Originally Posted By: DoelKees
Decomposing a sound into partials is a (often useful) approximation invented by humans, no more no less.

Kees


I'm not asking you about the decomposition. I'm asking you about the vibration of an actual string. Can it contain more than one mode of vibration at once?

Paul.

I'm not interested in discussing the meaning of that question, sorry.

Kees

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#2223106 - 01/30/14 11:56 AM Re: Simultaneous partials in a string: reality or myth? [Re: UnrightTooner]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: UnrightTooner
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner
OK, Mark, but the question remains, and I think it is the point that BDB is making in an argumentum ad absurdum, do the partials exist outside of observing them? Like does the sun rise or does the earth turn?


Yes of course they do, unless we want to go down a rat-hole of talking about quantum reality. But otherwise, partials are real, they are not an artifact of our hearing system. I find it quite surprising that so many seem to doubt this.

Would anyone argue there is such a thing as white light? At one time, yes, but Newton showed the more interesting reality. It's essentially the same argument with sound - all sound is composed of sine waves of various frequencies and intensities. There is no "piano wave" or "trumpet wave" anymore than there is a "white ray".

Paul.


Are there square waves, triangle waves and saw tooth waves, or just superimposed sine waves?


Just the latter - it is the superimposition that creates the waveshapes we see as square, triangle or sawtooth on an oscilloscope. Try it with an analog synthesiser and see what you get when you add sine waves of the right frequencies and amplitudes.

Paul.


It is an easy thing to create an electronic square wave generator, and there is no need to superimpose an infinite number of sine waves at exact intregal frequencies (partials) and at exactly the same amplitude to do so.

Do you see my point?


I do see your point, but it doesn't mean that the electronic square wave is not composed of partials. All of analog electronic communications uses this fact, whether you believe it or not.

For a simple demonstration on strings, though, try plucking a guitar string at different points along its length and hear the timbre change. You should be able to find the point where there are no even harmonics and the timbre sounds more like a square wave (or an oboe).

Paul

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#2223108 - 01/30/14 12:01 PM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
pyropaul Offline
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Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: DoelKees
I have no intention of guessing what BDB meant, why don't you ask him?

Kees


I asked you this question:

Do you believe that a vibrating string simultaneously contains multiple modes of vibration?

Given the area of your PhD research (and your impressive set of publications), I'm genuinely interested in your answer.

Paul.

To repeat:
Originally Posted By: DoelKees
Decomposing a sound into partials is a (often useful) approximation invented by humans, no more no less.

Kees


I'm not asking you about the decomposition. I'm asking you about the vibration of an actual string. Can it contain more than one mode of vibration at once?

Paul.

I'm not interested in discussing the meaning of that question, sorry.

Kees


That's a shame as it is pertinent to the discussion about pianos. To be honest, I don't find it interesting either, because there is nothing to discuss as it is an indisputable fact of the physics of the motion of a string. But hey, people are free to believe in flying spaghetti monsters if they choose.

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#2223111 - 01/30/14 12:12 PM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
DoelKees Offline
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Loc: Vancouver, Canada
Originally Posted By: pyropaul
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: DoelKees
I have no intention of guessing what BDB meant, why don't you ask him?

Kees


I asked you this question:

Do you believe that a vibrating string simultaneously contains multiple modes of vibration?

Given the area of your PhD research (and your impressive set of publications), I'm genuinely interested in your answer.

Paul.

To repeat:
Originally Posted By: DoelKees
Decomposing a sound into partials is a (often useful) approximation invented by humans, no more no less.

Kees


I'm not asking you about the decomposition. I'm asking you about the vibration of an actual string. Can it contain more than one mode of vibration at once?

Paul.

I'm not interested in discussing the meaning of that question, sorry.

Kees


That's a shame as it is pertinent to the discussion about pianos. To be honest, I don't find it interesting either, because there is nothing to discuss as it is an indisputable fact of the physics of the motion of a string. But hey, people are free to believe in flying spaghetti monsters if they choose.

OK, then, I'll say some more stuff, but I get the feeling I already said it. The motion of the "ideal string" taught in high-school can be completely described as the sum of in infinite number of harmonic vibration modes. The motion of a real string can not. A piano is more than a single string and is quite complicated. Partial analysis is a useful approximation but... etc. as I posted already.

Kees

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#2223114 - 01/30/14 12:15 PM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
prout Offline
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Posts: 770
Originally Posted By: DoelKees

OK, then, I'll say some more stuff, but I get the feeling I already said it. The motion of the "ideal string" taught in high-school can be completely described as the sum of in infinite number of harmonic vibration modes. The motion of a real string can not. A piano is more than a single string and is quite complicated. Partial analysis is a useful approximation but... etc. as I posted already.

Kees


Well stated. This argument is getting stale.

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#2223145 - 01/30/14 12:59 PM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4912
Loc: Bradford County, PA
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner


It is an easy thing to create an electronic square wave generator, and there is no need to superimpose an infinite number of sine waves at exact intregal frequencies (partials) and at exactly the same amplitude to do so.

Do you see my point?


I do see your point, but it doesn't mean that the electronic square wave is not composed of partials. All of analog electronic communications uses this fact, whether you believe it or not.

.....


Hmmm... if I take a log and cut it and split it into cord wood, does that mean the log was always made of cord wood?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2223154 - 01/30/14 01:19 PM Re: Simultaneous partials in a string: reality or myth? [Re: UnrightTooner]
pyropaul Offline
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Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: UnrightTooner
Originally Posted By: pyropaul
Originally Posted By: UnrightTooner


It is an easy thing to create an electronic square wave generator, and there is no need to superimpose an infinite number of sine waves at exact intregal frequencies (partials) and at exactly the same amplitude to do so.

Do you see my point?


I do see your point, but it doesn't mean that the electronic square wave is not composed of partials. All of analog electronic communications uses this fact, whether you believe it or not.

.....


Hmmm... if I take a log and cut it and split it into cord wood, does that mean the log was always made of cord wood?


No, it was made of quarks. You just didn't divide into fundamental units.

Why do you think computers emit radio frequency interference? Part of the reason is that their square wave clocks emit harmonics that are in that part of the spectrum. Anyway as Prout said, this is getting stale. I'm an electronic engineer by trade so I just use this stuff quietly, irrespective of whether others believe it or not.

Paul.


Edited by pyropaul (01/30/14 01:20 PM)

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#2223163 - 01/30/14 01:31 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
UnrightTooner Offline
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Paul:

In a former life I had an FCC technician license. smile
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Part-Time Tuner
Who taught the first chicken how to peck?

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#2223228 - 01/30/14 03:41 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Mark R. Offline
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Posts: 1958
Loc: Pretoria, South Africa
Well, now suddenly Kees submits the argument that a piano has multiple strings...

But still, nobody as yet has shown where the "approximation" of partial analysis falls short in a real string, nor has anyone shown that real partials (modes) cannot co-exist in a real string.

Until such time, I'll stick with the understanding that a real, vibrating string does contain partials, and that the string's motion is exactly the sum of those partials. They might be damped at different rates, they might be bounded by one slightly non-rigid termination of varying impedance, etc.etc., but together they still constitute the whole motion. (What else would the motion be made up of, if not its constituents?)

This understanding certainly seems to be good enough for tuning the dang thing, even for Kees doing his spectrograms on it.

Many fascinating responses to my opening post, I thank you all.
_________________________
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1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2223231 - 01/30/14 03:48 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
prout Offline
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An excellent paper on the complexities of string motion and coupling on a grand piano. Well worth the effort of wading through the math.


http://hal.archives-ouvertes.fr/docs/00/78/75/51/PDF/RR-8181.pdf

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#2223235 - 01/30/14 04:03 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
DoelKees Offline
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Loc: Vancouver, Canada
[quote=Mark R.
But still, nobody as yet has shown where the "approximation" of partial analysis falls short in a real string,/quote]
I did show that (subtract partials and see), noone reads what I write it seems.

Kees

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#2223251 - 01/30/14 05:02 PM Re: Simultaneous partials in a string: reality or myth? [Re: prout]
Withindale Offline
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Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: prout
An excellent paper on the complexities of string motion and coupling on a grand piano. Well worth the effort of wading through the math.

http://hal.archives-ouvertes.fr/docs/00/78/75/51/PDF/RR-8181.pdf

Well worth the effort of wading through the math.... or reading about the results of the simulations, e.g:

Observations made on real signals show that the pressure and soundboard motion spectra, including the bridge, have a denser and richer content than the strings. The simulations help here to understand these differences and identify the additional spectral components.

QED.


Edited by Withindale (01/30/14 06:41 PM)
_________________________
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Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2223257 - 01/30/14 05:19 PM Re: Simultaneous partials in a string: reality or myth? [Re: Withindale]
prout Offline
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Registered: 11/14/13
Posts: 770
Originally Posted By: Withindale
Originally Posted By: prout
An excellent paper on the complexities of string motion and coupling on a grand piano. Well worth the effort of wading through the math.

http://hal.archives-ouvertes.fr/docs/00/78/75/51/PDF/RR-8181.pdf

... or read about the results of the simulations, e.g:

Observations made on real signals show that the pressure and soundboard motion spectra, including the bridge, have a denser and richer content than the strings. The simulations help here to understand these differences and identify the additional spectral components.

QED.

Sorry Ian, I don't get your point. I am, at the moment, training in a flight simulator, something I have to do every six months for a week. When I completed my initial training on this particular jet, I did my first flight in the real airplane with a full load of paying passengers. I guess the governments of the world have confidence in the fidelity of simulations to describe perceived reality.

This paper has interested me over the last few months because it helps me to understand the complexity of the interactions that go on in a piano when a key is pressed. My own simulations at home are an attempt to quantify some of those complexities. I do this for fun.

Edit: It doesn't make my playing any better, but it does help me to better understand the results of my tunings.


Edited by prout (01/30/14 05:20 PM)

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#2223264 - 01/30/14 05:50 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
prout Offline
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This discussion seems to have moved from physics to metaphysics. I have always thought that knowledge is a good thing, and that what constitutes knowledge is an understanding of how something in the physical world can be described. That description is, by its nature, a simulation of the perceived reality, since the description itself does not exist outside my mind. Am I missing something here?

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#2223294 - 01/30/14 07:18 PM Re: Simultaneous partials in a string: reality or myth? [Re: prout]
Withindale Offline
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Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: prout
Originally Posted By: Withindale
Originally Posted By: prout
An excellent paper on the complexities of string motion and coupling on a grand piano. Well worth the effort of wading through the math.

http://hal.archives-ouvertes.fr/docs/00/78/75/51/PDF/RR-8181.pdf

... or read about the results of the simulations, e.g:

Observations made on real signals show that the pressure and soundboard motion spectra, including the bridge, have a denser and richer content than the strings. The simulations help here to understand these differences and identify the additional spectral components.

QED.

Sorry Ian, I don't get your point.

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.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2223299 - 01/30/14 07:34 PM Re: Simultaneous partials in a string: reality or myth? [Re: Withindale]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 770
Originally Posted By: Withindale
Originally Posted By: prout
Originally Posted By: Withindale
Originally Posted By: prout
An excellent paper on the complexities of string motion and coupling on a grand piano. Well worth the effort of wading through the math.

http://hal.archives-ouvertes.fr/docs/00/78/75/51/PDF/RR-8181.pdf

... or read about the results of the simulations, e.g:

Observations made on real signals show that the pressure and soundboard motion spectra, including the bridge, have a denser and richer content than the strings. The simulations help here to understand these differences and identify the additional spectral components.

QED.

Sorry Ian, I don't get your point.

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.

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#2223302 - 01/30/14 07:42 PM Re: Simultaneous partials in a string: reality or myth? [Re: Withindale]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: Withindale
Originally Posted By: prout
Originally Posted By: Withindale
Originally Posted By: prout
An excellent paper on the complexities of string motion and coupling on a grand piano. Well worth the effort of wading through the math.

http://hal.archives-ouvertes.fr/docs/00/78/75/51/PDF/RR-8181.pdf

... or read about the results of the simulations, e.g:

Observations made on real signals show that the pressure and soundboard motion spectra, including the bridge, have a denser and richer content than the strings. The simulations help here to understand these differences and identify the additional spectral components.

QED.

Sorry Ian, I don't get your point.

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.


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.

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#2223369 - 01/30/14 10:40 PM Re: Simultaneous partials in a string: reality or myth? [Re: prout]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 1957
Loc: Seattle, WA USA
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.
_________________________
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#2223426 - 01/31/14 01:12 AM Re: Simultaneous partials in a string: reality or myth? [Re: Ed McMorrow, RPT]
Withindale Offline
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Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: Ed McMorrow, RPT
All models contain approximations and simplifications.... The real test is how useful a model is for making predictions.

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.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2223468 - 01/31/14 05:16 AM Re: Simultaneous partials in a string: reality or myth? [Re: pyropaul]
Mark R. Offline
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Registered: 07/31/09
Posts: 1958
Loc: Pretoria, South Africa
Originally Posted By: pyropaul
Originally Posted By: Withindale
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.


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.


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

"Q.E.D."
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2223481 - 01/31/14 06:49 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 770
Originally Posted By: Mark R.
Originally Posted By: pyropaul
Originally Posted By: Withindale
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.


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.


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.

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#2223483 - 01/31/14 07:20 AM Re: Simultaneous partials in a string: reality or myth? [Re: prout]
Withindale Offline
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Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: prout
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.

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.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2223503 - 01/31/14 08:35 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Mark R. Offline
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Registered: 07/31/09
Posts: 1958
Loc: Pretoria, South Africa
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:
Originally Posted By: DoelKees
A "sine wave" with a time dependent amplitude is not a sine wave. It does not even have a well-defined frequency.


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:

Originally Posted By: DoelKees
I assure you if you reassemble all the partials and resynthesize the sound you do not get the original sound back: just the part that is well approximated as a sum of partials.

This is really all old well-known stuff, investigated in depth in the literature. For example there is a sound synthesis method from the '80-ies by Rodet where you explicitly split the sound into something that is modeled by partials + a residual that can't be modeled like that.


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 wink , so for my part, this thread can go into decay. smile
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2223539 - 01/31/14 09:56 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
DoelKees Offline
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Loc: Vancouver, Canada
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

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#2223555 - 01/31/14 10:21 AM Re: Simultaneous partials in a string: reality or myth? [Re: DoelKees]
ando Offline
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Registered: 11/23/10
Posts: 3546
Loc: Melbourne, Australia
Originally Posted By: DoelKees
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.


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.

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#2223561 - 01/31/14 10:28 AM Re: Simultaneous partials in a string: reality or myth? [Re: ando]
DoelKees Offline
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Registered: 05/01/10
Posts: 1696
Loc: Vancouver, Canada
Originally Posted By: ando
Originally Posted By: DoelKees
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.


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

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#2223665 - 01/31/14 01:47 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
TimR Offline
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Registered: 08/17/04
Posts: 3187
Loc: Virginia, USA
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.
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#2223957 - 02/01/14 01:28 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1126
Loc: Montreal, Quebec, Canada
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.


Edited by Mark Cerisano, RPT (02/01/14 01:29 AM)
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2224004 - 02/01/14 05:18 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark Cerisano, RPT]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
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?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2224114 - 02/01/14 10:36 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 770
Originally Posted By: Mark R.


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".



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.

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#2224119 - 02/01/14 10:52 AM Re: Simultaneous partials in a string: reality or myth? [Re: Withindale]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1126
Loc: Montreal, Quebec, Canada
Originally Posted By: Withindale
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?


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
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2224131 - 02/01/14 11:24 AM Re: Simultaneous partials in a string: reality or myth? [Re: prout]
Ed McMorrow, RPT Offline
1000 Post Club Member

Registered: 12/09/12
Posts: 1957
Loc: Seattle, WA USA
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.
_________________________
In a seemingly infinite universe-infinite human creativity is-seemingly possible

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#2224146 - 02/01/14 11:46 AM Re: Simultaneous partials in a string: reality or myth? [Re: Mark Cerisano, RPT]
bkw58 Offline

Silver Supporter until December 19, 2014


Registered: 03/14/09
Posts: 1672
Loc: Conway, AR USA
Originally Posted By: Mark Cerisano, RPT
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.


The first good, succinct, easy-to-understand video on the subject that I've seen anywhere to date. Bravo!
_________________________
Bob W.
Retired piano technician
Piano Technicę

"Never argue with a fool, people may not be able to tell you apart." - author unknown

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#2224147 - 02/01/14 11:47 AM Re: Simultaneous partials in a string: reality or myth? [Re: Ed McMorrow, RPT]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 770
Originally Posted By: Ed McMorrow, RPT
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.

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.


Edited by prout (02/01/14 11:51 AM)

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#2224227 - 02/01/14 03:07 PM Re: Simultaneous partials in a string: reality or myth? [Re: Mark R.]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1936
Loc: Suffolk, England
Originally Posted By: Mark Cerisano
My video on the harmonic series ... http://youtu.be/dCmy6N3DnV8

Mark, you answered my question perfectly.

I am lost in admiration for your vocal partials and, if I may say so, performed like a true native!
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

Top
#2224232 - 02/01/14 03:18 PM Re: Simultaneous partials in a string: reality or myth? [Re: Withindale]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 169
Loc: Montreal
Originally Posted By: Withindale
Originally Posted By: Mark Cerisano
My video on the harmonic series ... http://youtu.be/dCmy6N3DnV8

Mark, you answered my question perfectly.

I am lost in admiration for your vocal partials and, if I may say so, performed like a true native!


Agreed. Thanks Mark - your video confirmed what I was trying to say all along - the partials we hear are all present in the complex vibration of a piano string. Thanks, also, for including the guitar demonstration - particularly of the change of timbre as the pluck point is changed, thus exciting partials in different amounts.

Paul.


Edited by pyropaul (02/01/14 03:18 PM)
Edit Reason: typo

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#2226555 - 02/05/14 07:34 PM Re: Simultaneous partials in a string: reality or myth? [Re: bkw58]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1126
Loc: Montreal, Quebec, Canada
Originally Posted By: bkw58
Originally Posted By: Mark Cerisano, RPT
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.


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


Wow. Thanks Bob. That is really appreciated.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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