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#2306325 - 07/24/14 08:05 AM Re: Partial strength - hammer voicing or soundboard ? [Re: Mark Cerisano, RPT]
Olek Online   content
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Registered: 03/14/08
Posts: 7881
Loc: France
Originally Posted By: Mark Cerisano, RPT
Science is not nature, it mearly tries to describe it in useful terms so we can predict its behaviour.

Did you watch the video? There are four examples that show partials are not imagined, and string vibration can be thought of as a combination of sine waves.

I think I know what you may be getting at though.

If string vibration was indeed produced directly from individual sine tone generation, then the synthesizer algorithms of the 80's should have been able to accurately reproduce authentic sounds that could not be distinguished from the real acoustic.instrument, which of course is not true.


That said, PIanoteq and the GT2 (2?) are impressive in realism today.

The GT have even inserted the vibration we perceive in the keys when they are bottoming wink My brother, violinist , had a rehearsal with one, and told me after 54 minutes the "digital tone" is not noticed anymore, they could work normally.

In daily professional use, the sensors (rail) can worn out in +-10 years, and need changing. (not cheap, but unavoidable, anyway with the first models)


I do not understand BDB idea, partials cannot be dismissed, as they are responsible for the tone recognizing, different processes of tone production creating different ranges of partials hence different presence or absence of those in the final tone)

Their stability in piano tone, and predictability, can really be put in caution, hence the necessity to control what ETD's are proposing.






Edited by Olek (07/24/14 08:13 AM)
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#2306366 - 07/24/14 09:07 AM Re: Partial strength - hammer voicing or soundboard ? [Re: BDB]
bkw58 Offline

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Registered: 03/14/09
Posts: 1766
Loc: Conway, AR USA
Originally Posted By: BDB
Harmonics are an artificial construct which reflect the way that a waveform is approximated by a Fourier series. The waveform depends on the initial conditions of the wave, that is, the shape the string is when it begins to move. That shape is determined by the hammer. Later, it may be modified by the impedance of the bridge and soundboard.


Hi BDB. I am trying to understand what you are saying. "Artificial" is a rather elastic word. Are you using it in the sense of "produced by man; not occurring naturally" or in another way?
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#2306377 - 07/24/14 09:23 AM Re: Partial strength - hammer voicing or soundboard ? [Re: BDB]
Robert Scott Offline
Full Member

Registered: 12/19/03
Posts: 285
Loc: Minnesota
Originally Posted By: BDB
Sure, I understand. There are several ways of looking at things. Partials are an abstraction that come from the Fourier series approximation of a periodic function. My only objection is to those people who think there are harmonic fairies magically making sine waves of all different frequencies hiding in a vibrating string, and they are what give a piano its characteristic sound.


BDB, I also come from the field of mathematics, and I fully understand what you mean when you say that harmonics are an artificial abstraction. I agree that could be said of harmonics. But not of partials. They are not the result of Fourier analysis of a periodic waveform, but rather the result of real physically separate modes of vibration in the string. This is evident from the fact that they can be excited separately by plucking the string in just the right place and lightly damping the string in another place. They are also not harmonics because they are not phase-locked to the fundamental as real harmonics are, and since the whole waveform is not strictly period.
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#2306410 - 07/24/14 10:57 AM Re: Partial strength - hammer voicing or soundboard ? [Re: Robert Scott]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 2189
Loc: Seattle, WA USA
Robert Scott,
Great explanation.

The string is a wave medium with specific dispersal rates determined by the elasticities and mass.

I think what BDB is saying is that the initial deflection of the string carries all the information that will be revealed over time. Of course the properties of the wave medium and it's boundaries change the shape of the initial deflection over time. So the sum total wave form of taut piano strings is non-periodic. But each separable component wave is periodic.
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#2306425 - 07/24/14 11:24 AM Re: Partial strength - hammer voicing or soundboard ? [Re: Robert Scott]
BDB Online   content
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Originally Posted By: Robert Scott
BDB, I also come from the field of mathematics, and I fully understand what you mean when you say that harmonics are an artificial abstraction. I agree that could be said of harmonics. But not of partials. They are not the result of Fourier analysis of a periodic waveform, but rather the result of real physically separate modes of vibration in the string. This is evident from the fact that they can be excited separately by plucking the string in just the right place and lightly damping the string in another place. They are also not harmonics because they are not phase-locked to the fundamental as real harmonics are, and since the whole waveform is not strictly period.


Exciting the string in different modes is not the same as the actual existence of partials as separate vibrations in a string.

What I really do not understand is why this is so important to people. I view beats as the results of combinatorics. Others view them as the creation of harmonic fairies. If it works for you, fine. I have posted recordings of my tunings. Most of you have not. If you want, you can make an appointment to drop by and experience my tunings in person.

There may only be limited circumstances where the difference matters. Since I view beats as the result of combinatorics, if the waveform varies, so do the beats. This means that voicing affects tuning. This is most evident in the bass, where softer hammers excite the string more closely to the fundamental mode, enough so that the coincidence of maxima and minima change, and the beats are better if the pitch is lower.

Oh, and there is the other fact that I mentioned somewhere else, about the speed of the hammer being bounced off the string being related to the frequency of the note. There are no harmonic fairies throwing them off any faster, although the characteristics of the hammers will make a difference.
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#2306426 - 07/24/14 11:24 AM Re: Partial strength - hammer voicing or soundboard ? [Re: Ed McMorrow, RPT]
prout Offline
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Registered: 11/14/13
Posts: 830
Originally Posted By: Ed McMorrow, RPT
Robert Scott,
Great explanation.

The string is a wave medium with specific dispersal rates determined by the elasticities and mass.

I think what BDB is saying is that the initial deflection of the string carries all the information that will be revealed over time. Of course the properties of the wave medium and it's boundaries change the shape of the initial deflection over time. So the sum total wave form of taut piano strings is non-periodic. But each separable component wave is periodic.


So perhaps we could think (idealized of course) of disturbances of the piano string as ripples on a pond. There are many different periodic waves simultaneously that exist, with different parameters, pass through each other and, to the observer at a particular point, constructively or destructively interact.

Clearly there are relationships amongst the waves, as they acoustically couple (longitudinal and transverse waves for one) and are all affected by bridge bending, soundboard movement, which changes the instantaneous tension of the string.

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#2306592 - 07/24/14 04:31 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Mark R. Offline
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Registered: 07/31/09
Posts: 2041
Loc: Pretoria, South Africa
Why the insistence on fairies, BDB? You are doing the discussion no favor by belittling it.

Any spectral analyzer, be it aural (frequency filter or analyzer, i.e. frequency domain) or visual (stroboscopic, i.e. time domain) shows modes to be present, simultaneously, in a string.

It also shows the beats of an (non-unison) interval to occur not between the fundamentals, but between the coincident partials. Just look at some of the spectrograms that Kees posted.

(Think about it: why would 174.6 Hz and 220 Hz beat at 7 Hz? Multiply the one by 5, the other by 4, and you have a 7 Hz beat. The beat is not happening at the fundamental!)
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#2306619 - 07/24/14 05:14 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
BDB Online   content
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So if you have an instrument like an organ, which produces pure sine waves, there would be no beats between 174.6 and 220, and you could not tune it, because there are no partials.
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#2306630 - 07/24/14 05:34 PM Re: Partial strength - hammer voicing or soundboard ? [Re: BDB]
prout Offline
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Registered: 11/14/13
Posts: 830
Originally Posted By: BDB
So if you have an instrument like an organ, which produces pure sine waves, there would be no beats between 174.6 and 220, and you could not tune it, because there are no partials.


Harmonics are a subset of partials. A Major third will beat at the 5 and 4 harmonic ( assuming the fundamental frequency is the first harmonic) in the same manner that it will on a piano. Organs ( including the Hammond C3 and B3 ) all have sound generators that produce, simultaneously, a multitude of harmonics - the pipe by its shape, and the B3 by multiple sine wave generators.

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#2306645 - 07/24/14 06:11 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
BDB Online   content
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The point is that sine waves have no partials. Take two sine waves. They will beat, not because partials coincide, but because of combinatorics.
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#2306649 - 07/24/14 06:17 PM Re: Partial strength - hammer voicing or soundboard ? [Re: BDB]
prout Offline
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Registered: 11/14/13
Posts: 830
Originally Posted By: BDB
The point is that sine waves have no partials. Take two sine waves. They will beat, not because partials coincide, but because of combinatorics.


That is an interesting concept. Do you have any math that would predict the beat ratios, either of an organ pipe or a piano string?

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#2306666 - 07/24/14 07:03 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Chris Leslie Offline
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Loc: Canberra, ACT, Australia
Originally Posted By: BDB
The point is that sine waves have no partials. Take two sine waves. They will beat, not because partials coincide, but because of combinatorics.


I tried this with a simulator with no iH and with P1's only, ie with pure single sine waves per note. The only beating intervals are nearly coincident unisons. I find it impossible to recognise normal intervals with any degree of accuracy without hearing any beats, and therefore impossible to aurally tune with any accuracy.
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#2306733 - 07/24/14 10:32 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 2189
Loc: Seattle, WA USA
BDB,
I don't see the significance of your wave model to pianos. It seems incomplete.

The partial tones are there as a result of simple harmonic motion in a somewhat less than perfectly elastic two dimensional medium with somewhat elastic boundary conditions.
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#2306744 - 07/24/14 11:03 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Chris Storch Offline
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Registered: 08/13/09
Posts: 203
Loc: Massachusetts


In my mind I've named the guy on the right Joseph Fourier...

Doesn't seem to be a particularly rapid beat rate, but I'm sure he's getting his point across.
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#2306755 - 07/24/14 11:37 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 2189
Loc: Seattle, WA USA
At any rate, it is an illustration of "ill-temperment".
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#2306839 - 07/25/14 06:57 AM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
WilliamTruitt Offline
Full Member

Registered: 07/12/14
Posts: 99
Loc: New Hampshire
Or Unjust intonation....

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#2306871 - 07/25/14 09:19 AM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
pyropaul Offline
Full Member

Registered: 11/16/10
Posts: 189
Loc: Montreal
As I posted into another thread, just put graph sin(4.4*pi*x)+sin(4.41*pi*x) into google, select horizontal zoom and zoom out. The "beats" that you hear are an amplitude modulation effect. If you put graph sin(4.4*pi*x)+sin(6.61*pi*x)- essentially a major 12th that's off by 1Hz, you will still see an amplitude modulation (that you can also hear as beats). So you can tune any interval with pure sinewave. Of course sin(A) + sin(B) is "combinatronics". You don't need partials to tune, you just need to remove any amplitude modulation to zero. Also, organs do not produce pure sinewaves - even a B3's tonewheel generator does not produce a pure sine. Even if it did, you'd still be able to tune it.

There's no technical difference between "partials" and "harmonics" - they are both sinewaves at a certain frequency - just that the latter have an exact integer multiple ratio to the fundamental. Essentially our ears are spectrum analyzers that operate in near real time (there's about a 20ms processing delay in our brains) - so we hear the frequency relationships, but are unable to distinguish the phase relationships. If you don't believe the latter, synthesize a tone from sinewaves using whatever method you like and then offset the phase of the different oscillators - you will not hear any difference for any static setting of phase. Of course, if the phase is changing, this is perceptible as a frequency modulation.

Paul.

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#2306890 - 07/25/14 09:44 AM Re: Partial strength - hammer voicing or soundboard ? [Re: pyropaul]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 830
Originally Posted By: pyropaul
As I posted into another thread, just put graph sin(4.4*pi*x)+sin(4.41*pi*x) into google, select horizontal zoom and zoom out. The "beats" that you hear are an amplitude modulation effect. If you put graph sin(4.4*pi*x)+sin(6.61*pi*x)- essentially a major 12th that's off by 1Hz, you will still see an amplitude modulation (that you can also hear as beats). So you can tune any interval with pure sinewave. Of course sin(A) + sin(B) is "combinatronics". You don't need partials to tune, you just need to remove any amplitude modulation to zero. Also, organs do not produce pure sinewaves - even a B3's tonewheel generator does not produce a pure sine. Even if it did, you'd still be able to tune it.

There's no technical difference between "partials" and "harmonics" - they are both sinewaves at a certain frequency - just that the latter have an exact integer multiple ratio to the fundamental. Essentially our ears are spectrum analyzers that operate in near real time (there's about a 20ms processing delay in our brains) - so we hear the frequency relationships, but are unable to distinguish the phase relationships. If you don't believe the latter, synthesize a tone from sinewaves using whatever method you like and then offset the phase of the different oscillators - you will not hear any difference for any static setting of phase. Of course, if the phase is changing, this is perceptible as a frequency modulation.

Paul.


Using your logic, a single string, which contains partials, for example, due to iH, of 440, 881, and 1322.3 must beat like crazy all on its own. The only poster here who has heard that is Isaac. Maybe we learn to ignore the beating of a single string when tuning.

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#2306907 - 07/25/14 10:16 AM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Mark R. Offline
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Registered: 07/31/09
Posts: 2041
Loc: Pretoria, South Africa
BDB,

Granted, organ pipes produce sine waves, yes. But they don't produce only one sine wave per pipe. Where do you think the different timbre of different stops comes from? Each pipe produces a multitude of sine waves. (To wit: its specific harmonic series.) The timbre of each stop comes from the relative strength of the fundamental and each overtone.

So, even in an organ, 174.6 does not beat against 220. Rather, the fifth partial (i.e. fourth overtone) of the first pipe beats against the fourth partial (i.e. third overtone) of the second pipe. Exactly as in a piano, except that the overtone series in an organ is harmonic (f, 2f, 3f, etc.)

And just like a piano string doesn't disintegrate because it moves as a sum of modes, neither does the air column inside an organ pipe disintegrate because it contains several simultaneous standing waves.

Still, no fairies.

Conversely: a pure, single-frequency sine wave of 174.6 and a pure, single-frequency sine wave of 220 Hz will not beat - most certainly not at 7 Hz! As Chris Leslie wrote, with pure, single-frequency sine waves, the only beating intervals are near-coincident unisons. [Edit: the 174.6 and 220 of an organ, or a piano for that matter, do beat, because their respective partial series contain near-coincident partials.]

Finally, a question:

If 880 is only a "fairy" inside an A220 string, why can I get an un-damped A880 to ring by playing A220? (Should we be "fairying" notes, rather than ghosting them?)


Edited by Mark R. (07/25/14 10:20 AM)
Edit Reason: given in post.
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#2306924 - 07/25/14 10:47 AM Re: Partial strength - hammer voicing or soundboard ? [Re: Mark R.]
BDB Online   content
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Actually in an organ, each stop is a fairy. Add them together and they make a different tone. It does not follow that just because you can add things together, you can take things apart from something that started out not put together. You could try this: Pick something up with your hand. Then chop your fingers off, put them back together, and see if it works as well as it did before.

Everything that you say is a result of partials can be explained through combinatorics. Just look at how waves may interact to see that.
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#2306937 - 07/25/14 11:14 AM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
gynnis Offline
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Registered: 02/16/14
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Loc: Florida, Connecticut
I think a little hunting on youtube will yield some nice strobe pictures of vibrating strings that have multiple harmonics on them. Violinist all know how to play harmonics, so strings can support multiple pitches that are in harmonic relationships with each other.

By the way, the inner ear is the ultimate Fast Fourier Transform device.

If you want to hear partials, just strike a bass not with the damper up on a note an octave and a fifth above. You will hear the latter string vibrate in sympathy with the third harmonic of the bass string.
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#2306944 - 07/25/14 11:30 AM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
prout Offline
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Registered: 11/14/13
Posts: 830
BDB: An organ pipe produces a unique tone as a result of its length/width ratio, taper, pipe material (wood, tin), and whether or not it has a reed. These variations give rise to various standing waves of various harmonics in the pipe.

gynnis: BDB has a different way of thinking about sound wave structures from many of us. The fact that we produce pictures of vibrational modes on a string, and that a violinist can create harmonics by touching the string at a node point, does not mean that they actually exist as independent entities. It simply means that we create a paradigm for observation, and we see what we expected to see. From that observation we can model and predict certain string behaviours to a reasonable, but not exact, level of accuracy.

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#2306953 - 07/25/14 11:58 AM Re: Partial strength - hammer voicing or soundboard ? [Re: Chris Leslie]
A443 Offline
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Registered: 04/28/12
Posts: 1411
Originally Posted By: Chris Leslie
Originally Posted By: BDB
The point is that sine waves have no partials. Take two sine waves. They will beat, not because partials coincide, but because of combinatorics.


I tried this with a simulator with no iH and with P1's only, ie with pure single sine waves per note. The only beating intervals are nearly coincident unisons. I find it impossible to recognise normal intervals with any degree of accuracy without hearing any beats, and therefore impossible to aurally tune with any accuracy.
I did similar experiments in 90s and had the same observations: sine waves don't beat audibly like coincident partials do. There is a HUGE range that still sounds in-tune, even when it's not. It's not impossible to tune aurally but, you'd have to listen using a completely different skill set--and accuracy is not very consistent. f
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#2306974 - 07/25/14 12:57 PM Re: Partial strength - hammer voicing or soundboard ? [Re: A443]
Robert Scott Offline
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Registered: 12/19/03
Posts: 285
Loc: Minnesota
A single pipe on a pipe organ does not produce a pure sine wave. The "flute" pipes produce close to a sine wave, so it has very weak harmonics. But even these weak harmonics are enough to be heard when tuning a pipe organ, so even the flute stops can be tuned by beats using intervals like octaves, 4ths, 5ths, and 3rds. Pipes in other stops have even richer harmonics as they deviate more from sine waves.

As for experiments with pure sine waves, here is a trick you can add: Take the sound of two sine waves that have a nice frequency ratio, like 3:4. As was mentioned already, you will not hear any beats because there are no harmonics to beat. But, take that same sound and add a little distortion. Turn up the volume until the speaker cones are buzzing a little, or place a paper clip on the speaker cone - anything to slightly distort the sound. Then you will be creating harmonic distortion, and beats will suddenly appear.

@BDB: Combinatorics is the study of things like latin squares, projective planes of finite order, balanced incomplete block designs and Hadamard matrices. I don't think this field describes how beats are produced.
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#2307019 - 07/25/14 02:36 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Gadzar Offline
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Registered: 12/15/06
Posts: 1804
Loc: Mexico City
@BDB



Can't you really see the diferent modes of vibration?

These are partials. If they can be heard, if they can be seen, then they exist and are not an abstraction.
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#2307025 - 07/25/14 02:50 PM Re: Partial strength - hammer voicing or soundboard ? [Re: Gadzar]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 830
Originally Posted By: Gadzar
@BDB



Can't you really see the diferent modes of vibration?

These are partials. If they can be heard, if they can be seen, then they exist and are not an abstraction.


One must be careful to understand the experiment and the method of recording the observations. Remember wagon wheels turning backwards in a movie on a wagon clearly moving forward? What you see is an artifact of the recording process.

One can clearly see the fan blades stopped when strobed at the correct rpm, yet we think that the fan is still moving because we can feel the airflow. A movie made of that fan would clearly show that is stopped.

Our hand cannot easily pass through a solid wood tabletop. It is clearly solid because we can't see through it. Yet there are theories and observations that show the space occupied by atoms is mostly empty, and, it is possible for our hand to pass through the tabletop, just not very probable.

All I am saying is that BDB provides a different view and food for thought.

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#2307043 - 07/25/14 03:39 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Gadzar Offline
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Registered: 12/15/06
Posts: 1804
Loc: Mexico City
Prout,

The video was addressed to BDB.

Don't tell me you also believe partials do not exist!

Do you?
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#2307047 - 07/25/14 03:48 PM Re: Partial strength - hammer voicing or soundboard ? [Re: prout]
Gadzar Offline
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Registered: 12/15/06
Posts: 1804
Loc: Mexico City
Strobos hide us part of what is happening, so what we see is an incomplete succession that can be missinterpreted.

What I've posted is a ultra high speed video, exactly the opposite.

It hides nothing to our view as strobos do.

Your analogy is invalid here.



Edited by Gadzar (07/25/14 03:55 PM)
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#2307057 - 07/25/14 04:19 PM Re: Partial strength - hammer voicing or soundboard ? [Re: Gadzar]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7881
Loc: France
Originally Posted By: Gadzar
Prout,

The video was addressed to BDB.

Don't tell me you also believe partials do not exist!

Do you?



It i seen how the bad center (that one woobble a lot) is sending some twisdting wave on the small piece of wire there.

I cannot believe it is the end of a long bass wire. not it is tense enough
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#2307071 - 07/25/14 04:47 PM Re: Partial strength - hammer voicing or soundboard ? [Re: Gadzar]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 830
Originally Posted By: Gadzar
Prout,

The video was addressed to BDB.

Don't tell me you also believe partials do not exist!

Do you?



This could be a totally different topic. I don't believe in anything. I never have.

I do partial analysis using accepted techniques. It allows me to visualize, in my mind, a way of thinking about sound waves. I don't know and I don't care if there is some sort of absolute "truth" about things. BDB's thoughts are as valid as anyone's posting here on this thread.

Some people (mostly fundamentalist types, not necessarily religious) spend their lives espousing an absolute faith in some idea or phenomenon. I spend my life asking questions, positing ideas, in the hope of being shown a different way of thinking about something. I gain much in the process.

I welcome BDB and his ideas.

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