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Beyond Impact Spectra


Don Noon
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From the thread about playing in the white...

I'm placing less and less value on bridge impact spectra, and more and more value on how the interface between the bow and string works, with vibrational feedback from the fiddle. That won't necessarily show up on impact spectra, or at least not in a way that is easy to interpret.

Hi David, can I have a chat with you next year in Oberlin about that? I'm interested in this.

 

I'm also interested in this, but don't expect to be at Oberlin next year. Why wait? Why Oberlin? We can discuss this topic now, here, in a new thread. What do you have, David? Anybody?  I'll wait a bit and see where this goes before laying out my unfocused thoughts.

 

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From the thread about playing in the white...

 

I'm also interested in this, but don't expect to be at Oberlin next year. Why wait? Why Oberlin? We can discuss this topic now, here, in a new thread. What do you have, David? Anybody?  I'll wait a bit and see where this goes before laying out my unfocused thoughts.

Hi Don, I'll take a shot at it.

 

I try to achieve a bowing character target for the violin and I then accept whatever the sound qualities that result.  This may appear at first to be backward but it really is.

 

If we want an easy to play violin which responds well to a low bow force and a slow bow speed then we should use top and back plates that are easy to get moving--they should have low impedance.

 

On the other hand if we want a violin to have more bowing resistance needing a higher bow force and bowing speed then we should use plates with high resistance to movement--they should have a high impedance.

 

The impedance i of a plate is dependent upon both the plate's mass M and its stiffness K:

 

i = (MK)^0.5   (The MK part is from Marty Kasprzyk's initials)

The plate stiffness K for mode 5 (or for mode 2) can be found from their mode frequencies F and plate masses M:

 

F= (K/M)^0.5     

 

F^2 = K/M

 

K= MF^2         This John Masters stiffness expression can be substituted into the above impedance equation:

 

i= (M^2F^2)^0.5        and this reduces to:

 

 

i = FM       

 

Thus a plate's impedance for any mode is simply its mode frequency times its mass.  I divide this by 1000 to make it look smaller.

 

The attached graph shows how the back plate mode 5 frequencies of four different violins changed as I reduced their weights.  Also shown are the lines for two different impedance levels.

 

The top plates showed a similar pattern but cutting the f holes and adding the bass bars made the graphs messy so I'm just showing the backs for illustration.

 

Itzhak Perlman played the No. 4 violin and didn't like it and I haven't made a violin since then.

 

But I've recently begun to suspect that the top impedance should be properly matched to the back impedance to give a back to top impedance ratio Ri:

 

Ri =  FbMb/FtMt                  This can be rearranged a little:

 

Ri = (Mb/Mt)(Fb/Ft)           

 

The Mb/Mt   portion is simply the ratio of the back plate weight to the top weight ratio and it would be interesting to see what these ratios are for good instruments.  I'm guessing the backs typically weigh about 1.5 times as much as the tops.

 

The Fb/Fportion is simply the old fashioned back plate tap tone frequency to the top plate tap tone frequency. I don't have data on good instruments either. If both plates are tuned to the same frequency then their ratio is 1.0 and the impedance equation is reduced to just the plate weight ratio.

 

Recall that the impedance is a measure of how difficult it is for the plate to move.  Obviously if the plate moves a lot it will produce a loud sound.

 

We know from the Strad 3D project violin testing by Bissinger that the top produces about 1.5 times the amount of sound that the back produces. It appears to me that the back is deliberately made with a higher impedance through the use of maple wood to achieve this top to back sound output ratio.

 

 

 

 

Back Impedance-graph-.pdf

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I was asking David for a chat because I (probably incorrectly) assumed that his feedback vibrational thing is something that can only be assessed in actually playing the instrument and as I am interested in the bow part of the equation I wanted to have demonstarted by the master himself how he does that.

As you goys start throwing around formulas and numbers I feel terribly lost, first of all because I don't really get them and secondly because they are not easily transferable to bowmaking.

 

You guys want to make the perfect fiddle, bowmakers want to make the best bow ever, truth is in reality they don't really exist without another..

 

Florian

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As an ancient Hurdy-gurdy maker, I wanted to avoid the musician's hand when measuring input admittance at the Cello bridge. It was funny to motorize a bow-wheel made of felt. There was a  sounding difference between the wheel and a usual bow, but not so much on the graph of the admittance.

I didn't know if I was right to do that, and after reading the article of Zhang/Woodhouse,I was reassured.  "The influence of different driving conditions on the frequency response of bowed-string instruments", was presented by Jim W. at the 2013 SMAC Stockholm.

Jim W. wrote:

A series of experiments are carried out with three different driving conditions in the case of a cello: hammer, normal bowing of a string, and step excitation by a breaking wire. The results suggest that there is nothing fundamentally different about the hammer method, compared to other kinds of excitation methods.

This article is on the proceedings of the Stockholm Music Acoustic conference 2013. I have a copy, but I don't know if already published

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I was going to make a joke about putting down my bow and playing with an impact hammer, then I remembered some of the pieces that contemporary composers have written for me...but I did have a sudden recall of witnessing a discussion between my dad and and one of the big NY dealers back in the 1970's about how often violins that sound good pizzicato turn out to be disappointing when played arco. The upshot was never trust a pizzicato test... 

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The impedance i of a plate is dependent upon both the plate's mass M and its stiffness K:

 

Marty,

 

While that's all true for a static structure, when you're talking about the vibrational character it probably is too simplified.  For a theoretical example, suppose you have two plates of identical overall mass and stiffness (equal impedance according to your math).  Due to differences in arching, graduation, whatever, the bridge foot of one fiddle happens to sit on an antinode at 1000Hz, and the other fiddle has the bridge foot on a nodal line of the 1000Hz mode.  The impedances at 1000Hz will be vastly different, as will the sound output and playing characteristics at that note... and also the notes of which 1000Hz is an overtone.

 

Examining actual frequency-dependent impedance is beyond my measurement capability currently, requiring (among other things) a bridge-mounted accelerometer.  And I'm not sure I would even want to bother with it, as I think I can feel the situation well enough just by playing.  And playing is what really matters in the end, anyway.

 

 I'd be intrested to see a bowed responce in compairision to a hammer.

 

Here's one.  The bowed response is a low-resolution plot of a bowed semitone scale, only in the first position (only up to ~1000Hz on the fundamental), so the high frequencies drop off compared to the impact spectrum.  The impact is also of the same low resolution.  Some features are apparent, as are some big differences.  It's very hard to get a well-calibrated, wideband bowed spectrum.

post-25192-0-25728200-1386119112_thumb.jpg

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Wow! What a coincidence.

 

I was re-reading James Beament's "The Violin Explained: Components, Mechanisms and Sound" - and was focusing on his chapter discussing resonance and response. I was drawn to Chapter 5: Resonance and Response because I have been musing whether our focus on resonances is telling the full story. We have seen the resonance graphs (impact spectra) of Don and many other researchers. What grabbed my interest in Beament is that he is not enthusiastic about resonance graphs because there is so much variability in them. This sounds like my remarks about the "noise" in the graphs - too much variability to suit my needs for simplicity.

 

The other analysis method that Beament prefers is the response curve. This shows the variations in total sound from bowing at successive semitones. I like this concept and will be studying it further. In the meantime I hope others will get out their copy of Beament and start reading. 

 

BTW, Beament was the late husband of violin maker and author, Juliet Barker. This book shoots down quite a few myths and red herrings. (I loved the section on Varnish.) All in all, it is a very good read indeed. You do not need to be a rocket scientist to enjoy this book.

 

Mike

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Hmmm, I'm not sure how much more I'm willing to say about all this.

The basic concept is that a bowed violin doesn't just blurt its sound out into the room in the same way as when it is struck. Some of the vibration feeds back through the bridge, and changes the way the string vibrates, and changes the nature and timing of hair adhesion to the string. So the violin is actually driven differently, with a consequent change in sound. A wolf note is an extreme example of that feedback loop.

 

A related factor seems to be bridge mobility, or excursion, although it's probably not correct to describe it as a separate factor. Violins seem to work and sound best when this is within a narrow range... not too much, not too little, just right. Perhaps this could be described in terms of impedance. Of course, impedance is all over the place at different frequencies, depending on how the frequency couples with mode activity in the violin body, so we're probably talking about a narrow band of frequencies which are having the most critical impact on the dynamic motion of the bridge.

 

Florian, there is probably also a feedback loop from the bow, which will also alter the slip-stick interface between the hair and the string, altering the sound of the violin because of a change in the way it is driven, but I've done much less experimenting with that, because I'm not trying to make bows. But I do know that violins can be adjusted to work better with specific bows, and that which bow is being used during a sound adjustment can alter how the instrument needs to be adjusted. I think that last sentence is something that most people I know who are considered really really good at adjusting would agree on.

 

Anyway, some of my descriptions may be technically off a little bit, and I'm not willing to go into the series of experiments and observations which led to my conclusions (hypothesis?), so it follows that I'm not in a position to defend them if anyone wants to rip them apart now. ;)

 

But maybe some people can use this to get some ideas.

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Hi Don, I'll take a shot at it.

 

I try to achieve a bowing character target for the violin and I then accept whatever the sound qualities that result.  This may appear at first to be backward but it really is.

 

If we want an easy to play violin which responds well to a low bow force and a slow bow speed then we should use top and back plates that are easy to get moving--they should have low impedance.

 

On the other hand if we want a violin to have more bowing resistance needing a higher bow force and bowing speed then we should use plates with high resistance to movement--they should have a high impedance.

 

 

 

 

What about a nice sounding violin ?

 

Hmmm, I'm not sure how much more I'm willing to say about all this.

The basic concept is that a bowed violin doesn't just blurt its sound out into the room in the same way as when it is struck. Some of the vibration feeds back through the bridge, and changes the way the string vibrates, and changes the nature and timing of hair adhesion to the string. So the violin is actually driven differently, with a consequent change in sound. A wolf note is an extreme example of that feedback loop.

 

 

Sure, but the practicalities are a downer. :)

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Marty,

 

While that's all true for a static structure, when you're talking about the vibrational character it probably is too simplified.

 

 

Hi Don,

 

The impedance equation i= (MK)^0.5  I used is indeed for a dynamic case in a narrow band near resonance and it came from John Schellegs's 1962 paper "The Violin as a Circuit".   I don't believe anybody has since shown it to be incorrect.

 

I still think if you want a hard to bow violin it should be heavy and stiff or maybe stiff and heavy.

 

 

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The impedance equation i= (MK)^0.5  I used is indeed for a dynamic case in a narrow band near resonance and it came from John Schellegs's 1962 paper "The Violin as a Circuit".   I don't believe anybody has since shown it to be incorrect.

 

 

The equation appears to be correct for a simple dynamic oscillator, but I don't think you can use it for all vibrations of a complex plate.  The "M" and the "K" would have to be effective mass and stiffness of the vibrating parts of the mode of interest, very difficult to determine.  You can't just use the plate mass and overall bending stiffness and apply it to all the modes.

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... .

The basic concept is that a bowed violin doesn't just blurt its sound out into the room in the same way as when it is struck. Some of the vibration feeds back through the bridge, and changes the way the string vibrates, and changes the nature and timing of hair adhesion to the string. So the violin is actually driven differently, with a consequent change in sound. A wolf note is an extreme example of that feedback loop.

... .

This is pretty much what I was saying or at least tried to say: we need to investigate response rather than just resonance. A response includes this feedback effect.

 

The problem is that this is a more difficult experiment to perform. Recording the sound of a violin struck with a small hammer is a lot simpler to do than recording the sound from a bowed instrument for a complete range of semitones. Try it.  :wacko:

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If you are trying to study small differences in frequency response, there's a problem with bowing.  The sound you get from bowing depends on the point of contact, among other factors.  The response for any overtone depends on whether the hair is at a node, an antinode, or in between.  For the same reason, it also makes a difference whether the hair is flat or tilted.  A small difference in point of contact can make the difference between an absent overtone and a strong overtone.  Note that the position of a node is determined by the frequency and distance from the bridge, not by the violin.

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I think the wolf note and the playability of violins, or other bowed string instruments, indeed can be well described by a proper model for the bowed string and the bridge admittance at the string notches. At least that is Woodhoses approach to the problem. Also late K Guettler. The impact admittance spectrum coupled with their models would e.g. predict wolves and the more difficult notes to get going. Difficult to interpret directly by the tech equipment without their skills, but it is feasible. Higher peaks in the admittance curve goes with the need for higher minimum bow pressure to get a bowed note going.

Vibration feedback should also be measureable e.g. by impact spectra in some form. But a translation from spectra to percepted experiences still needs to be done.

The admittance curve looks different on the G and E string side of the bridge. The balance between the activity on those two sides might depend on how stiff the top and bass bar is to the back plate. What is a good balance here?

The mid frequency range is called the "transition hill", that is the region where the e side get a stronger response than the G side in the admittance curves. The balance point can proably be moved by the bass bar stiffness somewhat, and the stiffness of the back plate. A balance there seems intuitively appealing to me.

Haven't done much on this. But George Stoppanis software do have Woodhouses "playability function" included without the individual string impedances. So it is possible to calculate minimum bow force functions using his program for a given fixed string impedance. Do not know if it is open for use by others than him yet, though.

I guess not too much or too less is good, as David mentiones, although I do not know if we are thinking about the same things.

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We start with a complex aural experience and change it to a complex visual experience.

Then we try to relate the two experiences.

Does this bump correspond to that buzz??

 

We do have some physics to help, BUT ...  WOW.

We do have some artistic descriptions  to help ...  OH MY !!!

 

It is NOT rocket science  because when you make an error with rocket science

the experiment turns into  BOOOOMMMMM     (rather than a no sale)

 

 

I saw an old player violin.  The bow is replaced with celluloid cones mounted on a spinning shaft.

About 2 inch base down to a 1/4 inch shaft.  Did not sound too god,

but very repeatable.

 

For a bowed stimulus I found one octave gliss on each string.

Then do the FFT on all of them.  

(almost) Every frequency gets swept several times.

No accuracy problems fingering wise.

If you overshoot the octave, no problem.

 

The result looks a lot like a bridge thump. (Well actually a bunch of them)

 

Now try a knuckle bump on the back while recording from

the front.   Well, maybe thump several different places. Hummm.

 

Thumping really does give a good summary of the violin.

If you like summaries.

 

Translating from the FFT pictures to players 'good'

is a difficult problem.

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Thus far, my observation is that playability issues only involve the fundamental of the note being played.  If, for example, there is a strong body resonance at the first or second harmonic, I have only noticed a tonal effect, but no problem with playability (until you try to play the note where the resonance is the fundamental).  Anyone find differently?

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For a bowed stimulus I found one octave gliss on each string.

Then do the FFT on all of them.  

(almost) Every frequency gets swept several times.

No accuracy problems fingering wise.

If you overshoot the octave, no problem.

 

The result looks a lot like a bridge thump. (Well actually a bunch of them)

This is precisely what Oliver Rogers did for many years.

He even had an experimental rig set up in a pick up truck which was employed in a VSA competition to record and compare both

workmanship and tone winning instruments (as well as on Strad for comaprison).

I understand that the article he wrote on this experiment is available on line.

Can someone help find it please?

It might be very interesting for this collective group of folks to take a look and compare instruments that were thought worthy of tone prize and those specifically rejected for a tone prize.

Having looked at the data, some spectra seem to point to obvious tonal problems but in other instances it's baffling why certain instruments, whose spectra looks very much like tone prize material, were rejected.

As far as testing instruments is concerned, I've fallen back to playing them. Only occasionally, if I'm interested in something very specific, do I rely on spectrum analysis.

Specta would be much more useful if they were weighted by such criteria as a frequency's proximity to musical notes and harmonic support of various frequencies. (see below)

In a spectrum analyzing program I've been working on with my friend Bob Hoffman, when you click on a frequency it then shows the closest note and

the octave and third harmonics, which is a more reliable predictor of the timbre of any particular note

Oded

post-95-0-78075700-1386205053_thumb.jpg

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Specta would be much more useful if they were weighted by such criteria as a frequency's proximity to musical notes and harmonic support of various frequencies. (see below)

In a spectrum analyzing program I've been working on with my friend Bob Hoffman, when you click on a frequency it then shows the closest note and

the octave and third harmonics, which is a more reliable predictor of the timbre of any particular note

 

I saw this chart on Schleske's website; it's in German and I'm not sure I know what's going on, but it appears to be a cumulative amplitude response where all the overtones are represented and color coded.  This I think is a good (if compicated to generate) picture of timbre and overall strength, as related to notes of the scale.  I have thought about trying to make a similar plot, but it's too tedious with my simple tools (Audacity, Excel), and I'm not willing to make a project of it.

 

http://www.schleske.de/typo3temp/pics/fcd91b4eda.gif

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We start with a complex aural experience and change it to a complex visual experience.

Then we try to relate the two experiences.

Does this bump correspond to that buzz??

 

We do have some physics to help, BUT ...  WOW.

We do have some artistic descriptions  to help ...  OH MY !!!

 

It is NOT rocket science  because when you make an error with rocket science

the experiment turns into  BOOOOMMMMM     (rather than a no sale)

 

 

I saw an old player violin.  The bow is replaced with celluloid cones mounted on a spinning shaft.

About 2 inch base down to a 1/4 inch shaft.  Did not sound too god,

but very repeatable.

 

For a bowed stimulus I found one octave gliss on each string.

Then do the FFT on all of them.  

(almost) Every frequency gets swept several times.

No accuracy problems fingering wise.

If you overshoot the octave, no problem.

 

I'm struggling to see how fourier transforming these measurements would be the thing that you would want to do. Can you explain?

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I saw this chart on Schleske's website; it's in German and I'm not sure I know what's going on, but it appears to be a cumulative amplitude response where all the overtones are represented and color coded.  This I think is a good (if compicated to generate) picture of timbre and overall strength, as related to notes of the scale.  I have thought about trying to make a similar plot, but it's too tedious with my simple tools (Audacity, Excel), and I'm not willing to make a project of it.

 

http://www.schleske.de/typo3temp/pics/fcd91b4eda.gif

Good illustration of complicating rather than simplifying.

Oded

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I have recently been having a playing problem with my big viola.

I have not made any measurments.

 

In orchestral playing, it is often asked that you play pp tremelo on F, the one a fifth below middle C.

My viola would refuse to play the fundamental in these conditions.  Only a high pitched quiet rustle.

I suspected a tailpiece problem since no standard tailpiece is made for 18" (450 mm) violas. The 

tailpiece installed was from a small cello. Short bridge-tailpiece gap.  I carved  an appropriate tailpiece

and found the problem improved.

 

I have since tried other instruments, violins, pp tremolo on the low string (middle C).

The same problem occurs.

 

In every case, normal mp play sounds the fundimental with good sound.  But pp tremolo has no

fundimental, to my ear, no analysis yet.  

 

After dreaming about this for a few more nights, I will get some spectra, tailpiece thumps, etc.

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