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Apr 9, 2021 - 11:04:32 PM
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1121 posts since 1/9/2012

I've posted two more notes about calculations relevant to the physics of banjo sound.  The details are monumentally geeky.  The head discussion, Arithmetic of Spring Forces on the Bridge, involves logarithms, Hankel functions, Taylor expansions, stress, strain, and Young's moduli.  However, if the numbers don't match between measurements and theory, the theory is wrong -- or in need of serious modification -- no matter how plausible, elegant, or self-evident.  The note about the "inharmonious clonk," An Elementary Account of Plucked String Clonk,  involves elementary linear differential equations.

The head calculation shows that the primary sound consequence of break angle is actually mostly due to the head distortion.  The idea is simple.  On a banjo at rest, the strings push down on the bridge and the head pushes up, establishing an equilibrium.  If the bridge is displaced, they apply a return-force.  That force and the bridge mass determine a resonance whose frequency becomes the center of the most efficient conversion of string vibration into sound.  The discussions linked in a recent post evaluate the string contribution in detail and punt on the head.  Arithmetic of Spring Forces on the Banjo Bridge gives a simplified model of the head contribution and puts the numbers all together.  For steel strings and tight mylar head, the head contribution turns out to be about ten times larger than that of the strings.  You can probably get the gist of it all just from the diagrams.

The "clonk" is a feature of acoustic string instruments.   It refers to all the sounds that come from the onset of a pluck, which bangs on the instrument body, and are only remotely related to the pitch of the string. These play a very important role in banjo sound because they are loud and persist for much of the time between plucks.   An Elementary Account of Plucked String Clonk is a simple version of the underlying physics.  In particular, the math is something done in second-year college courses.  Again, the diagrams tell much of the story.

Apr 10, 2021 - 4:00:54 PM

4559 posts since 6/3/2011

David
Thanks for the interesting article and links.
quote:
Originally posted by davidppp

I've posted two more notes about calculations relevant to the physics of banjo sound.  The details are monumentally geeky.  The head discussion, Arithmetic of Spring Forces on the Bridge, involves logarithms, Hankel functions, Taylor expansions, stress, strain, and Young's moduli.  However, if the numbers don't match between measurements and theory, the theory is wrong -- or in need of serious modification -- no matter how plausible, elegant, or self-evident.  The note about the "inharmonious clonk," An Elementary Account of Plucked String Clonk,  involves elementary linear differential equations.

The head calculation shows that the primary sound consequence of break angle is actually mostly due to the head distortion.  The idea is simple.  On a banjo at rest, the strings push down on the bridge and the head pushes up, establishing an equilibrium.  If the bridge is displaced, they apply a return-force.  That force and the bridge mass determine a resonance whose frequency becomes the center of the most efficient conversion of string vibration into sound.  The discussions linked in a recent post evaluate the string contribution in detail and punt on the head.  Arithmetic of Spring Forces on the Banjo Bridge gives a simplified model of the head contribution and puts the numbers all together.  For steel strings and tight mylar head, the head contribution turns out to be about ten times larger than that of the strings.  You can probably get the gist of it all just from the diagrams.

The "clonk" is a feature of acoustic string instruments.   It refers to all the sounds that come from the onset of a pluck, which bangs on the instrument body, and are only remotely related to the pitch of the string. These play a very important role in banjo sound because they are loud and persist for much of the time between plucks.   An Elementary Account of Plucked String Clonk is a simple version of the underlying physics.  In particular, the math is something done in second-year college courses.  Again, the diagrams tell much of the story.


Apr 10, 2021 - 7:56:19 PM

13896 posts since 10/30/2008

I remember reading articles on instrument soundboard (or banjo head) physics with pictures of sand vibration patterns, way back in the 1970s in Bluegrass Unlimited. The patterns were interesting and pretty, but the missing element in all this scientific inquiry was WHAT DO THE SCIENTIFIC RESULTS SOUND LIKE?!?!

I'm not being dismissive, I'm an engineer and I appreciate measurements. But why has all the work failed to reach a measurement(s) that describes the sound of a great pre-war Flat Head Mastertone?

The same question might be asked of Stradivarius violin "measurements".

Apr 10, 2021 - 8:58:57 PM

8443 posts since 8/28/2013

quote:
Originally posted by The Old Timer

I remember reading articles on instrument soundboard (or banjo head) physics with pictures of sand vibration patterns, way back in the 1970s in Bluegrass Unlimited. The patterns were interesting and pretty, but the missing element in all this scientific inquiry was WHAT DO THE SCIENTIFIC RESULTS SOUND LIKE?!?!

I'm not being dismissive, I'm an engineer and I appreciate measurements. But why has all the work failed to reach a measurement(s) that describes the sound of a great pre-war Flat Head Mastertone?

The same question might be asked of Stradivarius violin "measurements".


I think the reason why measurements have yet to describe the sound of a Mastertone is because not enough measuring has been done yet. With all the factors involved, such as the materials used, the final set-up, and even the human ear and mind and their differences (some people prefer Stellings, just as some prefer Guarnerius fiddles) and yes, superstitions and preconceptions.

Mr. Politzer at least has given us some of the physics behind how a banjo works in general.  Without some knowledge of how things actually function, one can't really make any statements about why something sounds good or bad, be it a Mastertone or a Resotone. 

The physics may not currently be the entire answer, and may never be.  But it's a start.  

Apr 10, 2021 - 9:11:45 PM

1121 posts since 1/9/2012

And why can't you tell a Vermeer or Rembrandt from a swap-meet clown picture with a photometer?

Actually, my collaborator Jim Woodhouse is big on "physical modeling synthesis." He gets a computer to generate instrument sounds using the claimed equations and asks whether people can hear differences, make identifications, etc. (That is to be contrasted with computer synthesis that uses any trick available to make something sound like you want; for example, frequency modulation is a very powerful tool.)  Woodhouse can vary parameters in the equations that are meant to represent physical design quantities. He did just that with the equations in the Acta Acustica papers in a recent post.  (Unfortunately, it was the journal's first attempt at embedding sound files, and they screwed it up.  The proper versions are in Woodhouse's own site euphonics.org.  That has an enormous amount about the science of acoustics.  The banjo sound files are all in section 5.5 -- an extreme case - the banjo.  My favorites are E.6 and E.7.  (Section 5.4 is pretty good as well on synthesis.)

Apr 10, 2021 - 9:24:29 PM

128 posts since 9/30/2009

I'm quite interested in the description of the "clonk". I've felt an initial pop or tick as I strike a note and this "starting transient" is a great explanation of what I've felt. I find setup and string choice can influence the intensity of the "clonk", and that I certainly use it and appreciate its presence in the attack and drive of my playing, especially for dances.

Thank you David for trying to define what goes on in these instruments. I don't pretend to understand the mathematics or theory involved, but it does help provide a grounding for some of the behaviors I've noticed in working with banjos for many years.

Apr 10, 2021 - 9:45 PM

1121 posts since 1/9/2012

jfhascall

The sound samples I described above as "my favorites" among the banjo synthesis at euphonics.org are, in fact, the separation of a synthesized sound into sound due to modes of the strings, E.6, and sounds due to modes of the body, E.7. When we were working on it, I liked mixing the two in variable proportion and listening. (That didn't make it into the paper, but you can't do everything.)

Apr 10, 2021 - 10:06:24 PM
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Bart Veerman

Canada

4915 posts since 1/5/2005

quote:
Originally posted by The Old Timer


why has all the work failed to reach a measurement(s) that describes the sound of a great pre-war Flat Head Mastertone?

The same question might be asked of Stradivarius violin "measurements".


 

I'm guessing, for that, you need to teleport yourself to another branch of science: neuroplasticity - specifically, the folks who apply their research to the human hearing thing.

I've logged a lot of hours in such a lab at our local university, guinea pigging in tinnitus-related research. It's amazing to find out how your ears can be fooled into thinking what you hear isn't what you're really hearing.

The human hearing is not absolute like an oscilloscope or whatever recording device - it operates according to a different set of rules: Perception, Interpretation and Evaluation - these 3 items chase each other in a continuous circle while comparing new results to previous experiences.

Previous experiences are deleted when you engage in a different activity, especially when you go to sleep and when you wake up the next morning your brain reboots thus nixing yesterday's "markers."

This is a biggie when it comes to trying out new bridges: quite a few posts over the years mention, I'm paraphrasing now, "a bridge has to settle for one day before it can sound good." Nope, not at all - it's your brain that requires a reboot before it can fully appreciate the way your banjo sounds now instead of comparing it to the way it sounded before.

It's OK to disagree with all this but here's a simple experiment that illustrates how your hearing can be fooled:

Put a mute on your bridge (if you don't have one, a clothespin will do just fine) and play your banjo for about 4~5 minutes. Quickly remove the mute and continue playing - for humans it'll take approx 10~30 seconds until your brain figures out what happened and finally decides to allow you to hear the proper un-muted banjo sound.

David: I apologize for the detour to your post and its crazy valuable info but I hope it's not too inappropriate, considering your amazing scientific expertise.

Apr 10, 2021 - 10:30:01 PM
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1121 posts since 1/9/2012

Bart Veerman

Topic drift -- I'm a huge fan when it gets interesting. Regarding the chasm between perception and physical stimulus, I have a serious, recent book to recommend: "Musical Illusions and Phantom Words" by Diana Deutsch. She's a professor of cognitive psychology at UCSD. The book is not at all technical, but you have to pay attention. One of its great features is that you can hear the sound samples for yourself. If you have a cell phone, you just point it at the page. Otherwise, you type the URLs into your computer. For many years now, she has been discovering more more examples of people hearing things that are strikingly different from what's actually there in terms of sound as pressure waves in air. The right attitude is that these are not parlor tricks. Rather, they're insights into the workings of the mind.

Apr 11, 2021 - 7:37:56 AM

13896 posts since 10/30/2008

Bart, I smell what you're stepping in!!! You made my point very well. I guess it boils down (as usual) "you know it when you hear it -- maybe".

Thanks!

Apr 11, 2021 - 10:14:50 AM
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Alex Z

USA

4212 posts since 12/7/2006
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Mr. Bart:  "I'm paraphrasing now, "a bridge has to settle for one day before it can sound good." Nope, not at all - it's your brain that requires a reboot before it can fully appreciate the way your banjo sounds now instead of comparing it to the way it sounded before."

This is very interesting.  Over the years, by experience I have learned not to judge differences in tone at the end of the day.  Sometimes nothing sounds good.  In the morning, the ears seem refreshed and more discerning.  Have chalked it up to noise fatigue over the course of the day.  The "brain reboot" is a good explanation.

Also have learned by experience that if I'm trying out banjos, playing a guitar beforehand makes the banjo sound bright and harsh.  And if I'm trying out guitars, playing the banjo beforehand makes the guitar sound muted and unresponsive.

Wouldn't it be great if someone invented, say, a DNA injection that could make your banjo sound -- to your brain -- like a different banjo.  "Do you want the 1937 flathead Granada juice or the  '34 Bella Voce archtop?"  smiley

Apr 11, 2021 - 12:57:19 PM

2772 posts since 12/4/2009

Hello,

I listened to each sample and followed up to the mass of the bridge. This is where to me the logic fell flat. 2.2 grams is the ideal weight for a bluegrass banjo bridge. The approximate sounded tubby and dimminished in tone, almost muted.

Given the plectrum instrument used, 1.5 grams would be considered the optimum bridge weight. For Bart and other Banjo Bridge makers is this true or is the math wrong?

Edited by - Aradobanjo on 04/11/2021 13:04:41

Apr 11, 2021 - 8:40:37 PM
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Bart Veerman

Canada

4915 posts since 1/5/2005

quote:
Originally posted by Aradobanjo


This is where to me the logic fell flat. 2.2 grams is the ideal weight for a bluegrass banjo bridge. 


 

I tried skimming through the various PDFs that David posted but couldn't quite find the section you referred to. Truth be told, had I found it then chances are I couldn't have followed the formulas anyway - my math skills and I went our separate ways a few decades ago...

Whether the 2.2 gram weight is the ideal weight for a BG bridge or not, would, no doubt, fill several pages with highly passionate opinions smiley

Apr 11, 2021 - 9:35:57 PM

128 posts since 9/30/2009

I found that going to the Euphonics.org website that David posted helped a lot. It's quite the project and the section on the banjo really went deep. I definitely had to skim a lot but the section on bridges, weights, and flexibility was quite interesting. My take was not that a 2.2 gram bridge is considered ideal, rather that it was the weight bridge that Deering sent out and that they used for the real world data that drove the computer modeling. To say that one bridge on one banjo tested under a set of uniform procedures gives you an answer that you can use in the real world is probably not realistic. However, the sound clips of differing bridge weight examples actually helped clarify for me the trends that happen as bridge weight changes, and that is something I'll be testing as I voice specific instruments. As far as what actually sounds good on any particular instrument, I think Bart has correctly made the point of what a subjective and changeable thing that is.

Edited by - jfhascall on 04/11/2021 21:36:51

Apr 12, 2021 - 6:27:33 PM

2772 posts since 12/4/2009

quote:
Originally posted by Bart Veerman
quote:
Originally posted by Aradobanjo


This is where to me the logic fell flat. 2.2 grams is the ideal weight for a bluegrass banjo bridge. 


 

I tried skimming through the various PDFs that David posted but couldn't quite find the section you referred to. Truth be told, had I found it then chances are I couldn't have followed the formulas anyway - my math skills and I went our separate ways a few decades ago...

Whether the 2.2 gram weight is the ideal weight for a BG bridge or not, would, no doubt, fill several pages with highly passionate opinions smiley


Hello Bart,

Every banjo bridge from you and others has been 2.2 grams +/- .1. I followed the math. However, math is based on hypothesis and proven only by physical and logical rigor. Ken LeVAn provided the empirical study on the different weights, woods, and styles a few years ago. 2.2 grams came out tops then in the straw polls he conducted. Thin ( < 2.2 grams) did not cut the "muster".  This seems to contradict the math modeling.  Thick (> 2.2 grams) did not cut the muster either.  

Apr 13, 2021 - 4:15:58 AM

2772 posts since 12/4/2009

Hello,

Listen to Sound G4 and G5. G4 is more pleasant that G5. Well, the same is true with bridge height. 5/8” vs the world of bridge heights is to be ascertained from this analysis.

Bela Fleck and Noam Pickelny play banjo with 1” bridges. This is to meet their hands. Euphonics gives “dire” warnings to those who venture beyond a certain mass and height. You instrument will sound just like we predict; muted, muddy, and mushy.

Tony Trischka’s interview with Bela Fleck here on BHO said they tune their heads more loose to prevent hearing loss. Optimal use is calculated for vehicles with dynamometers. Imagine a banjo dynamometer. If this math built a banjo, would we go crazy with desire or deaf from its loudness?

I am so glad to see this work. Can math solve every problem? No. Solutions are very constrained to limited variables. Everything else is approximate. Banjos are cool instruments. Math built them. Yet, early banjos didn’t have the math we have today. Not until the use of frets did math become important. The 5th string is still missing in the calculations. The 5th requires complex approximating.

JD, Bela, Sonny, Noam, Earl, Don Reno, Tony T and others have achieved an optimal stroke of plucking the strings. A sample of observation sets could see what angle of attack they achieved for optimal. Did Math pick the optimal attack angle?

As the saying goes, this is left for the readers to figure out.

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