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May 15, 2021 - 7:04:25 AM
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74531 posts since 5/9/2007

I use the weight of my bridges to dictate the tone of the banjos they go on.
I tend to use the weight range of 2.25 to 2.3 grams for a well-rounded bluegrass tone from a maple bridge topped with ebony.
I usually make a clawhammer bridge from sycamore with a rosewood top and a weight range from 2.4 to 2.7 grams.
Sometimes I remove too much wood from the bridge being worked on and have to start over.

Being averse to throwing anything away I have a collection of bridge "mistakes" that are too light in weight and have tones that are over-trebly/weak bottom end.
Yesterday I was thinking of an old article I'd once read about Bill Keith winding a banjo string around the legs of his bridge.
So I selected a bridge that weighs only 2.0 grams and wound a 2" piece of mechanics wire(.030" diameter weighs .10 grams/inch).

I twisted the wire with needle nosed pliers tight around the treble leg of the bridge using care to get it tight without splitting the wood.
I added .24 grams of weight with the piece of wire to a new 2.24 grams total.
This "fattened" the tone back to where I don't feel it's too trebly.
A nice return of the bottom end.

Edited by - steve davis on 05/15/2021 07:33:33

May 15, 2021 - 7:30:34 AM

3460 posts since 9/12/2016

sometimes I wire them some times i bolt or screw them




May 15, 2021 - 10:14:47 AM

1147 posts since 1/9/2012

There are two parts to the simplest physics story of what's going on with bridges.  Total bridge weight enters the first part and contributes to the overall response below about 3000 Hz.  How the bridge flexes determines its special voice at yet higher frequencies.  (It's all here [see April 2021]) and accounts for what screws and wire actually do.)

As an intermediary between strings and head, the bridge is an active element.  It is an oscillator with inertia given by its mass and a return-force determined by the break angle (acting on strings and head).  Their ratio defines a resonant frequency which shapes the head-alone vibration spectrum (blue curves) into what actually happens with the bridge (red curves).  (The black is a guitar for comparison.)

Any increase of bridge mass shifts the smoothed spectrum peak (i.e., that's around 650 Hz in the accompanying graphs) to yet lower frequencies.

I did measurements with eight very different bridges with the same weight and break angle.  They performed identically below 3000 Hz and were obviously quite different above.  My computer-savvy buddies modeled the first of those bridges and identified the particular bridge flexing motions that gave that bridge its unique voice.

May 15, 2021 - 12:31:10 PM

3460 posts since 9/12/2016

so which way does it flex, that seems to be still a mystery to me.I also wonder about a single resonant frequency being defining on so many frequencies above and below it.I see it as part of the strings oscillation more so than it's own properties.I don't claim to be any expert ,just a student of banjo.
Keep up the great work

May 15, 2021 - 12:36:07 PM

74531 posts since 5/9/2007

I figure the added mass or weight decreases bridge vibrations and decreasing bridge weight increases the bridge's reaction to string vibes.
It would seem that more bridge vibes favor the trebles/less vibes (more mass) favors the lows.

May 15, 2021 - 2:10:17 PM

3460 posts since 9/12/2016

The outside strings sit right over the outer feet , getting a short immediate route in comparison. Heavy hard things seem to reflect sound back, more sustain ,so mine are kinda like a reverb tank ,but that is only in my head on my bridge .
I figure it likes to rock some on that middle post along with a possible flexing about half between the first and middle leg ,same with middle and third

May 15, 2021 - 6:32:45 PM
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1147 posts since 1/9/2012

quote:
Originally posted by Tractor1

so which way does it flex, that seems to be still a mystery to me.I also wonder about a single resonant frequency being defining on so many frequencies above and below it.I see it as part of the strings oscillation more so than it's own properties.I don't claim to be any expert ,just a student of banjo.
Keep up the great work


My apologies for being pedantic.  (It's actually been paying the bills for my whole adult life.  I could answer in a sentence or two, but I can't imagine that would be of any help.)  Here's an attempt to answer as best I know: 1) how does it flex?  2) how does one bridge flexing frequency spread its effect over many sound frequencies that we hear, i.e., over a whole region?  and 3) how do I suggest thinking about sound getting through the bridge (and why it doesn't actually take a particular path)?

1) The only flexing I'm confident about is for one bridge design, and it comes from a calculation.  There certainly exist technologies that would allow observation of any particular bridge.  (There are people where I work who measure far tinier motions; they're funded by your tax dollars, but I don't have access to what would be needed.  My buddy in England can do vibration measurements on a particular point with the relevant sensitivity, but getting measurements on a whole, three-dimensional object [rather than a patch of a single, flat surface] is much harder.)

The accompanying figures are output from a "finite element" computer calculation.  The inputs are the physical properties of the head and bridge of that shape.  The choices of where and how to tap the bridge were guided by doing it on a real banjo and measuring the bridge motion.  All tap locations and directions gave some enhancement of the response in those two frequency regions, i.e., around 3500 and 5000 Hz.  But the response was most pronounced for those tap choices.  So, that's the numerical calculation we looked into.  "F=ma" for each little piece of the system tells you how it moves in response to the tap.  You can decompose the motion into frequencies and look at how the bridge and head move in those regions of large amplitude response.

As I noted previously, below 3000 Hz, eight very different bridges that I tested gave the same tap response when mounted on the same banjo (with same weights, tensions, break angles, etc.).  As I understand it, that's because none of those bridges have their own flexing resonances in that frequency range.

2) A single, undamped, ideal oscillator has a mass and a "spring constant."  Their ratio gives the (angular) frequency (squared).  If you apply a force at some particular single frequency, the oscillator will move with that applied frequency.  The amplitude of that oscillator's motion will be proportional to the force and inversely proportional to the oscillator's mass.  Furthermore, it will depend sensitively on the relation of the oscillator's "natural" or "resonant" frequency to the forcing frequency.  If those two frequencies are equal and if the oscillator really were to have absolutely no damping, its amplitude would keep increasing the longer the external force is applied.  Away from that matched, resonant condition, the damping is of little quantitative importance.

There are different ways to describe in words what happens when you put a bridge with a flexing resonance on the head.  The accompanying pictures remind us that the head has to move in consonance with the bridge feet, no matter what.  Also, remember that the head, on its own, has a great many resonances very close together in frequency, while the bridge will have just a few far separated ones in the audible range.  One way of looking at it is to say that it is the resonances of the combined system that are of interest.  Those are the individual peaks in the graph I reproduced earlier in this thread.  (That graph is actual banjo measurements; the computer model does a fine job of reproducing them.) There are many separate head resonances that combine with the particular bridge resonance so that all parts move with the same frequency in the single, combined resonance.  Not surprisingly, the head motion is somewhat distorted near the bridge from what it would be without the bridge.  The bridge motion is only slightly distorted from bridge alone motion and is only slightly different for each of the combined bridge-head resonances.

I like a different way of looking at the combined system because I can do the calculations (at least some of them) with paper and pencil and it focuses on the trends, i.e., broad, enhanced regions, rather than on individual resonance peaks.  One can view the process as having the action of the strings go THROUGH the bridge to the head.  The bridge has a few widely separated resonances.  (The lowest one is when there is no flexing; for that resonance, the bridge moves as a rigid solid, and the return force is given by the strings and head — that's the one I can calculate!)  The most important damping of the motion of the string-forced bridge is its loss of energy to outgoing waves in the head.  Damping of an oscillator gives its forced response a width in frequency.  That's the smooth red curve in the lower of the previous graphs, which comes from the no-flex lowest bridge resonance.  A yet more detailed physics argument shows that only including outgoing head waves yields a running average of the actual case, in which there are incoming waves, too (those having reflected off the rim).  They make the actual response stronger or weaker, depending on whether they are arriving in or out of phase with the outgoing one.

3). In everyday experience, we encounter objects that sound different depending on where we tap them. Also, there are distinct effects of sound bouncing around, reflecting off walls, etc.  It seems to go in paths — although it is awfully good at going around corners.  To understand how sound travels from strings to the head, we have to pay attention to wavelength.  Important: wavelength = (speed of sound in the material) / frequency.  You can look things up, but roughly the speed of longitudinal compression and rarefaction waves in wood is about 10 times greater than it is in air.  The lowest note on a soprano recorder (about a foot long) has a wavelength of twice that (two feet).  (The frequency is 523 Hz.)  The speed of sound in air is about 13500 inches per second.   The lesson is that the wavelengths in wood of banjo sounds are much, much longer than the height of the bridge.  Flexing motions do occur at high, audible frequencies, and those do care where and how the string force is applied.


May 15, 2021 - 7:00:23 PM

jfb

USA

2397 posts since 9/30/2004

Steve
What scale device do you use for weighing grams if you could share?
Thanks

May 15, 2021 - 7:56:06 PM

3460 posts since 9/12/2016

David I am going to have to read this several times ,It is understandable,but is going to take some thinking. ,but seems right on .I always wonder how it works when frequencies higher than the head's resonant pitch, hit it .There has been a lot of supposed patterns and holograms over the years. Anyway thanks and you didn't even use math.

May 15, 2021 - 8:17:19 PM

3460 posts since 9/12/2016

Question David can you elaborate on the head having many resonant frequencies ,I thought they only had one.
, I have seen guitar builders point out note areas on guitar tops though,

May 15, 2021 - 10:12:31 PM

1147 posts since 1/9/2012

Many resonant frequencies:  "Pitch" is something our brains perceive.  "Frequency" has a physics/math definition.  It's even more specific than how often things repeat per second.  The crucial additional aspect is the magic of "Fourier transforms."  In math and physics, motion with a particular frequency is precisely sinusoidal in its variation with time.  If it's not sinusoidal, it's not just one frequency.  Rather, it must be the sum of various frequencies.  If the motion repeats precisely in time, then all those component frequencies also repeat in the same time interval.  The lowest may repeat just once, but you can have components that repeat multiple times in that same interval.

Our brains have evolved to work very hard at trying to identify a pitch with particular sounds.  Sometimes it's easy and sometimes hard.  Pitches of electronically generated, single frequency, pure sinusoidal sounds are easy to identify.  Some natural sounds (e.g., very musical ones) are easy.  Some are hard.  Drum and cymbal sounds only sometimes barely seem to have a definite pitch, and some drums (e.g., kettle) do better than others.  Banjo head tap tones for tension adjustment are easy for some people and hard for others.  In that case, the perceived pitch is not a particular frequency produced by the head but the common frequency differences between a great many produced high frequencies.  (See the Addendum to the Picker's Guide to ..., i.e., page 17 - 21, for what I believe to be going on.)

Start with a string (fixed ends, under tension).  It has a pitch, and that pitch corresponds to a frequency.    On that same open string, you can play harmonics (or "chimes").  The pluck mechanism is different for each, but, after you let go, the string vibrates on its own.  12th fret, 7th, 5th, 4th, and the series goes on, although not all chime points are actually over frets.  The (ideal, fixed end) string has an infinite number of resonances, each with its own frequency.  The lowest corresponds to the pitch you normally hear.  However, all the others are always present in some amount.  You dramatically alter the various amounts when you play the "harmonics."  The first resonance above the lowest is at double the lowest frequency.  And the infinite series has frequencies spaced one to the next by that amount.  The transverse motion at different points along the string has a simple form, too.  For an ideal string, it is an integer number of half sine waves.  Add one more half sine wave, and the frequency goes up by that common interval.

Thin wooden soundboards (e.g., guitars and violins) have been studied for a long time.  Details of the instrument determine the lowest few resonances.  The wood and (compared to banjo) heavy bridge and turn most of the higher frequency string energy into heat instead of sound.  What remains is not completely negligible and has a simple property regarding frequency: the high resonant frequencies are very nearly equally spaced (just like the string).

The banjo head is dramatically different.  We increase the tension to values so big that tension dominates the force that pulls the head back to its equilibrium level when it is displaced.  To be sure, the head has its own inherent stiffness, but that contributes negligibly in practice for the small amplitude vibrations.  In physics/math, the term for a pure tension force system is "membrane."  In the ideal membrane approximation at a given tension, the low ones do depend on the size and shape.  But they quickly approach that ideal spacing rule, with closer and closer with increasing frequency.  This is an important part of the piercing sound of banjo compared to guitar: much more of the string's high frequency motion is turned into sound — because there are more resonances closer together.  Again, a given oscillator with a given frequency will move at any frequency you drive it with.  The amplitude of that motion becomes its biggest when the drive is close to the oscillator's own frequency.  And I should have said: each resonance of the head or soundboard can be considered as an independent oscillator, and each is driven by the many frequencies of the string.

"Note areas" on guitar tops are presumably places where the vibration is particularly large when that note is played.  (The cochlea, an organ in the inner ear, uses that kind of spatial response to separate a sound into its Fourier components so that different frequencies can stimulate different nerves.)  There are analogs on banjo.  (I'll ignore for now another important layer in the banjo story: sound radiation efficiency.)  The approximate circular symmetry means that the distinction of areas is mostly in terms of radial position.  For example, people damp out the highs by damping the head near the rim: that's where they stuff.  Builders in the late 19th Century put the bridge nearer the rim if they wanted to enhance the highs.

May 15, 2021 - 10:50:50 PM
Players Union Member

Eric A

USA

1196 posts since 10/15/2019
Online Now

I also once tried to add weight back on to a bridge that I had thinned too far (too trebly) using toothpicks and elmers glue. I was disappointed in the results. It was a very crude job though. Might have added more glue than wood! Wasn't sure how much I should read into that.

Now I just save those "too thin" bridges because I figure there's a place for them setting up some banjo somewhere, perhaps even as an outer limits benchmark if nothing else. Just as I also have some bridges that I know are going to be too heavy. When setting up a banjo I try different bridges, in order from heaviest to lightest, until I find the one(s) that sound best on that banjo on that particular day. Too heavy and the 3rd/4th strings just won't pop clearly. Muddy. Too light and the 1st string becomes grating on the ears.

Winners tend to end up within a range of .2 to.3 of a gram, but the range is a little different on each banjo.

Edited by - Eric A on 05/15/2021 22:53:52

May 16, 2021 - 6:13:40 AM

74531 posts since 5/9/2007

quote:
Originally posted by jfb

Steve
What scale device do you use for weighing grams if you could share?
Thanks


Sure thing,Butch.

My scale is a "Pro Scale LC-50"...$10 It has a 50 gram limit.

The important thing about any scale used is that it reads 2 decimal places or hundredths of a gram.

There is way too much difference in performance between a 2.10 gram bridge weight and a 2.19 gram bridge weight.

If a 1 decimal place scale is used it shows the 2.10 gram and 2.19 gram bridges to be the same calling them both 2.1 grams.

If someone wants a "Stanley" tone I send them a 2.0 gram maple/ebony.If they want a Scruggs tone I send them a 2.25 grammer for a fuller,more balanced tone over the entire neck.

I make my decisions based on customer input, the way different weights affect the final sound and especially how the banjo performs in challenging situations like a busy jam.

Good scales are cheap,but they must have 2 decimal places.

Edited by - steve davis on 05/16/2021 06:14:51

May 16, 2021 - 6:43:13 AM

3460 posts since 9/12/2016

thanks again David,, My simple dumbed down take away for storage in memory is --the head has overtones just like the classic string example .
I have found that when the banjo is in standard g tuning I can used a small steel rod as a slide in the vicinity of the mid point(12 fret) On the live side I can lightly slap all strings and head at the same time. The perceived head note and which way to slide the rod for a match up is very easy to hear,even for my tin ear. My needle nose pliers are my actual pseudo slide. I remember Siminoff giving recommended tensions once and they were actually the first overtones of the normal suggestions.

May 16, 2021 - 7:39:42 AM

1147 posts since 1/9/2012

"I remember Siminoff giving recommended tensions once and they were actually the first overtones of the normal suggestions." -- If the sound is not purely sinusoidal (which in nature is essentially never), people often disagree or aren't even sure themselves in what octave a particular note belongs.

May 16, 2021 - 9:52:31 AM

jfb

USA

2397 posts since 9/30/2004

Thanks for that information Steve
Helpful and appreciated

May 17, 2021 - 6:29:58 AM

74531 posts since 5/9/2007

The G# head note is the same octave as the banjo 4th string on the 6th fret.

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