Flexibility

[John Bertotti]

I am coming to terms with top plate thicknesses little by little but how about back thickness. Do you all just carve to a desired thickness or are you feeling the back? How much flex/deflection do you build in?? As I am understanding it the back thickness and its flexibility have some impact on how good the chop is. Am I completely mistaken?

[sunburst]

We want the back to couple well with the top (and air modes and do forth) so we want the thickness/flexibility of the back to work well with the top. Relatively speaking, a stiffer top needs a stiffer back, a less stiff top needs a less stiff back.

[John Bertotti]

Thanks! Subjectively speaking am I correct in thinking it won’t be as flexible as the top or is it very close? Am I also correct in thinking it might be good to get the top where I want it and fine tune the back once assembled?

[Dave Cohen]

Back plate stiffness vs top plate stiffness has an impact on the bass/treble balance of an instrument. I don''t like the word "tune", because that can be taken as implying that the parts of an instrument should be made to vibrate at a particular frequency. In fact, all of the parts of an instrument vibrate in numerous NORMAL MODES of vibration, and each of those modes has a characteristic peak frequency which depends on its physical characteristics (Elastic moduli, etc.) as well as its interaction with all the other parts of the instrument. Also, each of those modes vibrates over a small range of frequency. (not just at a single noaarow peak frequency). The actual motions of those parts at any given instant are not any particular one of those normal modes, but rather the sum of them. In physics language, the overall motion is said to be a Fourier superposition of all of the individual modal motions.

The body of a string instrument in which both the top plate and back plate are active can be modeled as a "three-mass oscillator", the three masses being the top plate, the back plate, and the air mass(es) in the sound hole(s). The coupling that John mentioned above refers to the fact that those masses are coupled to each other by springs. In the case of the plates, the springs are the "springiness" (aka elastic moduli) of the plates themselves. In the case of the soundhole air mass, the spring is the air inside the instrument's body cavity. In order to most effectively pump air in and out of the soundhole(s), the top and back plates have to have a mode in which the top plate and back plate are working together, similar to a bellows, to pump air in and out of the soundhole. And that "bellows mode" happens to be the lower main mode (aka "trampoline mode", aka (0,0) mode, aka T(1,1) mode - there's a lotta different notation used for this).

So what does all this mean for you in your shop? Yes, you can start with a slightly too thick back plate assembled to the instrument and gradually thin it from the outside until the bass response of the instrument comes into the range that you want (like?). Generally, as you thin the back plate, the bass response of the instrument will increase. A word of caution, though; if you go too far, you can overbalance the bass to the point where the treble seems to be too weak. Another way to do the same thing is to use James Condino's method, in which he glues temporary linings to the OUTSIDE of the sides, and temporarily screws the plates to those temporary linings, does his adjustments until he likes what he hears, then removes the plates and the temporary linings, and finally assembles the instrument in the usual way. He has described that method briefly on this forum, as well as in more detail elsewhere.

[j. condino]

Dave: Thx for the mention.

I definitely want to point out that the origins of my method came from seeing one of your earlier mandolins that had a removable back. Yours had ultralight nylon screws on the inside of the plate pattern where traditional linings exist. Being a perpetually curious and broke mandolin builder, I was interested in the information I could learn from removing the plates, but could not justify loosing a fancy plate and the customers I showed it to were not willing to accept the screws. SO- I put the linings / screws / additions on the outside and then when everything is all said & done, any trace of the test rig gets routed away.

This system pretty much revolutionized my ability to tune mandolins and allows me to get very consistent instrument to instrument voices- something that was very difficult in the past. It has been well documented in numerous sources. I'm amazed the entire mandolin community refuses to adopt it. I have a student with a current build thread going, so we'll be using that test rig again next month and he'll likely show it off and comment about the results.

[John Bertotti]

Thanks! I will dig into that jig I do believe e I saw it somewhere was it a guild book?

[Dave Cohen]

James, thanks for the nod. What I did was intended for the laboratory and the interferometer. I did a first mandolin with a screw-on back in 2001. That one had a redwood top, and walnut back, sides, and neck. Took that one to Rossing's lab at NIU and did the interferometry with four different bracing patterns, and gave an invited paper at the 75th anniversary ASA meeting in NYC in 2004. The one ou saw in Tacoma in 2011 is the one I call "Fronkenshteen". It has a screw-on spruce top plate, a screw-on maple back plate, matching maple sides with a layer of CF cloth inside, and two bolt-on necks. One neck is conventional, with a conventional adjustable truss rod. The other is the all-CF hollow shell neck that you saw. Believe it or not, I've had several people ask if they could buy Fronkenshteen. I've held on to it because there is still information I can get from it.

I'm pleased that you credit my Fronkenshteen mandolin for the inspiration to do what you did. I also think that the direction you took the concept is original and justifiably yours. I got the idea for screws from reading about some luthiers using s temporary glue joint with a layer of paper in the join. That's still seemed too difficult to me, and I was intimidated by the potential for damage from applying heat and moisture. So I "borrowed" the concept of a removable plate, but came up with a safer (if clumsier) way, using lightweight nylon screws and nuts captured in the lining. But turning the temporary screw joins into a tool for adjusting the properties of the plates and soundholes during the building process is yours, and Bravo for that!

[j. condino]

For folks feeling left out of our thread derail, here is a link to a detailed discussion and description of my plate tuning jig:

https://www.mandolincafe.com/forum/t...lins-in-2-days



Another mandolin build with a different student using the test rig:

https://www.mandolincafe.com/forum/t...hlight=condino

[HoGo]

I adjust thickness on assembled mandolins before finishing but it's hard to judge when to stop and pretty damn hard to replace a top or back once thinned too far so James's jig solves that problem.

Just one side note... My first mandolin (that I made) had quite thin plates and flexible arching with wide recurve on both top and back. The sound was nice woody and balanced but not very loud.
Later I replaced top with one made to Loar specs and the tone has stronger core but the thin flexible back still acts in a way that makes for nice thick chop but lacks projection in solo playing.

[John Bertotti]

So if O have paid attnetion and understood correctly over the years I have another pondering. It has been said it isn’t so much graduations but stiffness of the plate, hope I got this correct, if so then you could possibly salvage a to thin plate with the strategic placement or sizing of a brace or two?

[sunburst]

So if O have paid attnetion and understood correctly over the years I have another pondering. It has been said it isn’t so much graduations but stiffness of the plate, hope I got this correct, if so then you could possibly salvage a to thin plate with the strategic placement or sizing of a brace or two?

Stiffness and overall mass are more important than grads. Graduating a plate, however gives us a way to minimize (somewhat) weight for a given stiffness. In other words, by graduating a plate we can reduce the mass of the plate without sacrificing stiffness to the extent that thinning an even-thickness plate would. Arching plays a significant roll as well.
As for salvaging a too-thin plate with bracing, we may be able to do that to some extent, but there is the structural aspect of the plate to consider.

[John Bertotti]

Excellent! Thanks @sunburst it would be natural there would be a point of no return and diminishing returns up to that point I imagine. Thanks everyone!! In my mind and hands it just seems like I’m on the verge of some sort of revelation, about what I’m not sure.

[HoGo]

Current trend among top violin makers seem to concentrate on arching shape/height depending on stiffness of wood and also final weigth of plates within some acceptable range (but generally close to structural minimum). Of course they note taptones but rarely try to reach exact notes. Thicknessing stops when the weigth is in range or when stiffness of the plate reaches critical point.
SOmetimes when their plate ends too heavy with graduations quite thin they judge it as problem of incorrect arching height - heavier wood usually gets higher arch and thinner graduations so overall weight gets in the range. Most of violinmakers are quite nerdy about selecting wood with their preferred density and stiffness (speed of sound).

[Dave Cohen]

There are a few things about "stiffness" that always seem to get glossed over. What's somewhat discouraging about this is that the information is not new; it's been around - and available - for a long time. If you thoroughly absorb the information in Daniel Haines' 2001 CASJ paper, you'll get good and broad understanding of wood properties. And the information was not completely new even then. Haines wrote that paper as a review, at least some of that data having been published in a previous paper. David Hurd wrote a paper in American Lutherie #97 (Spring, 1999) which summarized well the application of wood properties to estimating an initial soundboard thickness. So I'll list them below, in an attempt to keep them from being buried in a long paragraph:

1. When talking about "stiffness, use the term "Elastic Modulus" (aka Young's modulus). Most luthiers understand that "stiffness" depends on dimensions, including thickness, The Elastic modulus is a parameter for unit dimensions. Multiplying the modulus by the dimensions of your workpiece will give the stiffness. So it is that modulus, not the stiffness, that is characteristic of the particular piece of wood you are working.

2. Wood is orthotropic, meaning that the moduli are different in the three different coordinate directions. Because instrument plates are relatively thin in one of those dimensions, only TWO of those moduli are more important. The modulus in that third dimension can be ignored as a good approximation. Those important moduli are (a) the modulus along (i.e., parallel to) the wood grain direction, and (b) the modulus perpendicular to (i.e., across the plate) the wood grain direction.

3. The parallel modulus is MUCH LARGER than the perpendicular modulus. IOW, the wood is much stiffer along the grain than it is across the grain. Surveying the data shows that you can expect the parallel modulus in your piece of wood to be anywhere from about 7x to as much as 30x (or occasionally even more) larger than the perpendicular modulus.

4. The parallel modulus tends to vary fairly linearly with the density of the particular piece of wood. Generally, denser is also stiffer. So, you can get an estimate of how "stiff" your wood is along the grain by measuring its density. Cut off a little chunk from the waste of your plate material, make it rectangular, measure its dimensions with a ruler or caliper, measure its mass with a balance, and calculate D = m/V, where V = LxWxH.

5. Unfortunately, this is the harder part: The perpendicular modulus can be all over the map. Density is not a reliable indicator of the perpendicular modulus or stiffness at all. So the only way to know the perpendicular modulus is to make the measurements and calculate it. And while you're at it, might as well measure the parallel modulus as well. I have posted on sources of information about those measurements before. The differences between individual pieces of wood can be pretty large. The upside of that is that fairly crude measurements can be useful. You really only need two significant digits (significant digits are defined as digits which are the results of measurement).

6. THere's one more. Graham Caldersmith showed in 1974 that the OVERALL FLEXURAL STIFFNESS of a plate can be approximated as the square root of the product of the parallel and perpendicular moduli. And that product really will tell you about "how stiff" your plate is relative to your other plates (or anyone's other plates, for that matter).

So knowing that product (in number 6.), in combination with the density, will give you an idea of what the estimated initial thickness of your plate should be relative to your other plates. Regarding your question about bracing, the measured parameters are helpful there too. Generally speaking, braces along the grain don't raise plate frequencies much, but do serve to distribute the load from the static down force on the plate at the bridge from the strings. Braces perpendicular to the grain, on the other hand, will increase the stiffness and thus raise plate frequencies significantly. So, f'instance, if you have a plate with an especially low measured perpendicular modulus, you might want to splay your bracing pattern out some, or maybe add a small perpendicular brace, in order to raise the overall flexural stiffness of your plate. An example: An X-brace, instead of the usual (mostly) parallel bars, will do some of that for you.

[j. condino]

Most of violinmakers are quite nerdy about selecting wood with their preferred density and stiffness (speed of sound).

Yes sir.

The Oberlin Summer Acoustics workshops are the most numerically nerdy event that I have attended. All week is spent measuring and calculating everything possible. Most of the better violin builders and wood sellers I know always use a Lucci meter to measure the speed of sound through their materials; I know of only one other mandolin builder in the country that does and NONE of the tonewood suppliers I know do. ALL of the bowmakers I know obsess over it and will not purchase any materials without that number given. The speed of sound divided by density is commonly referred to as the radiation ratio. That is the number that I was taught to pay attention to for soundboards rather than just the individual values of those key numbers.

I spent decades crunching numbers and viewing computer models of soundboards before I came to the develop my ear based method for voicing. Numbers are useful. Computer modeling is useful. But- those are not my end goal. Showing up at a gig or jam session and blowing the doors off everyone else in the room IS my goal. Using a voicing method that relies on my ears and ability as a payer fits with my 1/2 century of playing gigs and buiding; I recognize not everyone has this ability or sensitivity in their hearing so they try other methods.

Of note for me is that while at Oberlin, I brought 25 tonebars from my favorite two trees of numerical analysis. We put identifying marks on all of them. I gave them to the numbers nerds and they shuffled off for about 45 minutes doing their thing. They came back with notes. Then they gave them to me and I along with another highly respected builder picked out our favorite three (two primary plus one spare). When we compared notes, we picked the same three bars as optimal from the batch. This told me that there is value in both methods and if you have one that is currently working for your approach and builds, don't get distracted. The best way to become a great mandolin builder is to build lots of mandolins and take good notes. The wood will tell you what it wants; the trick is listening!

I honestly believe (and hope) that in 100 years, builders will look at what we do today similar to putting leaches on the bottom of your feet and praying it works like some medieval cure. Until then, we tap and scrape and flex and sometimes chew on the wood and call it "tradition". I also occasionally toss it in the toaster oven for hours in the name of progress....

[peter.coombe]

My approach has been to measure the modal frequencies of the free plates using chladni patterns and correlate that with the sound of the finished instrument. More recently, after reading the Gore/Gilet books, I have also been measuring the frequencies of the main air mode, main top mode and main back mode of the finished instrument. I look for correlations, and there is a correlation, but you need to look at relative frequencies, as already mentioned above. Mandolins vibrate like guitars, so you can use all the guitar research stuff. For arch top oval hole mandolins I match the frequency of the ring mode of the top and back plates to within + - 5%. That was determined entirely empirically by making lots of mandolins and playing and listening carefully and writing everything down. After measuring the modes of the finished instruments I discovered that if the ring modes of the free plates are matched, then the difference between the frequency of the main top mode and the main back mode will be 4 semitones or very close to 4 semitones. It is very consistent, it happens with every mandolin. If the frequencies are far apart then you will not get 4 semitones. Surprise, surprise, 4 semitones is considered to be the optimum difference for guitars by Gore and Gilet in their book. However, F soundhole mandolins are different, and flat top mandolins are different again. The relationship between the free plate frequencies and the finished instrument is different, and with F soundhole mandolins the optimum difference is diffferent so it gets complicated. However, with the flat top mandolins I have been able to adjust the main back frequency by filing wood off the center brace and play and listen within a few seconds, correlating the sound with a known reference. These have an oval sound hole so it is no surprise that these sound best to my ears when the difference is 3.5-4 semitones. How to get that consistently is tricky because the back needs to be really stiff - i.e. the correlation between the free plates and completed mandolin is completely different for flat top than with arch top mandolins. If I match the ring modes of the free plates in the flat top, then the difference in frequency in the finished instrument ends up being about minus 3 semitones, so way out. The vintage Gibson Army Navy mandolin I measured was minus 3 semitones. I now build them with much stiffer backs and they sound way better, in a different dimension as far as sound goes. You can make flat top mandolins where the sound is a bit different, but at the same level as an arch top mandolin using this method. Mine deeply overlap as far as sound quality goes, and when I started making flat top mandolins I would never have believed that was possible.

All this stuff requires a database of measurements, so takes a heap of work making instruments and taking reams of notes, and hence a lot of time so is inefficient if you don't already know the solution. But I do now have the solution if any one is prepared to make the measurements. James' method is much more efficient, but I started this around 1996.

[pops1]

Question. I don't know if this would be correct or not. I think about a speaker. When I was custom building tube amps the same amp and speaker in a particle board cabinet and baffle board would sound brighter and more sterile than that same amp and speaker in a solid pine cabinet and baffle board. A stereo speaker would prefer the particle board cabinet as you are reproducing the sound, the guitar amp uses the pine cabinet to help color the sound. Is the top of the mandolin like the speaker and the back and sides like a cabinet? Too stiff of a back and you get sterile/bright sound, while a back that is not so stiff would help color the sound. Too wimpy and the sound could be muddy? I don't know if this analogy is correct or not, seems interesting to equate it to something different yet similar. Both are producing sound and the quality of tone depends not only on the top/speaker & amp, but also on the back and sides/cabinet and baffle board. I will be interested in hearing your thoughts.

[sunburst]

Quit a few differences between speakers and mandolins.
In mandolins we encourage multiple modes of motion in the plates, in speakers we discourage any other than the fundamental mode in the speaker cone so that the sound doesn't "break up". In the speaker enclosure, we generally discourage any movement at all and thus high density particle board is a preferred material. In a mandolin we encourage back movement coupled with top and air movement to pump air. In a speaker we want only the cone and air to move and everything else to inertly not "color" or absorb sound energy.
Obviously, we can't build an ideal speaker because the cone is not perfect, the box is not perfectly inert, and so the sound is different depending on speaker construction as you've observed.

[pops1]

Quit a few differences between speakers and mandolins.
In mandolins we encourage multiple modes of motion in the plates, in speakers we discourage any other than the fundamental mode in the speaker cone so that the sound doesn't "break up". In the speaker enclosure, we generally discourage any movement at all and thus high density particle board is a preferred material. In a mandolin we encourage back movement coupled with top and air movement to pump air. In a speaker we want only the cone and air to move and everything else to inertly not "color" or absorb sound energy.
Obviously, we can't build an ideal speaker because the cone is not perfect, the box is not perfectly inert, and so the sound is different depending on speaker construction as you've observed.

For a stereo speaker you are right, for a guitar amp/speaker we want the cabinet/speaker to color the sound and controlled breakup at times. That is why a solid pine cabinet is much preferred to particle board in tube amps. Even the thickness of the baffle makes a difference in sound. 1/2" particle board is bright and unpleasant sounding, whereas a 3/8" pine baffle is much warmer sounding. It will also contribute to breakup a higher volumes, along with the tubes distorting. This creates a much more pleasing sound than particle board. With a stereo we are reproducing sound, with a guitar amp we are creating sound, a big difference and why I asked.

[j. condino]

Peter, you've got me beat! I started building mandolins in 1998, in a world where I had lots of questions and was already and established guitar builder, but there was very little accurate and quantitative mandolin information. Many other folks around here were in the game for decades longer. I had no desire to simply copy an existing model and the lack of information was extremely frustrating, so I started taking notes. A LOT of notes, every chance I got and started working on a system that could manipulated during the build, not 200 hours into the build.

One of the biggest things for me to stress with students is to pick one method. The worst possible thing you can do is try to use one for the neck and a different one for the top and one for the back and another for the ribs or varnish, creating a dissonant pile of nothingness.

If you find a mandolin or building method that produces consistent results that you like, stick with that one. We speculate endlessly on what the real mojo is but often our perception of what makes the fairy dust and unicorn sound can be completely wrong and there is a coupling that we did not understand or identify that strongly influenced the end result. Please do not waste too much time on youtube and randomly combine 34 different methods with no clear path other than they look cool on video.

[peter.coombe]

I started making the first mandolin in 1993, and finished it on new years day 1994. By 1996 after having made around 25 mandolins I wanted to understand why certain mandolins sounded better than others, and I wanted to be able to be much more consistent so I could consistently reproduce the sound of the freaky good ones. That meant I needed measurements. I read as much of the violin literature as I could get my hands on, and started measuring free plate modes. The free plate modes are similar but different from violins, and we now know thanks to Dave Cohen that mandolins vibrate like guitars, not like violins. It took a few years before I stumbled on the correlation between matching the ring modes and sound. Absolute frequencies were all over the place, so there was nothing there, and that is where most people give up saying it is a complete waste of time. How you match the top and the back is important, not just in mandolins, but also in guitars and violins and almost certainly in many other instruments as well. When I started, there was sweet bugger all research done on mandolins so I was starting from scratch and assuming they were like violins seemed like a reasonable assumption at the time. I suspect that using detachable tops and/or backs you will end up at the same place as I do, or very close. Some people have contacted me over the years and have used my methods and have been very pleased with the results. It is not that difficult to implement once you have the solution, but finding the solution is a long and difficult journey. One of the most difficult things to keep doing is to measure everything, take pictures, and write everything down because that takes up time. Forget to write it down and that is lost information that took maybe 100hrs to get. If that instrument turns out exceptionally nice then bad language happens.

[sunburst]

Fellow veteran mando maker here. I think my first label bears a date in 1989, but I could be off a year one way or the other.
I took lots of notes, but as I learned more and more, I realized that the things I was writing down were not important, so all my early notes: shape of "tone bars", "tap tones", graduations etc. have been of little use. Unfortunately there was not much useful information available in those days, so I didn't know which direction to steer or what to write down. Sometimes I look at notes from a 20 or 30 year old build and say to myself "why did I write that and not what I want to know now?"
Basically, I tried adjustments on successive mandolins until I found consistency. If only the knowledge found here and other places today had been available then!