Why graduate a plate

[thistle3585]

What type of dynamic does graduating a plate, top or back, have to do with tone? Why not use the same thickness throughout? I have heard people compare the top to a speaker, in regards to how a speaker "pumps" so to speak. If that is the case, wouldn't the thickness of a recurve play a more important role? I know several builders that put a bit of recurve into their induced flat tops, so I have to believe they see some sort of value in doing it.

[UnityGain]

If Stratovarius and Lloyd Loar did it shouldnt that be enough proof?

Anyway, it has to do with using the thickness of the plate to fine tune stiffness. You want the middle of the plate to be strong and supportive and the outside to be able to move.

Speaker is a good analagy because its essentially the same thing. You want the cone of the speaker (soundboard) stiff to accurately transmit the motion from the coil (strings) to the air. You need the edge of the speaker cone (edge of the soundplate) to be flexible to allow the cone (soundboard) to move back and forth. The whole thing is supported by the speaker cabnet/basket (rims of a mandolin). On a mandolin plate you thin the edges to be more elastic and keep the middle thick for strength.

I'm sure its more complex that this but this is what I felt like posting.

Oh yeah, and an ungraduated plate would probably not produce very much sound at all because either the lack of movement (too thick) or the top would collapse (too thin).

Its kinda like asking what would happen if you built a guitar without any top bracing.

[sunburst]

There are certain aspects of arched top and back construction where I don't fully know why I do what I do, and graduating the thickness of plates is one of those things.
As far as engineering goes, a graduated plate can be made lighter and have similar strength to a plate with even thickness. In other words, the plate can be lighter and stronger if it's graduated than if it is of even thickness. That is speaking of the static properties though, not dynamic properties.

A mandolin top doesn't behave exactly like a speaker cone. The main "trampoline" mode is sort of speaker-like, but there are many other vibrational modes in the carved plate that aren't much like a speaker.

The best I can say is; when I carve a top with one system of graduations I get a slightly different sound than if I carve with another system of graduations. Why? I can't really tell you because I'm not so sure that I know. I assume that I change the resonances of the plate modes with different graduations, but I really don't know what I'm changing. I might be able to do some FFT research and find out some things, but I don't really have the inclination to do that.

So, my answer to the question "why graduate a plate" is: because it works the way I do it so I'm not making any major changes because I don't fully know why it works the way I do it. Much of what I do when carving the top in particular is with strength of the instrument in mind, and any effect that has on sound or "tone" is more or less accidental. Surely the mass and stiffness of the plate and how they are distributed as a result of graduation have some effect on the sound, but I can't tell you what it is.

EDIT
UnityGain's post wasn't there yet when I posted.

From what I've read, many Stradivari violins had tops of nearly even thickness, and I've also read of violins with "reverse" graduations with a thinner area under the bridge. The flexible coupling of a speaker cone to its "rim" is one of the ways it is different from a carved plate. The stiffness of a plate at the rim affects the frequency of the modes so there are probably sound differences to be had by carving the "recurve" area thinner of thicker, but it can't be made flexible like the edge of a speaker.

[Schlegel]

Sound is air moving, so you can think of a mandolin as a kind air pump, let's say a bellows. The top of the bellows needs to be stiff, not only to support the strings, but to move as a unit, in order to move the largest amount amount of air as possible. Now, if everything was stiff, no movement would be possible. A bellows needs flexible sides to pump up and down. A mandolin's sides are stiff, so the edges of the top must be flexible or springy to let the greater portion of the center of the top vibrate up and down. Thinner wood is more flexible, so the rim is made thinner than the top, but thinner is also weaker, thus the arch or recurve, whose geometry adds some strength to make up for the thinness.

I forget who here I stole that pump analogy from, but it made sense of it for me.

[TomTyrrell]

Actually there are a lot of archtop mandolins with tops having the same thickness throughout. These are the solid "pressed top" instruments.

[sunburst]

Schlegel, a mandolin does act as an air pump, but it does a lot more than that too. The air pumping modes are only two (or so, IIRC) of the modes that create sound from a mandolin. If the process was as simple as the top and back moving as units and pumping air only, graduated carving would seem to make a lot more sense, but there are many plate modes and air modes at work, and understanding how they are affected (or not) by graduated carving is not so simple.
Look at the work of Dr. (Dave) Cohen and Rossing (sp?) to start to get some ideas of how complicated plate movement actually is. There are also many papers written about guitar plate motion, and guitar plates behave similarly enough to mandolin plates that there is a lot to learn there to.
Speaking for myself, the more I learn about how mandolins work the less I realize I know about it.

[Schlegel]

I can believe that's not all there is to it, I just covered the factoid I felt could do justice to. The other factors... let's just say it's not my field of expertise.

[siminoff]

This is a wonderful question and many good answers are posted here. Plate graduation is necessary to control the uniform and progressively-reduced stiffness of the soundboard ranging from the center outwards, being stiffest in the center and becoming less stiff as the soundboard nears the rim until it gets to its point of minimum thickness (what most folks talk about as the “recurve”). From that point, for structural reasons, the soundboard gets thicker where it attaches to the kerfed lining and joins the rim. As Tom Tyrrell pointed out, there are many ungraduated but arched soundboards on less expensive mandolins that are of equal thickness (most being laminated). These evenly-thinned soundboards can deflect in many different ways (modes) and these instruments typically sound like the inexpensive instruments they are. (Shutt mandolins featured a brace-less carved soundboard and backboard that was .100” across its entire width and length. Even with its f-holes, these were not great-sounding instruments by comparison to the arched soundboard and backboard of the F5 that followed four years later.) Loar wrote an interesting article entitled What Sound Boards Do And How They Do It in the October 1925 issue of “Jacobs’ Orchestra Monthly” (in which he wrote a regular monthly column under the heading of “Acoustics for the Musician"). His October column describes his views of the arched soundboard and how it works along with some of his illustrations. (For those of you who have a copy The Art of Tap Tuning, Loar’s October 1925 column was reproduced as Appendix F in that book.)
Roger Siminoff

[Bob DeVellis]

Mass, and mass distribution, affect vibrations in interesting ways. Back when I was playing a bit of concertina, I remember a repairman talking about how he could lower a reed's pitch by filing it down. This struck me as odd. My first thought was that removing material would necessarily raise pitch. I was wrong. By removing material from the middle of a reed's length, the center of mass shifts to its un-thinned end region. The whole reed then vibrates at a slower rate, like a clock pendulum with its weight put at its end. With things of uniform mass distribution, like strings, less mass implies a higher frequency, all else being equal. But in more complex systems where mass isn't uniformly distributed along a surface, differences in mass presumably can produce differences in vibrational patterns. By analogy, this may apply to soundboards as well (although the fact that they're attached all around their edges may make the analogy a poor one. I don't know enough about it to say with confidence.) I believe that tuning braces involves some of this. Scalloping on guitars, for example, puts the mass at the extremes and thus supports the lower frequencies. Scalloping the braces makes the guitar bassier. Some builders, like James Goodall, graduate their flattop guitar tops in lieu of scalloping the braces (on the non-traditional models, at least) and report getting a similar enhancement in the bass response. I may have the details of this wrong because this is way out of my knowledge comfort zone but it might help people get a feel for how altering the distribution of thicknesses (and thus mass) on a soundboard can have all sorts of impacts on its vibrational patterns.

[Jim Hilburn]

I've often referred to Bob Bennedetto's book and video collection as a good reference for building archtop instruments.
He says that to achieve a bright cutting tone similar to the Epiphone sound of the 30's you would want a more consistant thickness of the soundboard combined with tonebar construction, about 3/16" across the entire top, again speaking of guitars.
To start warming up that tone you want the thicker center and thinner recurve combined with x-bracing.
That all makes sense in that a stiffer top would be a more re-active top with more mid and treble response. I don't think that's the direction you would want to go with a mandolin which is already quite bright. Bringing out the bass is what we're usually after.
Several builders, most notibly Steve G. have also gone to x bracing for that extra-warm tone, even though he's backed away from that recently, but that's a totally different subject.

[thistle3585]

So, what do you do to bring out the bass? My first build is clear, and loud, on the treble side with little bass. I wouldn't say the tone is thin but the bass isn't balanced with the treble. I originally contributed this to thicker plates, so I've thinned the plates on number two and just finished carving the braces and will glue the plates on this weekend. I like the ringing tone I get when rapping on the top, so I figured I'm done. I'm wondering if I need to do something beyond thinning the top or just close up the box and see what I get.

[Jim Hilburn]

Also from the Bennedetto source.
People are always talking about the top. How thick is the top? What wood is the top? Top this. Top that.
But it's the back that's at least equally important to the overall tone of the instrument.

[sunburst]

So, what do you do to bring out the bass?

Ah yes, there's that question again.
Bass response is mostly dependent on good coupling between the frequencies of the main plate modes (top and back) and the main air modes of the instrument. How do you get there? well, that depends on how you arch and graduate your top and back. Different builders do different things. For me, increased bass response comes mostly from leaving the top pretty much like usual and pairing it with a thinner back. I've lately heard two mandolins in particular that were very bassy, much too bassy in my opinion, and I have no idea what is making them sound like that, but if I knew I might be able to use whatever it is, in moderation, to bring out more bass in my own mandos if I wanted to.

I've told this story before, but here it is again.
I had my first mandolin on display at the ASIA symposium in 1989. John Monteleone came by and picked it up and played it. At that time I thought of him as pretty much the mandolin guru (I still consider him one of the mandolin gurus) and I asked him if he could comment on the instrument and give me any advise. I said I was confident with the aspects of appearance (binding and finishing and all, it was not my first instrument, just first mando) but didn't know what to do to improve the tone. He made a couple of suggestions about top arching and neck geometry, then said "You're on the right track, just keep building them."
As he walked away I was thinking "well, it wasn't much, but I did get a little advise". It wasn't until years later that I figured out what he meant. He meant he couldn't tell me how to build a mandolin with better tone, but that I would have to build them for a while and I'd start to figure out what works for me.

So here's my advise for improving the bass:
Just keep building them and you'll figure it out.

[alanz]

So how do some of the wonderful sounding flat top mandolins fit into the carved is better scenarios. Aren't most of the flat tops ... well, flat on both sides of each surface?

Just another little thought... wouldn't one think that the carving the sides would have an effect on sound too? Does anyone do this?

[Dave Cohen]

Roger, is there a location where the October, 1925 article might be downloaded or printed as a pdf?

http://www.Cohenmando.com

[siminoff]

Dave, et al., At the moment, I only have a copy of the article in its original form and then as I reproduced it for The Art of Tap Tuning, but making it available as a download is a good idea. I’ll begin to get it into a PDF format for download and will advise when/where it is ready. Good suggestion, Dave.

Back to the subject of “why graduate a plate,” in my previous response I failed to talk about the tonal attributes. I think it is well known that stiff plates have a higher resonant frequency and less stiff plates have a lower resonant frequency. The word “stiff” here also equates to weight. Light plates have a lower resonant frequency than heavy ones. Ideally, plates should be carved so that they are light, yet strong. The resonant frequency can be adjusted by changing the shape, size, or location of the tone bars. A flat soundboard with an x-brace pattern, whose braces are larger/stiffer/heavier in the center and taper off to airy thinness at their ends, works in a similar, but not identical way to a graduated soundboard. A graduated/arched soundboard with X-bracing is merely an embellishment to the idea of a graduated soundboard. Unfortunately, a graduated/arched soundboard with X-bracing does not allow for the bridge feet to sit over the braces (unless the X is position very high or low) as they do on a soundboard with two longitudinal tone bars. On a graduated soundboard, braces or tone bars are not needed for strength – their role is to adjust the resonant frequency of the soundboard. (A normally graduated Sitka soundboard without braces or tone bars will withstand a down pressure of about 75 pounds before imploding. The load of a full set of strings at pitch is only about 45 pounds.) Stiff tone bars produce a higher resonant frequency than less stiff ones. Tones bars closer to the center of the plate produce a higher resonant frequency to those near the outer portion of the plate. Generally speaking, thin, airy, supple soundboards produce “thin” timbre with poor note-to-note clarity and richer bass response. Thicker, stiff, less supple soundboards produce “bright” timbre with richer treble response. How do you find the right stiffness? Well, you can graduate by the numbers, or to know more about each specific piece of wood you can pursue the course of tap tuning, which is a method of determining the stiffness of the soundboard or backboard by measuring the note it produces when tapped.

Stiffness and pitch are inextricably connected. A musical string, for example, produces a known pitch at a known tension (stiffness). If you measure the tension of a mandolin .010” E string at pitch, you might find that it exerts a load of 12.575 pounds (for example). If you slack the string and then adjust it back to 12.575 pounds without listening to it, you will be right back at the E note. We can do the same thing to plates; adjust their resonant frequency by adjusting their stiffness – or adjust their stiffness by measuring their resonant frequency.
Thanks for all the good content you guys! Fun stuff!
Roger

[Dave Cohen]

"Light plates have a lower resonant frequency than heavier ones."

Not quite true, and misleading to the beginning luthier. First, I will assume that when you write about the 'resonant frequency', you are talking about the first or lowest resonant frequency. Both free plates and plates clamped at their edges (i.e., into a mandolin body) have not one resonant frequency or eigenfrequency, but several within the acoustic frequency domain. Unlike strings, the eigenfrequencies are not harmonic, i.e, the 2nd one will not occur at twice the frequency of the first one. Second, and more important, if a lighter plate has the same stiffness as a heavier plate, it will have higher resonant frequencies than the heavier plate. So other things being equal, a lighter plate has higher resonant frequencies than a heavier plate of the same stiffness.

Thinning a plate as it is carved does affect the stiffness more rapidly than it lowers the mass, so as plates are typically carved, their eigenfrequencies decrease even though their masses also decrease. But the catch is that the densities of woods are all over the map. Even within a single species in a single location, the densities and Young's (i.e., elastic) moduli will vary by a surprising amount. A beginning luthier will quickly be confounded if he expects a lighter plate to have lower resonant frequencies.

http://www.Cohenmando.com

[siminoff]

Yes, by “resonant frequency” I am referring to the plate’s lowest frequency. And while I absolutely agree that plates of different stiffness but identical dimensions will yield different resonant frequencies (higher or lower), my supposition in this context is that both plates are of the same material, i.e. both Sitka spruce, or red spruce, etc. Taking two red spruce plates that are carved to identical dimensions, the heavier (by weight) plate will yield a higher resonant frequency than the lighter one. And, measuring its deflection, the heavier plate of the same dimension and material is typically the stiffer plate.

I also agree that the densities of the woods are “all over the map,” but the plates can be tuned to identical frequencies by adjusting their thickness and/or the size, shape, or location of their tone bars or braces.

However, I’m not so sure I agree that the beginning – or seasoned luthier will quickly be confounded by the idea that lighter plates have a lower resonant frequency. I think this is information a luthier at any level wants to know. What I believe to be key here is that the resonant frequency of these plates can be adjusted by changing the thickness of the plate and/or adjusting the size, shape, or location of its tone bars or braces, and this frequency can be easily measured with conventional tools. It is as fundamental a procedure as adjusting the size of the apertures to tune the air chamber. Doing so leads to consistency, and I feel this is important to both beginning and seasoned luthiers.
Roger

[timeoutlaw59]

So when looking at the woods densitie how does one decide the thickness dimesions he will use? Or how far from the per say average prints (Stewmac) that he will stray when carving top plate thickness?

[sunburst]

So when looking at the woods densitie how does one decide the thickness dimesions he will use? Or how far from the per say average prints (Stewmac) that he will stray when carving top plate thickness?

Most builders use their experience to decide. Some tap tune, some deflection test, some do FFT testing, some use Chladni patterns, some just listen to the wood and feel the flex and weight.
To start with, though, most luthiers select wood with density within a range with which they are familiar. I find that very little difference in carving is needed for the rather slight variations in density within the wood that I use, and I usually vary the height of the arch rather than change the thicknesses much.
There are no simple answers here, and there are many ways to skin these cats.
Generally, denser wood thinner top or lower arch, less dense wood thicker top or higher arch, but that ignores stiffness which is at least or more important and can change everything.

[Dave Cohen]

Time, David Hurd had an article in American Lutherie back sometime in the late '90s which addressed your question. Look through the GAL website, http://www.luth.org, and you may be able to find it.

Roger, some anecdotes illustrate my concern. John Hamlett claimed that his F5 tops in red spruce weighed about 100-105 grams. With the red spruce that I have, I have never been able to get near that weight. My F5 tops in red spruce have always been at least 10-20 grams heavier than that. So unless John is wrong, and I have no reason to think that he is, then he has considerably less dense red spruce than I have ever been able to get. Same thing with redwood. I have determined densities of redwood from about 22 g/cm3 all the way up to about 36 g/cm3. With variations like that within a given species you just can't can't take for granted that you are going to get a certain result by carving a certain piece of, say, red spruce, in a certain way.

http://www.Cohenmando.com

[sunburst]

Dave, I just glued two red spruce F5 tops to their respective rims. They weighed 108 and 110 grams ready to glue to the rim, tonebars carved. I've had them as low as 100 grams.

[Dave Cohen]

Thanks, John, those anecdotes make the point. The red tops that I have carved have been more like 120-130g. Nice looking stuff from OSW, but too dense for my tastes. I have two extra carved redwood "A" plates sitting in my shop at the moment. One is only about 0.160" thick at the center, and weighs just over 100 grams. The other is about 0.190"-0.200" thick at the center (iirc), and weighs just over 75 grams. You just can't treat those two plates the same way. Aside from the densities, the ratios of the tangential to the parallel Young's moduli may be quite different, and the internal losses ("Q") in the two plates will certainly be different. I get a hint of the latter just by tapping them.

Just carving dense topwood plates thinner misses another point. The Young's moduli of a given piece of wood are not the only consideration. If one carves a very dense, high-modulus piece of wood thin enough to get it in the "right" range of stiffness and mass, it may very well be so thin that it will be at risk of catastrophic failure. While it may behave well as an instrument while it lasts (or maybe not), the smaller distance between outer and inner surfaces, where a greater fraction of the shear occurs, coupled with the runout inherent in a carved, arched plate, increase the risk of failure even though the stiffness may be comparable to a thicker, less dense plate. The thicker, less dense plate with the same overall stiffness may be may have a smaller risk of failure.

http://www.Cohenmando.com

[Bill Halsey]

I'm not so sure we have an apples/apples comparison here between free-plate masses from different makers, especially with F-5s. Tone bars & wood density aside, several factors that influence plate mass before the glue-up are similarity of outline, binding margin and, particularly, the scroll area. For example, many individual makers prefer to saw out the scroll more or less to the outline before assembly, while Gibson used to saw the scroll as an assembly. This, combined with variations in the thickness of the scroll, whether it is carved internally, and the extent to which the scroll is carved pre-assembly, might account for significant differences in mass between the work of various makers.

[Dave Cohen]

Bill, that's a good point. However, I weigh the ribset, then glue the plate oversize to the ribset, trim the plates flush to the outside of the ribs with a flush trimmer, clean up as necessary, and only then weigh the ribs-plus-top-plate assembly. I obtain the weight of the top plate by difference, i.e., by subtracting the weight of the ribset from the ribs-plus-top-plate assembly. That way, my top plate weights should only be a gram or so at most more than John's, according to his description of what he does, and assuming equal density woods. The fact that mine are much heavier tells me that the densities of my samples of red spruce were greater than that of his.

http://www.Cohenmando.com

[labraid]

I'm an advocate of locking oneself in a quiet room for hours on end, an unfinished plate and a few scrapers, a felt hammer and a note pad.. Away from computers, away from books. Boredom and frustration, coupled with a burning desire...

[siminoff]

Another consideration of weight is the rate of graduation from the minimum area (recurve) to the crown; i.e. just how rapidly or evenly one graduates from, for example, .100” to .150”. And, as Bill mentioned, this varies with different makers. Coupled with this is how consistently the boards are graduated, board for board. We’re carving several sets a day on a 3-dimensional pattern carver with pretty incredible board-to-board accuracy but our weights still vary board-to-board depending on the material (both species and wood from the same lot). We carve oversize so that we can use hold-down tabs on the margins, then pin rout to final perimeter shape including the cut into the scroll, so we end up with very accurate board-to-board sizing in both thicknesses and perimeter shape/size, but still end up with weight variations. The weight, of course, affects the top’s tuning.

David; are the weights you described with or without f-holes perforated?

Roger

[Dave Cohen]

Holes are cut.

http://www.Cohenmando.com

[Jim Ayers]

[QUOTE=siminoff;593712]Dave, et al., At the moment, I only have a copy of the article in its original form and then as I reproduced it for The Art of Tap Tuning, but making it available as a download is a good idea. I’ll begin to get it into a PDF format for download and will advise when/where it is ready. Good suggestion, Dave.

Has this been posted somewhere?

[amowry]

Just a thought regarding John's top weights-- I've seen you (John) say elsewhere that you cut most of the binding channel before the tops are attached. A lot of builders leave an overhang to trim off later. Maybe that accounts for a few grams of difference?

[sunburst]

Could be.
I weigh my top plates graduated, f-holes cut, tone bars carved, and the scrolls (on Fs) partially carved; they are ready to glue to the rim. After they are glued to the rim, the binding channel is completed, the scroll carving is completed, and they are sanded for finishing, so they loose some more weight during completion of the instrument, but I don't really know (or care) how much. It would be difficult to figure out the final weight because I do the pack plates the same way and finish the scroll carving with both plates glued to the rim.
The scrolls surely vary quite a bit in weight because they are just rough carved when I weigh the plates, but my red spruce tops tend to be within about 10 grams of the same weight.

[Dave Cohen]

I have gotten into the compulsive habit of weighing my parts at intervals in the process of fabricating them. I have noticed that they lose precious little mass as I whack away at the scroll(s). Now if you do away with the scroll altogether, you are looking at a difference of 20 grams or so on a mandolin. As I pointed out earlier, the closest you can get to comparing apples to apples is to weigh by difference. Weigh your rib set and record the value. Glue your top plate onto the ribs and trim flush when dry. Then measure the total mass of the top plate plus ribs. Subtract the weight of the ribs from the total. The difference is the mass of the top plate. Unless you are worried about the mass of the glue, that is. If you haven't made a mess of it, the mass of the glue shouldn't amount to much.

You can get the mass of the flush-trimmed back plate by repeating the procedure when you glue it on. In that case, subtract the mass of the top plate plus ribs from the assembled body mass (i.e., top plate plus ribs plus back plate) to get the mass of the flush-trimmed back plate.

http://www.Cohenmando.com