Tell me about Recurve

[erick]

I'm not a builder, but I'm fascinated with the physics of mandolin tone. I'm also an archer, and the recurve of a mandolin top's profile resembles the recurve of my bow. What's the deal with the recurve on the top- what does it do, and how does it do it? Interestingly, my Givens A has almost no recurve, but it still sounds great. I'd love to hear from builders about this topic...
thanks!

[Chris Baird]

Most archtop mandolins have thickness graduations that go from thick in the middle to thin near the edges and then thick again at the edge. One can either take wood off the inside to thin the wood out or from the outside. If taken from the inside there will be no recurve and if taken from the outside there will be a recurve. I don't know if a recurve serves any acoustic purpose. I just think it looks good.

[Michael Lewis]

Can of worms. Dave Cohen is the only person I know that can actually tell you what goes on regarding the recurve. The rest of us each have our ideas of what happens within the structure to effect the tone, but until more real scientific work is done in this regard we're all just guessing. I can easily imagine proportional relationships regarding arching, graduation, mass, etc., but it ain't science. We know that thinner areas of a top or back plate will be less stiff than thicker areas, and that straight sections support compression forces better than curved (as in recurved), so it starts out as "mix n match" until you get a feel for what works for you. Come to the IBMA Trade Show in Louisville and hear for yourself. There will be MANY mandolin makers showing various approaches to arching and recurve.

[HoGo]

The shape of recurve has huge influence on static strength of the top and back. Architecturally simple (parabolic...) arch will stand much greater load than "recurved" one. I changed shape of recurve on my mandolins and I noticed that wider recurve can give you more bass woof. You have to take the recurve shape into account when thicknessing/graduating plates.

[mandough]

Hi Hogo,
What do you mean by "wider recurve"?

[Dave Cohen]

In terms of dynamics, there may be some nonlinearities associated with both the recurve and the arch of the plate as well. That means that the frequencies of the plate modes would vary with the amplitude. I don't know that for a fact, though; I haven't done experiments specifically designed to look for any nonlinearities.

Strings are somewhat nonlinear. You may have noticed while tuning that as the string amplitude decays, the pitch (frequency) as monitered by your tuner drops a bit. Chinese (Beijing) opera gongs also show some interesting nonlinearities. There is a flat one which drops in pitch as it decays after being struck, and a slightly arched or domed one which rises in pitch as it decays. I need to do an experiment to look for nonlinearities, and also some FEM simulations to see if I can generate some. I've got both on my to-do list. My best guess at the moment is that if there is any nonlinearity, it would be a small one.

Of late, the violin building world is all atwitter over some oservations about old Italian violins. Some Strads and others have been found with nearly uniform graduations, and some others have ben found with reverse graduated tops and backs. That means that the plates are actually thicker in the recurve area and thinner in the middle of the plate. Also, it has been found that many of the plates on old Italian violins have an arch profile pretty close to a mathematical function called a curtate cycloid (aka trochoid). That curve is the path followed by a point on the radiius of a wheel as it rolls. This is another area where the FEM simulations would be really helpful.

To get back to erick's question, it is helpful to think of a top plate as a mass on a spring. It is essentially that, since it has mass, and also has elasticity, i.e., "springiness. If you have two identical springs, one with a 2 kg mass attached and another with a 1 kg mass attached, the one with the 2 kg mass attached will oscillate at helf the frequency. Conversely, if you have two 1 kg masses attached to different springs, the one attached to the stiffer of the two springs will oscillate at a higher frequency. So I tend to think of the graduated plate as a way for the luthier to exert control over the modal frequencies of the plates. By leaving them thicker in the center, you increase the mass, thereby lowering the modal frequencies. By carving them thinner in the recurve area, you weaken the spring, which also lowers modal frequencies. So the luthier can exert control over modal frequencies both by adjusting the mass of the plate, and also by adjusting the stiffnes of the plate. Now all I have to do is figure what modal frequencies are "good". Wish me luck; I've got that on my list too.

[Michael Lewis]

As usual, Thanks Dave! A few more pieces of the "puzzle" to put in place.

[Flowerpot]

If I remember my spring-mass physics right, the frequency of oscillation varies inversely with the square root of the mass. So doubling the mass from 1kg to 2kg would lower the frequency by around 30%, i.e. 0.707 of the original frequency. But the basic trend is there regardless.

And I wonder about the nonlinearity; it may not be that neglegible of an effect if you consider intermodulation. With intermodulation distortion, you start with two tones of different frequency and end up with sum and difference frequencies based on combinations of harmonics of the original tones. The ear is very sensitive to new frequencies being produced. Start with a note at 220 Hz and add harmonics (440 Hz, 660 Hz, etc), and the harmonics are partially "masked" by the lower note, making them hard to detect by ear until they grow to -30dB (I'm guessing a round number) compared with the fundamental. However, start with the same note and add a non-harmonically related note (e.g. 300 Hz) and you can hear it plain as day even when its relative power is 60 dB below the original. So if you hit a double stop on the mandolin, a small bit of non-linearity may produce a whole array of new frequencies which come across as a complex, full tone. Just a theory.

Oh and about the gongs: I had read somewhere that since most physical noise-makers are fairly linear, the higher frequencies always decay at a higher rate than the lower frequencies, like the crash of a cymbal, where the treble is short lived, and the lower freq's keep going a long time. In the gong, the non-linearity allows for energy conversion from the lower freq's to the higher, and you get that strange characteristic of a treble swell and peak that occur some time later than when it is struck. But it does not happen if you barely tap the thing (keeping the exitation small enough to stay in the linear region), only when you really whomp on it. I remember from orchestra, one conductor instructed the gong player that you can't just hit the thing cold and make it sound right, you had to drum your fingers on it for a few seconds before hitting it to "warm it up." I have no idea what that was about, but he seemed to take it as a matter of fact. I couldn't hear much difference myself, whether it was warmed up or not.

[Dave Cohen]

Flowerpot, you are right about the square root. The frequency is inversely proportional to the square root of the mass, but the trend is still there. More mass means lower frequency.

When I was last in DeKalb, Rossing showed me the two gongs. He didn't just ding them, but he didn't exactly whomp them either, and the effect was really pronounced. On the mandolin plates, I haven't seen any evidence of nonlinearity yet. Changing the current to the driving coil didn't seem to have a dramatic effect on the frequencies of the modal peaks, but then I wasn't exactly looking for that either.

[sunburst]

Mark, I was a percussionist in school. The gongs that I played were not the type that change pitch, and, yes, we were told to "warm up the gong" before hitting it. I was taught to tap around on the gong with the mallet, not to drum my fingers on it, until the edge started to move.
A gong in a massive and fairly flexible thing, and the lower frequencies can be seen moving, and felt with the fingers. I suspect subsonics.
Anyway, it takes a while to get all that mass moving, so I was told that "warming up" the gong established some movement so that those lower frequencies will already be there when you actually hit the gong. A head start, so to speak.

Seems to me, tho, that the standard gong used in an orchestra is a free plate and there is no nonlinearity that I know of or can hear. I don't see any close resemblance to a mandolin plate.(?)

[Flowerpot]

FYI, a quick Gogle of gongs and non-linearity reveals:

http://www.acoustics.org/press/131st/lay06.html

"In instruments such as bells, gongs, and cymbals, in contrast, nonlinearity affects the natural vibrations in quite a different way. Bells are nearly linear in behavior because of the thickness of the metal from which they are made, and their sound has a "clanging" quality because their overtones are not harmonic. In a cymbal, however, the shimmering "swish" is produced by chaotic vibrations brought on by nonlinearity in the thinner metal, and the stupendous sound of a large Chinese gong is dominated by nonlinear frequency-multiplication effects. These sounds can be measured and analyzed, and the same theory explains what is going on."

Edited to add:

The whole paper with figures appears here. It's not a purely scientific paper, but written in lay language, nice and readable but may not have a lot of "meat".

http://journal-ci.csse.monash.edu.au/ci/vol01/fletch01/html/

Edited to add: OK ther is some "meat" under the topic of mode locking, and it's more scientific than I though at first glance. Whatever, it's pretty interesting. The author does imply that plucked string instruments are quite linear by nature, as opposed to driven instruments like bowed or wind instruments..

[sunburst]

Interesting about the thick vs thin aspect of bells vs cymbals and nonlinearity. Tempting to speculate that thinner plates in mandolins might tend more toward nonlinearity.
I bet Dave has too much on his plate to think about that experiment!http://www.mandolincafe.net/iB_html/non-cgi/emoticons/biggrin.gif

[Dave Cohen]

I'm gonna have to hope for a long life with good health well into advanced age.

When Rossing and his students do holographic modal analysis on bells, gongs, steel pans, etc., they really pour a lot of current to the driving coil. They sometimes push the coil so hard as to worry about frying it. Not so w/ mandolins and guitars. They are quite easily driven, and the coil stays cool as a cucumber. These thoughts about nonlinearity have me thinking about driving the coil a lot harder next time I'm at it. I was gonna try some of that, as well as estimating the half widths of some of the modal peaks last February, but ran out of time.

[Luthier Vandross]

If you are trying to re-invent the archtop mandolin, I have a single bit of advice:

It had better look, play, and sound just like a Loar.


M

[Dave Cohen]

LV, the point of musical acoustics in particular and science in general is not invention or re-invention; it is understanding. I am attempting to understand stringed instruments. I don't make any claims on behalf of science about any instruments being "better" than any others. To do so would be dishonest if not impossible.

As to your assertion about Loar F5 mandolins, I have two thoughts. Most important is that there are many players of other types of mandolins who would take issue with you. There are a number of knowledgeable players on this board who prefer to play Neapolitans, as well as other types of mandolins such as the Lyon & Healy A, the Vega cylinderback, & etc., over F-style mandolins. Second is that while the Loar F5 was the prototype for modern archtop mandolins and is justly deserving of its current stature, there were nevertheless somewhere around 400 of them made, and like modern instruments, they are not identical. I have seen, heard, and played enough of them by now to corroborate that. I haven't played one that I would call "bad", but I have seen some variation in them. I have played a few that were not particularly loud, but sounded quite refined; others sounded loud, but maybe not as refined. Which one of those is the "Loar" to which you are referring?

Comparisons of historic and modern instruments is an entirely different topic than "Tell me about recurve".

[Mario Proulx]

Well said, Dave.

[ShaneJ]

This discussion brought to mind the mandolins with wider grained top wood on the bass side joined to tighter grained wood on the treble. What do you guys think about a bookmatched top with a wider recurve on the bass side than on the treble? Would the wider recurve accentuate the "woof" while the narrower recurve on the other side brought out the treble, or would the work against each other at different frequency responses and screw things up?

[SternART]

I've noticed a few luthiers are taking the recurve on an F5 style instrument, around past the scroll......more like an audio speaker.....rather than feather it into the scroll detail...... like on a Loar. Doug Woodley and Will Kimble come to mind.

[Luthier Vandross]

I was kidding, if I'm not explaining something (and maybe then too) I usually am.. the carve is an art, and everyone has his own style that changes with each instrument. I honestly think it's a package, it's a science, it's an art, blind luck, and magic when it works right.

I'm into the physics, here's a link to some useful stuff that helped me design my guitars.

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

In my experience, cavity resonance is a great place to start.


Miles

[Dave Cohen]

The whole issue of soundboard asymmetry, either in the plate itself or in the bracing, is complicated beyond what I am able to understand at the moment. I use an asymmetric bracing pattern, though I don't 'believe' that there is any magic in it. It is what I started with, and I am used to it, so I continue with it. The basic "tone bar" bracing is asymmetric. Otoh, Bob Benedetto insists that the tone bars in archtop guitars must be symmetrical, since the top plate motion is symmetrical. And he may have a point. Whether or not the bracing is asymmetrical, the plates modes are pretty much what they are. Rossing wrote in the Chicago Papers of the Journal of Guitar Acoustics something to the effect that "It doesn't seem to matter how you make it stiff, only how stiff you make it." Richardson's and Wright's holographic images showed that the bracing pattern influences mode shapes only subtly. So I think that local variations in the recurve width would act similarly. That is, the mode shapes and frequencies would still be a reflection of the overall stiffness and mass of the plate.

Miles, I didn't realize that you were kidding. That's the trouble with internet chat; you can't see someone's inflections, etc. So if you are kidding, ya gotta hit me over the head with it in order to get through to me.

[jbrwky]

Two mandos. One Montana, one Nashville. The recurve on the Nashville mando is noticeably more pronounced. It's got more dish, man.

[Will Kimble]

For what its worth, my impression is that there isn't a "bass" side or "treble" side of a mandolin when you are talking about sound production. #Those are just simple terms that help us distinguish which side of the mandolin we are talking about based on the relative pitch of the strings on that side. #Could just as well use gee/haw or starboard/port...

The strings excite the saddle, and these vibrations are transmitted through the posts to the bridge base. #The bridge base passes these vibrations - both treble and bass - to the top. #There is not a treble or bass side anymore.

My thought based on experience and not based on science (so don't get too excited Dave #http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif ) is that most of the bass comes from the top working in conjuction with the back. #It is very sensitive to body cavity and f-hole (or oval hole, or what have you) size. #

My other thought is that the thickness of the middle of the top - between the f-holes - contributes a lot to the treble's power and character. #

However, these are just 2 elements in a very complicated system. #Other KEY factors that influence tone and the balance of treble vs. bass reponse include wood choice, breakover angle, arching, recurve, tonebar size, shape & placement, finish, aperture size and placement, body size, and on and on.

Anyway, just trying to say that you may want to think of the "treble" side and "bass" side a little differently.

Will Kimble

[Chris Baird]

I don't know that there has been much research into the bass side treble side thing with mandolins. In violins there is definately a bass and treble side with the bass bar and treble side sound post. There is also the torsional effect from the bowing. I suppose a good way to find out may be to string a mandolin up backwards and see if it sounds any different. Of course it would take quite the talent to be able to play both ways equally well and make a report. A violin strung up backwards sounds considerably different. A mandolin doesn't seem to have the same properties that make a violin have a functionaly exclusive bass and treble side.

[Dave Cohen]

The issue of asymmetry is not exactly what this thread started out as, but since it has been brought up, here are a few more thoughts.

The violin does not have functionally exclusive bass and treble sides. The soundpost introduces a node, so that there is not a true (0,0) mode as there is in mandolins and guitars, but the sides of the plates are certainly not independent or exclusive. Further, the lowest T or B mode (the one with a node thru the area over the soundpost) in the violin's plates occurs at a frequency which is in reasonable proximity to that of the Helmholtz air resonance, i.e., around 300 Hz. You can see the holograms and associated text showing this in Roberts & Rossing, CASJ, Vol 3, No. 5 (Series II), pp 3-9 (1998).

Will's impression that there isn't a distinct bass & treble side to the mandolin plates is true enough in terms of mode shapes. It just goes along with something that acousticians have known for a long time, namely that the normal modes of plates are all global; they don't get localized by structure or anisotropy or bracing (at least, not at lower frequencies). But it doesn't address the issue of what assymmetry does or doesn't do. And I don't have an answer to that question either. Opinions are strongly held on both sides of the issue. As I mentioned above, Bob Benedetto is insistent that since there is no distinct bass or treble side, the tone bar bracing pattern in archtop guitars should be symmetrical. His pattern has both of the "tone bars" passing directly under the respective bridge adjusting posts. Most applications of the "tone bar" bracing pattern, both in archtop guitars and in mandolin family instruments, have been asymmetric, as per the typical "Loar" style bracing. No one has attempted to determine the difference between those two configurations objectively and/or quantitatively. I have that on my list also. I have built a mandolin with the back held on only by about 60 - 70 #2x3/8" screws. With that mandolin, I will be able to obtain the holographic modal analysis, sound spectra, and accelerance spectra, then loosen the strings, remove the back, change the bracing pattern, and then do the experiments again. All I need is the time and money to do the experiments.

Richardson (CASJ, Vol 4, No. 5, (Series II), pp. 30-36, (May, 2002) did a similar experiment with a classical guitar, but all of the bracing patterns were symmetrical. Even so, the bracing patterns which he tried were quite different from each other. In his paper, the modes shapes did not vary much, but the mode frequencies were quite different. So based on his results, my guess is that the difference between symmetrical and asymmetrical in my experiments will not be great, though it may be interesting.

In both classical and steel string guitars, you will find examples and adherents on both sides of the symmetry/asymmetry issue - too numerous to mention, from the early 19th century European classical guitar luthiers to current builders. Is there an answer? Probably. Will it reveal itself to us? Maybe.

[Chris Baird]

I wasn't trying to say the the plate sides work independatly of each other but that a violin strung up with bass strings on the sound post side and treble strings on the bass bar side doesn't sound right. Which is to say that the treble side is exclusively for treble strings at least in the functional sense(same with bass). #I forget the reason but it can be found in "The Violin Explained" by James Beament.

[peter.coombe]

My experience is that the free plate mode shapes stay pretty much the same no matter what you do. Frequencies will change, and can be very different between different pieces of wood. You can also change the relative frequencies with bracing - i.e. move one mode up a lot, but not affect the other modes very much, but this is tricky. Usually you will change all the modal frequencies to some extent, so it is very difficult to use bracing to change the frequencies to "ideal", whatever that is.

I agree with Will Kimble. There is no bass or treble side. Tonal quality is affected quite significantly by the frequency of A0, and this is a function of the area of the sound holes, the volume of the body cavity and the stiffness of the plates. It is a difficult thing to control - e.g. raise the arch and the volume of the cavity increases, but stiffness and hence the modal frequencies will also increase. This may or may not be a good thing. I think the thing to do is to stick to a constant body cavity volume and soundhole area and play around for the rest of you life with different wood, different archings, different thicknesses, and different bracings. Eventually you will work out how to make mandolins that sound exceptional consistently, and just before you snuff it after a few hundred instruments you might understand some of what is going on. Even then, as Will says, there are many other factors to consider as well. I have been going along this path for 10 years, am just about to reach my first 100, and am still discovering new ways of changing/improving the sound. I expect this will continue until I give up.

[HoGo]

I meant width of "sunken" area (which is usuallu called recurve) and depth of it.

[Mario Proulx]

Dave, no need for a screwed on back.

About 5 years ago, I wrote how to make a removable back on a mandolin over on the MIMF. It's in their archives.

I have a mandolin that's been opened up 29 times, now, for various tone bar/brace layouts, and one re-graduation. another is approaching its 20th opening.

The screwed on back would work, too, but the mass of all those screws, plus the large area/linings that it would require, would also affect tone. My method changes nothing from a standard setup.

Very, very educational! Peter has it right: we'll all be learning forever, but that's what makes this interesting.

Oh, I also don't buy into the bass/treble side thing. Just string up a mandolin with two identical strings, one on each side(where the 1st and 8th strings would be). Tune them up(make sure the intonation is the same for each) and play them for a minute. Same tone. As Will says, we use bass side/treble side to describe each half of the top, in the same manner we say "driver's side" when describing cars/trucks. In use, that top acts as one piece. We can, however, brace it assymetrically in order to get it to rock side to side in a controlled manner, which will have a pronounced affect on tone(good or bad that it is)

[sunburst]

in the same manner we say "driver's side" when describing cars/trucks.
http://www.mandolincafe.net/iB_html/non-cgi/emoticons/biggrin.gif
I still refer to the "driver's side" on instruments.
It was a reference to how much you could get away with in terms of detail and finish perfection where I used to work.
If in was on the driver's side it had to be near perfect. If in was on the passenger side slightly less perfection would go un-noticed.

To this day, if I look at an instrument critically in terms of fit and finish, I flip it over and look at the passenger side first.

[Dave Cohen]

Mario, the total mass of all of the screws is slightly under 20 grams. Remember that they are #2x3.8" screws. I used conventional dimensions for the back lining. 1/16"x1/4" mahogany strips were pre-bent and glued onto the ribs in the mold to make an effectively solid (non-kerfed) lining. The "tone", whatever it is, does not appear to be affected. Since the mandolin is an A-model, it is still lighter than a conventionally built F-model. Several people have offered to buy the mandolin.

I remember your removable back on MIMF; I prefer the screws for avoiding the perturbation(s) of heat and/or moisture with each iteration.

[Mario Proulx]

No heat or moisture required; juts a pocket knife <bg> To each their own....

You sounded like you were just thinking of it, and not actually having done so. How many times have you been back inside? What did you change?

[Dave Cohen]

I completed the mandolin in May, 2001. The experiments are yet to be done; something else has always taken priority on my trips to DeKalb. Right now, it has the typical asymmetric tone bars bracing. The first change will probably be to the Benedetto symmetric tone bar pattern. Then, in no particular order, I could try X-bracing, The Lawrence Smart variation on the "X", my wacky braces, ....etc. Any suggestions, Mario? Any bracing pattern you would like to see us do the modal analysis on?

[Mario Proulx]

I like your "wacky" braces, so try those. I'm also curious about the perfectly symmetric version. Shoot, you can waste a year just moving an X brace back and forth, open and closed, side to side.....

Ever try just a single brace? A "Y" system? A de-coupled X? Carbon fiber/spruce laminate?

Get that screw gun out! <g>

BTW, you gonna be at IBMA again?

[Dave Cohen]

I have "tried" some different patterns, though I don't have much data yet. Back in 1997 when Rolfe Gerhardt was living in Richmond, I got him to build a test bed mandolin. I did SPL spectra on several different bracing patterns, and we got a local musician to audition each iteration. The results were not really definitive. They didn't show clear trends, though we all disliked the "X" braced iteration most.

Let's see: Never tried a single brace. If by "decoupled" X, you mean cutting out the box joint, then the answer is yes. I tapered the braces to nothing at the box joint, so that we had essentially four braces radiating from the center in an "X" pattern. We all thought that that modification was a big improvement over the conventional X. Haven't tried a "Y" pattern, though I sometimes do my wacky braces with a Y pattern for the bass side - er, uh, driver's side - bars. I have used some cf/spruce sandwich braces selectively in some of my instruments. I didn't feel that the results were worth the hazards associated with working with the stuff.

Otoh, I'm using cf creatively in necks now. I just completed a batch in which I bury a cf spline (horizontally) deep in the neck and follow up with some vertically oriented cf members to make either an inverted "T" or a "U" configuration. This is along the lines of a thread in which you and I posted on MIMF a while back. For neck reinforcement, I can just cut the stuff slightly undersize with a hacksaw while keeping some water on it. That way, I don't have to worry about raising fibrous dust when machining it, since no machining is necessary. Still use a respirator when cutting it, though.

[peter.coombe]

Dave, I have heard about that experiment from Rolfe. Where did the X cross? Where you cross the X can have profound effects on sound. Absolutely the worst sounding mandolin I have made had the X joint right in the centre of the top. If you move it foreward, the tone of the instrument improves hugely. In oval holes there is a limit because of the soundhole, but you can move it quite a way foreward on F soundhole mandolins.

[Dave Cohen]

Peter, Rolfe e-mailed Steve Gilchrist and executed the X-brace exactly as per Gilchrist's instructions. The X did cross in the center of the plate, i.e., right under the center of the bridge. By moving it "forward", I assume that you mean toward the heel, as in the 1998 American Lutherie article by Lawrence Smart. As I stated above, I have that one on my list as well.

[peter.coombe]

Interesting. I have a Gilchrist catalog and according to that, the X brace crosses in front of the bridge, i.e. on the heel side of the bridge, although not as far foreward as I do mine. I have looked inside my own Gilchrist (2000 Model 3C) and the X definately crosses in front for the bridge. Right under the bridge IMHO is the worst place to cross the X and I am not at all surprised everyone disliked the sound of this bracing method.