About the Following Article:

On September 17 and 18, 1994, a luthiers' gathering was held at Luthiers' Workshop in Waltham, in the Metropolitan Boston area. It's proprietors, and hosts of the meeting, were Tom Knatt, Alan Carruth, and Jerry Weene. People came from Connecticut, New York State, and Maine, as well as from Massachusetts. The 20-30 people who stopped by at one time or another included: Oscar Azaret, Julius Borgess, Nick Clarke, Tom Dowey, Tom Higgins, Lewis Santer, Walter Stanul, T.J Thompson, and Paul Wyszkowski. It was a less formal occasion than a "proper" convention or "Symposium," but participants learned a great deal, had fun, ate good food, and attended a few "structured" talks and demonstrations. Morale was high, as it became increasingly evident one doesn't have to attend a bombastic 400 person event in order to have a truly uplifting and highly instructive experience.

Knatt and Carruth gave a plate-tuning demonstration. Tom Higgins conducted a "hands on" French polish workshop, which for me was a high point: It was the first time I attended such a workshop and had a chance to actually get my hands on a "muneca" (French polishing pad) and _polish,_ not just watch. I now French polish all of my guitars.

I was scheduled to give a talk about my work with the Kasha design, but did not know until the last minute whether it was going to be a lecture, or, as I was told, "just 7 or 8 guys standing around a workbench" to look at my guitar. I nevertheless asked for a blackboard -- a familiar "weapon" from my math-student days, brought along a piece of yellow chalk ("surplus" from those days), and prepared several typed pages that were a mixture of outline notes and more "talkative" paragraphs. No recording of thelecture was made, but the following, based on those notes, is as close as one can get to a transcript.


by Gila Eban, Copyright 1994 (Published here with her permission)

As most of you know I build classical guitars in what's known as the Kasha Design, named after its inventor, Michael Kasha. That's what I'm here to talk about, I've been doing this for many years, along with building traditional classical guitars.

You may also know that between 1978 and 1981 I worked with Jimmy D'Aquisto while starting my own shop in Michigan for building classical guitars. Why am I telling you this? Because I tell everybody that I studied musical acoustics on the Long Island Railroad. Until 1979, my boyfriend worked two miles from Jimmy's workshop in Farmingdale. So I'd ride with him in the mornings and return in the evening to his residence. But in 1979, he changed jobs and moved to White Plains. That made the commute to Farmingdale extremely long, which gave me time to read Catgut Acoustical Society Newsletters, or papers referenced in those newsletters. I was also very fortunate to have some very good people tell me about guitar acoustics "first hand." Fred Dickens, Graham Caldersmith and Tom Rossing. They all had a lot of influence on my work.

Most talks about the Kasha design start by telling you about 3000 years of the guitar's history, or at least twenty years of the Kasha design's history, and frankly the upshot of all that is that people end up hearing essentially the same talk again and again. Well this is gonna be a little different, more of an "advanced" Kasha lecture, exc_yoooze_ the expression. It's also going to be different because a lot of what I'll say is very intuitive. I'll back it up with what I know about acoustics, and I do have some data that I published. But unlike many other Kasha luthiers, I see my work as being as much about _questions_ as it is about answers, the questions presumably leading to arguments about possible answers, and tests to see if they hold water.

I'm going to assume everybody here knows the basics about guitar acoustics and construction, as well as the essential features of the Kasha design. Just to recap some of those, let me sketch a brief inventory of what we need to know. It is not "textbook-precise" but I feel it's good enough for our purpose. I'll add a few remarks that are not highlighted often and which I'll use
later, in hope to maybe present in a different light.

1.) Most things that vibrate do so at many frequencies simultaneously. In theory there are infinitely many frequencies, but, usually, beyond the lowest 20-30 ones, the amplitude is negligible.

2.) There is a "lowest frequency" we call the fundamental. Often it is the frequency with the highest amplitude, but don't take that for granted. Then we have the second harmonic (first partial) third and so forth. We can say very loosely that one "chosen" harmonic, most often the fundamental, gives the sound its "identity." With strings and air-columns this means a note on a musical scale.

3.) To each harmonic there corresponds a "vibration-shape," called "mode." The fundamental frequency usually corresponds to a mode I'll call "whole-body-one-piece," The shape we're all familiar with from strings. On assembled soundboards, it can be visualized via "Chladni patterns" obtained with the help of glitter, coffee-grounds, (fresh, I hope!) or even 60 grit abrasive powder. Laser "holograms" give an even better picture of "vibration-shapes."

The mode for a string's second harmonic has two halves on the string moving in opposite directions. The point in the middle doesn't move and we call it a _node,_ or nodal point. A guitar top has two analogous modes, one (denoted (1,0) ) with an immobile line along the center-joint of the lower-bout, a higher one, the (0,1), with an immobile line roughly parallel to the bridge. So we can have nodal lines as well as nodal points.

The important thing for what follows is, the higher the mode, the more _nodes_ it has! I'll call this _Multi-Node_ (or multinode) vibration. Points, or areas, of maximum vibration are called

The thing that makes a musical instrument's tone "interesting" depends on how much of each harmonic we have. Or, using 3 above, how much of each mode is present. Alternately, we can observe how fast, or for how long, the overall amplitude builds up and/or fades out.

I'll call the combination of harmonics a tone's "Recipe," and the time-dependent change "Game-Plan." Actually, I should make a distinction between a "List of Ingredients" and a "recipe," the latter includes some sort of game-plan. It turns out that the ingredients and the game-plan are related. A recipe with a lot of high harmonics means the tone's game-plan is to start very rapidly, giving a "bright" sound. If there are less highs the game-plan will evolve more slowly and we'll have a mellower tone, or, as Kasha (following Backhaus) calls it, a "brilliant," tone.

The more dignified lingo used in this context is "Frequency-Domain" and "Time-Domain." Now that you have an idea what they mean you see it's no big deal. The question of how the amplitude builds up and fades out over time also ties in with a term you must have heard before: Things that change with time are said to be transient. The buildup-stage is called "Onset Transient" and the fade-out stage is called "Decay Transient" or just "Transient."

5.) We can _lower_ the vibration-frequencies of an object by making it heavier, bigger, or less stiff (in a string, under less tension). The converse for raising frequencies.

6.) The string in itself makes no real audible sound. We need something that can vibrate and push more air.

7.) Getting to the Kasha soundboard I'll just steal from "Guitars" by Tom and Mary Anne Evans: "Accordingly, Kasha structures the soundboard into a series of different sized zones, each of which operates in the particular frequency band in which it is most efficient. These zones are both defined and activated by the radiating struts. The struts on the bass side of the soundboard are longer than those on the treble, so that low notes bring proportionally larger areas into play; some of the struts on the treble side are designed to reduce the area that can vibrate at high frequencies."

The bridge mimics that pattern, although nothing in the previous quote tells us why it should. We see a wide bridge and long radial bars on the "bass side" of the soundboard, and a narrow bridge and short radial bars on its "treble side."


To put it very informally, the two diagonal bars sort of (presumably...) "fool the bridge" into "thinking" that is where the top ends. Many people, even traditional guitar makers, call them "Treble Confinement" bars or "Treble-Cutoff" bars. We call them "Perimeter Bars."

So far, the picture of a Kasha soundboard is basically the way most people try to "explain" it: Woofer, midrange, and tweeter, except the transition is less clear-cut than in a 3-part, discrete- component or "lumped component" loudspeaker. And _this_ is where a lot of the trouble begins!

8.) Brace profile is important, as it's believed to strongly influence the tone's "game plan." You can shape it so the tone builds up very quickly, corresponding to lots of highs, or use another shape for a slower buildup, corresponding to more lows and a mellower tone.

_Other features_ came to be associated with the Kasha design. Weights or steel bars in the neck, modified back bracing, many other things. While I work with some and question the validity of others, I feel that the "Business end" of the design is the top and bridge.


We all know the basic facts about strings. There may be some hidden lessons when we get to deal with soundboards.

There are two ways to change the harmonics makeup of a string, for now we'll assume it's plucked, as in a guitar.

First, we decide on the length we're going to allow to vibrate. That's dictated by what we're playing. The note we choose determines the fundamental and a whole series of higher harmonics. In other words, it tells us what the ingredients of the recipe will be. For example, the open fifth string has as ingredients (barring tiny imperfections): 110 Hz, 220, 330, 440 and higher integral multiples of 110.

Another word we can use is... confinement! A word we heard somewhere before... We confine the vibrations (of any significant amplitude) to a fraction of the string's length. Half the length is an octave higher, as we all know. If we want the A string to produce a B note, we have to use confinement. There's nothing we can do with the game-plan to get a B note on the open A string. Confinement determines the list of ingredients.

Once we know the ingredients, there's the question, how much of each one??? A lot of it depends on the properties of the string itself, but we can also use the following 3 factors:

1.) Point of plucking. If that point is where, say, the third harmonic has a node, that harmonic won't really be in the recipe. Plucking where a given mode has an antinode will bring more of that mode out. Generally, plucking near one of the ends of the strings will bring out more highs, that's the main part of the "ponticello" effect all classical players discover by themselves or learn.

2.) The shape of the plucking object, hence of the string's original displacement, a rounder/larger shape means less highs, a smaller/pointier shape more highs. It's important to note that in a way, the string "preserves" something of the shape it had right when it was released. You can look that up in acoustics textbooks.

3.) The speed of the string's release, slower means less highs, faster means more highs, and while at it you can see the connection between "ingredients" and "game plan" at work.

When we say "multinode" we might as well say "high harmonics" or "high-order modes." Let's not be too picky as to whether the "high" modes start at #3 or #25, I think the ideas will be plenty clear without this added precision.

There's a book you should get hold of, called "Tone Production on the Classic Guitar" by John Taylor. It came out in 1978 and has gone in and out of print over the years. My copy doesn't even have an ISBN on it. I think it's out of print now, but I hope that some day, The Bold Strummer will take up the cause to get it back in print again. The book explains these three mechanisms very well.

Taylor also talks about 4.) The direction of plucking. That relates to the string-soundboard interaction, not to the string alone, and we won't say much about it right now.

Taylor's book and the discussion of strings applies to players. Could there be analogous mechanisms we can apply as makers, to the sound-box, and in particular, to the top? How much of this theory will carry over to vibrating _plates?_

I think, at least on an intuitive level, that it's much more than what's implied in most acoustics treatises. Plates are more complicated than strings. But I find that many of the things that gave me good results with soundboards can be explained by making analogies to strings.

Many of the "obvious" things carry over: The top has its own series of harmonics. As with strings, the fundamental corresponds to a "whole body one piece" mode, the higher harmonics to "multinode" patterns.

The frequency-ratios are no longer tidy integers or fractions, they are weird numbers but just "real numbers" nevertheless. Nothing oddball, except we don't hear as "nice" a tone out of a plate. Moreover, when we have the guitar's two plates, plus the neck and sides, modes from different parts couple and resonances are so closely spaced, Graham Caldersmith refers to that as "The Resonance Continuum." So we don't hear as "nice" a tone out of an assembled soundbox either.

Well, players have their "tone-production" so we'll have our (considerably messier) "tap-tone production." You get used to it after a while.

What's the plate-analog of confinement? If there even _is_ one? Some notes played on the guitar don't have many plate-modes to reinforce them, until you're all the way up to the frequencies of the resonance-continuum. So this is a bit like trying to get a B note on an open A string. We'd like to "confine" plates, varying size much like we do on the string. But on strings, we can't argue there isn't confinement: By fretting a note, we instantly define a new boundary for the string, which we can also remove instantly. It's much less clear just how anything resembling this may happen on a top.

Two dimensions are harder than one, so it's unlikely that everything carries over from 1 to 2 dimensions in an obvious way. But I'm sure you're starting to see an attempt at "confinement"
somewhere in there. The Tom Evans quote is typical of that outlook. An article which Paul Wyszkowski wrote for the G.A.L Quarterly in 1982 expresses the same idea. It implies this

At high notes/frequencies, a small part of the "treble plate" is active. The rest of the soundboard is too big for those high frequencies, much like the woofer in a Hi-Fi speaker cabinet is too big for the kind of frequencies the tweeter puts out. More and more of the top becomes active as you go down the musical scale. At the low notes, the long "bass drivers" are set in motion, resonating with the low harmonics and especially the fundamentals of the basses.

Paul described this as "variable area of maximum vibration amplitude" a very elegant phrase, and stated that "there should be only one dominant radiating area (a monopole) for each frequency..." monopole radiation is a good idea.

If indeed we buy into the idea of these variable areas, also called "local modes," the question arises of just how to provide boundaries for all those local modes. We talked about the two diagonal bars, but still: Why shouldn't the bridge "think" it's "seeing" one big, roughly triangular, plate? A boundary is created by a discontinuity, so the best "candidates" for this are... the radial bars, which most people think of as only "driving" bars! If the "Dr. Jekyll" driving bars also work as "Mr. Hyde" boundary bars, it's very tempting to think that the more radial bars you have, the more effective your use of this idea is. This was one of the first things I questioned when I made my first Kasha model, the grounds for that were simple common-sense about the diminishing returns of an "overbuilt" guitar sound-board.

The above as you see is very much a "confinement" approach. And it's a part of the design that many people have questioned for years. You may have heard the genteel phrase, that the design is "controversial." I think that's the part people find the most controversial. Well, now we see that whatever "local mode" population may or may not be "in there," it's going to have to make some compromises.

Years ago, there were arguments back and forth, for or against asymmetric guitar soundboards. The soundboards of most string instruments are very asymmetric but for some reason the guitar was always mostly symmetric and for guitar acoustics aficionados this was a big deal.

People had so much "fun" arguing about it that nobody said: "Let's go take a look at what the vibration modes of Kasha models _really_ look like?" Back then, nobody knew. Some questioned the "monopole" hypothesis, some said that even with asymmetric bracing, modes will still be symmetric, except maybe at extremely high frequencies.

I felt very early on that, enticing as this "confinement"/monopole picture may be, I wasn't all that convinced, I didn't think it was the whole story. A different view is implied in what Kasha wrote. In my earliest (1983) Kasha design article, I mention something called "the Antinodal Structure." That thing was never explained adequately to me... All I was told was what I wrote there: It was the reason for cutting arches in the top's upper-transverse bar. It dated to long before the waist-bars had any arches in them!!! Kasha's 1972 "Builders' Manual" says: "ANTINODE STRUCTURE. The upper bout is freed for greater vibration by arching bars away from the top." OK, so I cut the arches like a good girl. But I wondered: The confinement strategy says this: There's some boundary (the waist bar and the diagonal bars) that's confining vibrations, whatever is outside that boundary isn't supposed to vibrate, therefore it does not matter. I mean, when you fret a note on the string, do you really want the portion of the string behind your finger to vibrate? So the area outside the perimeter bars should not matter. The area above the waist bar certainly should not matter. Why then would the upper-bout suddenly be an issue? Why would anyone care to make it flexible? Why would anybody worry if there were arches in the upper transverse bar or not?

It seemed Veerrry Fishy...

I began to believe that the braces behind the perimeter bars could do more than create 2 big huge dead-spots on the top. I think I got very good results by lightening up that structure. Now with hindsight and with what I told you about higher modes and multi-node vibrations, you should begin to see something else emerging: Working not just with the top's analog to the string's "confinement" tactic, but also with the "multi-node" idea.

Now the new picture was this: At low frequencies/modes, the whole top vibrates pretty much like the so-called (0,0) modes you see in the literature, whole-body-one-piece. At higher modes, I didn't believe we could or even wanted to immobilize all parts of the top outside the perimeter bars. I didn't believe those monopoles were always possible. So then I thought, in the absence of "bass bars" on the "treble side," the bracing should help obtain not smaller "monopoles, but "multi-node" vibration, just the highs we need.

One could still ask: "Why not make the perimeter extremely stiff? How do you know it's too stiff and not insufficiently stiff?"

I felt that on one hand, OK, it's a new design, it's a different sound, so all bets should be off as far as abiding by _anything_the traditional makers say is "good."

That attitude has good aspects -- you're not afraid to innovate. It has bad aspects: So many fine traditional guitars can't be all that wrong. I looked at the most general things they had in common. Doing a new design, I felt, does _not_ give you a carte-blanche to practically double the weight of your top or back, or to ignore considerations of splitting braces and avoiding runout on the top. If you change something that can affect overhead costs or marketability, you'd better be sure you're getting a good bang (improved sound hence player's approval) for the buck, (inconvenience to luthier or player).


Anyways, there's a whole litany of things about whether the guitars really do practice what the design preaches. I did a lot of work on that while building my first Kasha model, which was finished in 1981. As I said earlier, nobody at the time knew exactly what the vibration patterns of Kasha models looked like. Fred Dickens has been extremely generous and helpful to me and
after I finished this guitar, I was able to get Chladni patterns of it in his lab. I wish he was more active in guitar acoustics today. Any encounter with him is an unforgettable experience. he cuts right to the core of the issues and questions, and when he sets about finding an answer, it's always in a superbly methodical, rigorous and insightful way. The Chladni patterns of that guitar were all marvelously symmetric!...

I actually took it as a good sign, that there were no badly overbuilt or underbuilt areas on the top. I also began to realize what later became common knowledge: At the low modes, the guitar doesn't know it is a Kasha model, we wouldn't be able to tell if it is or isn't were it not for the bridge. There were the (0,0) modes, the cross-dipole (1,0), the (0,1) and (1,1) above that.
I did know there must be some asymmetric behavior, because there was a high note, I think the high D or E on the first string, where I could _feel_ an area on the treble side of the top having lots of activity. I got a wah-wah effect is I pressed repeatedly on the top. It didn't happen on the bass side.
But this was too high a frequency for us to see it with the setup we had. It still tended to confirm what I had believed all along: Somehow the "confinement" behavior and the "multi-node" behavior existed side-by-side, and it was wise to, let us say, _invest in
To be real "business-like," the thing to do is _hedge your bet,_ so let me tell you one idea for that. This also came out of the multi-node idea, and the attempts to combine both "philosophies." I'm gonna talk now about the bridge.


The silver inlay, I talk about that in this article I'm distributing at this meeting, so I'll repeat it here only briefly, it had to do with the following dichotomy: Let's say you have two guitar players, Sally and Igor. All Igor does is play bass-lines on the lower part of the sixth string of his guitar. You know those rock bass-riffs. All that Sally does is play harmonics, you know the 7th and 5th or even 4th fret ones, plus so-called artificial harmonics, as high in pitch as she can get, on the sixth string of her guitar.
Now both come to order Kasha models. I give them the usual bunch of stuff to read about the design. A while later, Igor says, based on what he's read, that he wants only the longer radial bars, and a wide bridge. Sally says, based on what she's read, that she doesn't want all the "bass bar" stuff, only shorter bars and a very narrow bridge (under the sixth string of course) would do for her. (As an aside, I got the names from a physics textbook which had a few "Sally and Igor" orbital mechanics problems. It was probably to celebrate the first American-Russian space-flights, so the "Sally" probably alludes to Sally Ride).

OK, so Sally and Igor work on a space-station. They play their guitars for a while, and then difficulties come up: With all the budget-cuts, Sally can't pay for her trip home, unless she sells her guitar. The only other guitarist on the station is Igor, who, based on what he has read, isn't going to want her guitar...

You get the idea: The "treble plate" may live very happily without the big bars and the "bass plate," the last thing we need is for the treble strings to be coupled to long radial bars and a big fat bridge weighing a ton. But the sixth string still needs the higher partials! Those are needed both for playing its harmonics, and also to fill in, enrich, the bass notes, who cannot live musically on the fundamental frequency alone. But it needs the fundamental, or at least some low partials, very much.

The first requirement says we somehow have to divide the bridge, maybe quite radically. The second says that too much division isn't good. We have to negotiate a compromise between the two demands, so I designed a bridge that gives a lot of latitude in deciding how much "separation" or "continuity" I'm gonna have.

The above was in "confinement" language. What about the multi- node/game-plan aspect? Let's go back to the string and see if we can dig up more analogies:
As far as shape of the plucking object and the speed of the "release," I think the most likely candidate is... the bridge!

We could say _very very_ informally that the bridge plucks the top. Very roughly, I'd say its mass corresponds to the "timing" of the release, while its size, especially width, to the "shape" of the "initial excursion."

We know from the string that this "initial shape" has an effect on the "recipe" of the tone. We also noted earlier that this shape is "preserved" during the string's vibration. If it didn't have
energy losses, the same shape would repeat itself every time the string completed one cycle.
Brace profile will alter the way the top bends when it vibrates. In the string, we know that the "shape of the envelope," which can be regarded as a combination of "sub-shapes," is directly related to the "recipe," said Sub-shapes" having something to do with the ingredients. So again it won't be a surprise to find the analogous thing happening in the top.

The rest falls into place: A lot of division or kerfing corresponds to "bending in many places," many nodes, while a large stiff bridge on the top would behave more like a trampoline with a
person jumping on it, whole-body-one-piece.

There's also the well-known analogy to the _location_ of plucking the string, putting the bridge at the center of the top's lower bout will encourage more low modes than putting it closer to the edge. We hear this particularly well in drums. We hear the difference when we tap the top too. Again going to Taylor, he mentions the point of diminishing return, we all know it's easy to get the string's lower harmonics but the 4th fret one and higher ones are very tricky or even practically impossible.

This bridge is a very complicated object, but of one thing I'm sure, the bridge, contrary to what Taylor says or implies, is extremely important, at least in this design. I found that some areas on it are very sensitive to tiny alterations, others much less so. A lot may have to do with where the braces are, so the same undoubtedly applies to fan bracing. Tie-block length varies widely among traditional guitars. What works well for one maker may well be a disaster for another. I'm sure a lot of it has to do with bridge/bar overlap.

In the Kasha design, we have a notion of where the bars end under the bridge, and for bar-profile, there's an idea of a "bright" profile versus a "brilliant" profile. I haven't seen that anyone else works with the bars and bridge as parts of the same structural unit. This bridge has a lot of room for variety in it, much as a brace does. Maybe some day we'll have a notion for bright and brilliant bridge shapes too? It's an interesting thought.

Another result that came from remembering that highs correspond to many nodes, has to do with top-thickness. Here's an everyday analogy: Suppose you had a thin cotton handkerchief. Fold it over once, easy! Folding it once more, so now it's in 4 layers, is also easy, you could probably go twice more with no problem.

Now take a thick towel or wash-cloth of the same size. You can fold it over once with ease, but doing it again will start to cause problems. There's no way you could fold it in 8 or 16 pieces without the thing getting out of shape, edges starting to crawl out etc. etc, and if you try to push them back "in" you'll encounter some resistance.

Note that Taylor also writes: "The stiffness of a string prevents it from being bent at a sharp angle and so limits the number of modes in which a string may be persuaded to vibrate." In other words, multinodal behavior is not solely or necessarily the result of discontinuities.

A similar thing may well be happening if we take our little "treble plate" and, in addition to it's being scaled down, we also make it thicker! I got very good results by making it thinner than the bass side of the top.
The "confinement" paradigm doesn't say much to confirm or negate this argument. It makes common-sense that when dealing with a smaller-diameter "top," its thickness should be scaled down too.

I had a chance to try this out on an unassembled top: On a recent (unassembled) soundboard, the treble side just happened to be as thick or thicker than the bass side, contrary to the 0.010-0.012" difference the _other_ way I've been using for many years. I took out a tiny sanding block with 180 on it and thinned the treble side from the outside of the top. I feel it improved the tap-tone improved considerably.

All in all, I think these analogies provide an excellent framework for looking at the Kasha design. But that's just analogies. What would the physics books say? From what I've seen, there's a lot in them about the mode-frequencies of bars and circular plates, always with uniform material and uniform thickness, but virtually nothing about how the geometry will affect the relative amplitudes of the modes. Recently a physics PhD I know wrote that "the reason you've never seen anything in a textbook about relative mode-amplitude is that they are the very devil to calculate!" However, there may be experimental ways to look into this, and who knows, somebody might already be doing it. As I said before, we know these factors, top-thickness, bracing etc, have an important effect on the guitar's tone, which has to involve the relative amplitude of partials. Irrespective of what the very devil wants <G> we deal with that all the time as luthiers! If we're not good at it, we don't get paid.


Finally, back to the question: What _do_ the vibration modes of Kasha models look like? This is where fortunately I could get some real hard-data and I published most of that in my 1986 "Waist-Bar" article.
When I decided to take out the top's waist-bar, I took the back waist-bar out too. Everybody was _sure_ the guitar would fall apart after two or three months from stringing it up. Well it didn't.
Now the first one has just turned ten years old, and I gather that it's in excellent condition.

With both waist bars absent, just about all the modes we measured dropped in frequency, we could finally look at some _really_ asymmetric modes, and boy there sure were interesting and unusual ones!
At 468 Hz, you can see vibrations somewhat "confined," the long bass bar, now in its Mr. Hyde incarnation, isn't moving much. But at other modes, all of the top, or all the parts of the top that "matter" (i.e excluding the far reaches of the upper bout) is vibrating. So the idea of "treble confinement" isn't the whole story. In any case, so far I haven't seen any of this "smaller and smaller monopoles" business. The "confined" monopoles seem to have run out of the stable via the antinodal structure. We definitely get asymmetric modes here, but how they radiate sound is something we still need to learn more about.

It's important to note that when we look at the lower resonances, we'd never guess the guitar is a Kasha model or anything asymmetric. The things that Fred Dickens, Graham Caldersmith and Tom Rossing did so much research on apply every bit as much here. In fact you can _hear_ whether a guitar has a double-reflex or not. So if those guys say something about the lower resonances you better listen.

On the other hand, I'm not sure if the prescription for a fine guitar means fixed, rigid rules for where to place those low resonances: If you read the waist bar article, you'll see that compared with traditional guitars, many of the modes dropped, a few took some real nose-dives, and two that I know of (the (1,0) and (0,1) ) literally traded places! If we believed that placement of the low resonances is a real delicate issue, we'd expect some real odd-ball "pathologies" or abnormalities in the performance of those guitars, but none were present! All in all this project really put many things in a new perspective, which I think is useful to makers of all types of classical guitars, yet they may not have come to light without this kind of project. I personally don't know if I would have dared take out both waist bars from any of my traditional guitars.

Anyway that whole thing was basically a "muscle project," so OK, we now know I'm tough and the Kasha design is tough, but so what? Is it "better" than having waist bars? Yes and no. It did not produce a "quantum-leap" increase in loudness. It may not be such a good idea for flamenco guitars. But the thing is, we now know we have a choice, and there's probably a lot we can do with the added area, possibly not only for the lower/bass-frequency modes -- the confinement vs. multi-node issue suggesting we might get more highs out of the new situation.

One thing it showed was that "dark" and "bassy" don't mean the same thing. I still think my darkest-sounding guitar is one with a waist bar, whose low modes are all higher in frequency than the guitars without it. This suggests we can lower all the mode-frequencies, (which making the top thinner will also do) and still create a recipe with lots of highs.

Just a short note on the "prescription" issue, let me mention a recent theoretical result, a math article titled "You Can't Always Hear the Shape of a Drum." If we had a very good computer- simulation, we could plug into it a given structure, like a guitar top, and get an idea of what its vibration-frequencies are. We can figure them fairly easily for square and circular plates.
This is the "inverse problem:" Given a set of frequencies, can we decipher the shape of the structure that's making it? For a circular plate, we can. But it turns out that for some two-
dimensional objects, we cannot! In other words, there is no unique shape for producing their unique sound.