parabolic philosophy

Finding resonance

Most any object has a certain pitch or resonance when struck or dropped on the floor.  It depends on the size, density and mass of the object, among other things.  Some objects are specifically designed to have a certain pitch, such as a cymbal or bell, triangle or drum (which can be tuned to a certain extent).  

It stands to reason that a guitar soundbox should be a variable resonator. In that sense, it must allow any frequency within the spectrum of sound ranges played to find resonance.  

How can it do this, when the box itself has a certain “thud” frequency (the Helmholtz frequency) when tapped, and braces can be tuned to a certain tap tone within reason?  Some luthiers rely on these tones in designing and building, and knowing their effect can certainly be useful.  But there are not enough of these individual tones to cover the entire spectrum of 44 notes/frets on a typical guitar and allow it to produce balanced volumes for all. 

For example, the two lower braces on many Martin guitar backs resonate with the A string, and much of the back can be frelt vibrating when the A string is plucked.   However, the back does not resonate with the low E, D or G strings (which it can) and those strings are typically quieter on Martins (as on many others, too) than the A because only the A’s energy gets reinforced by the back.  (This is in addition to the effect of the top bracing on sound balance.)

In fact, I think the notion that the braces are what makes the sound is questionable in itself.  I believe that the braces serve to:  

1.  Balance the forces of string tension.

2.  Support the soundboard and back across the grain.

3.  Transmit the energy from the strings efficiently to where any and      all particular frequencies would like to find resonance.

The biggest question is how item 3 happens and why!   On steel string guitars, the X brace seems the obvious main transmission line, since it extends over much of the top, but then what?  How does it work?

Sound is Round--A Revolutionary New Theory (?)

In 1989, I bought a Dobro with a 10” cone, which gave more bass end than a model with a smaller cone, according to the company.  It made sense, as bigger diameter speakers have more bass.

By then, I had re-voiced about a dozen or so guitars, and was mostly pleased with the results, as were their owners.  

However, when I usually got close to being what I considered finished, I would invariably find one string that was quieter than the rest.  Plucking that string, I would feel over the X legs and belly braces and always find a dead spot, where there was no vibration.  Marking that spot with a piece of tape, I would unstring and feel the brace underneath, invariably finding a tiny imperfection in the shape of the brace.  Careful sandiing to even it out would often fix that string’s volume, and then produce a different dead string because I had simply moved the imperfection to another place on the brace.  And so forth, until the balance was good and the braces felt free of any irregularities.  

But I still had no means of predicting where to look to fix quiet strings, no obvious pattern had emerged.

One night while playing some Dobro blues and gazing absently at a coverless stereo speaker, it occurred to me that they both worked the same way.  Except that the Dobro’s string vibrations directly energized its cone, eliminating the electronic middleman of the speaker’s amplifier.

Then came the epiphany:  when a single note is played into either cone, the whole cone doesn’t vibrate; only a ring  in the cone vibrates.  And the diameter of the ring would be inversely proportional to the frequency of the note.  Simple physics.  In the same way, each drummer’s cymbal has its own pitch, and the larger they are, the deeper the pitch.

I imagine this “revelation” is common knowledge to designers of speakers.

To test this theory, I excitedly unstrung the Dobro, removed the many screws attaching the cover plate, and restrung it without the plate.  Back in open D tuning, I plucked the low D string and felt the aluminum cone with my fingertips.  What I felt was a ring about one half inch wide, centered about an inch or less in from the outer edge.  When I picked the fifth string, the ring moved inward about an inch, and so on up to the high D, which vibrated a ring an inch or less out from the wooden biscuit/bridge saddle.   

Then came the thought, perhaps more a leap of faith, that a guitar top must work in exactly the same manner--like a speaker cone with its sides cut out.  Of course, speakers do not have braces, which makes them different than guitar tops.  I had already noticed that the area of the top over most braces did not vibrate--only the areas in between braces did.  In fact, it is possible to map out the brace pattern on many guitars just plucking all the strings and feeling the top, and where it isn’t vibrating.  The exception is that the areas over the scalloped part of braces sometimes does vibrate if the scallop is deep enough .  

I have concluded that if a brace is balanced in strength to match the forces from string tension acting at any point along that brace, the top will be allowed to vibrate over it.  And if the brace is too weak, it will also allow vibration over it, which is why areas over deep scallops vibrate, whereas over the peaks that scalloping leaves, there is no vibration.

But what if the braces could be shaped so that they do not dampen the soundboard where they are glued?  That would certainly allow more of the soundboard to vibrate and make sound!  

Another important factor in allowing vibration over braces is the physical shape or contour of the brace itself.  My work has led me to the conclusion that sound vibrations travel over the surface of a brace, and that any irregularities such as corners or ridges dampen/absorb vibrations, thereby inhibiting their release into the soundboard.

basically, I reshape the guitar’s bridge and internal braces into flowing shapes that speed the vibrations from the strings into the top, and to balance the string tension at any point on the braces.  If a brace is stronger than needed, it will dampen the soundboard where it is glued underneath.  I have found that most of the braces in the guitar are too heavy and keep a lot of pretty wood from vibrating the way it would like to.

I have written two articles on this subject which were published in the Guild of American Luthiers magazine, ‘American Lutherie’ (#47, Fall, 1996 and #66, Spring, 2001).  Copies of the magazines are available from the guild at  I will be glad to send copies of my articles to anyone who sends me a S.A.S.E.  I have also given workshops at two GAL conventions, in 2001 and 2006.

In lutherie, there are (at least) two viewpoints on the back:  loose vs. stiff.  It is my opinion and observation that the back can reinforce the mid range and bottom end if it is allowed to with “loose’’ parabolic braces.

The “stiff” back faction contends that heavy back braces increases projection, and they may well be right.  In Spring, 2008, a major guitar company sent me a production dreadnought in a project to compare my work with a stock guitar.  When played in a room with a dozen or so company players, the re-voiced guitar unanimously sounded loudest to the player.  But across the room, the stock one more often sounded louder to the listeners.  And I’ve read an account of  comparing two classical guitars in large auditorium ( in which the stiff back guitar was much louder.  

With a loose back, the entire lower bout and much of the upper bout can vibrate, reinforcing that of the top.  Holding such a guitar is a delight, as you can feel it as though it’s alive.  Back in 2000, I had a discusson with Bob Taylor on this subject, and it was his opinion then that he didn’t want the sound of his guitars to change when held against the player’s body.

However, he had the opportunity to play the guitars I’d worked on.  I’ve seen only two Taylors since then, one a 2001 dreadnought, and a 2006 GSRS, which I re-voiced.  Both had back braces that were a very cleaver (of course) machined compromise of parabolic braces that allowed the outer half of each bout tovibrate and reinforce the mid and bottom ranges.  They also felt alive.  And, the GSRS had a parabolic lower belly brace!  (However, it ended up about 60% of its original size before it stopped dampening that area.)

One was a D-28 which had been so radically scalloped that the bridge rotated so much that a Bridge Doctor had been installed.  The owner didn’t want to pay to have the braces replaced, understandably.

Another was a Mossman dreadnought which had also been over scalloped.  It was necessary to remove the back in order to replace the X brace, bridge plate (which had cracked when the bridge belly pulled up, putting all the force along the bridge pin line) and finger braces.  The belly braces were still usable.   

I also worked on a 1954 OOO-18 that had been worked on previously.  Most of the braces had not been shaped enough to make much difference, but the 2+ inches at the end of the X brace legs had been crudely chiseled down completely to nothing!, destroying the low E volume.  It was necessary to carefully shape and fit two spruce pieces to repair the damage and make proper shaping possible.  That guitar ended up in the killer range.