[Herb Hunter]

I wanted to make sure I understood the intonation issue that the V-bracing addresses so I asked Taylor Guitars:

I would like to confirm, with your indulgence, that I understand how V-bracing can possibly improve intonation.

Assuming that when I fret the 6th string at the fifth fret I’m able to obtain a fundamental of exactly 110 Hz from the vibrating string, is it the case that as a given soundboard is excited by that 110 Hz string fundamental, it vibrates sympathetically not at 110 Hz but, say, 110.1 or 109.9 or some other frequency close but not equal to 110 Hz? I would call that intonation distortion, the unplugged analog of amplifier distortion. I, therefore, assume that V-bracing introduces less intonation distortion than traditional bracing.

Very soon after, Andy Powers was kind enough to send me a reply which I’m posting with his permission:

Totally ignoring the string compensation parameter of intonation, we'll think only in terms of resonance and vibration for a minute or two. A guitar body amplifies string sound by functioning as a coupled resonator. The string vibrates at a pitch and is attached to the body, transferring its vibration to a larger surface which will try to vibrate at the same frequency. If the body were so tuned to vibrate at exactly the same frequency as the string, life would be great. However, along with the intended fundamental note, we have overtones, and to a weaker degree, undertones. These are mathematically related other pitches summed together with the intended pitch. If we looked at A 110Hz, we should also have 220 Hz, 330Hz and so on, as well as a half-formed 55Hz. Now, in order to replicate this, a guitar body would need to respond to all of these, at exact frequencies.

Now, about sympathetic resonance and coupled resonance. If two things are exactly in tune with each other, like two bars of metal both tuned to 110Hz and one is made to vibrate, the energy will be transferred to the second bar, making it vibrate, whether they are touching or not. Here's the complication: the effect happens on a bell curve. In other words, if the 110Hz bar is vibrating, a bar at 109.9 Hz will vibrate to a lesser degree, as will 110.1Hz. 110.2Hz and 109.8 Hz bars will vibrate as well but to a still lesser degree.

This "resonating umbrella" occurs not just for every note, but every overtone and harmonic.

The guitar itself has its own set of resonances, made complicated with braces, shapes, and placements. I think most people are somewhat familiar with Chladni patterns and the way that exciting a surface can visually illustrate the different ways a top can vibrate. What is usually left out of such demonstrations is fact that all of these patterns are actually summed together when a guitar is played, and not isolated, since guitar strings do not introduce pure sine wave signals, but multi-frequency content. (Then, we have the nerve to go and strum chords....) When you sum these things together, you end up with a surface that resembles wrinkling tin foil-a convoluted and rough looking surface trying to vibrate in different ways according to every note and harmonic.

Then, you can add the complexity of modern equal temperament tuning, which, for the sake of practicality (of which I'm a fan) corrupts the mathematic precision and relationship between notes and harmonics.

So, what we're left with is an imperfect resonator. This imperfect resonator introduces a level of resonance interference or distortion. In other words, the notes and overtones coming from the strings are not perfectly replicated, and impart a small amount of "out of tune" as a result. As an example, the E5 note on the high string at the 12th fret has a frequency value of about 659 Hz. An octave below is the open high E string at 329 Hz. If a guitar has a natural resonance hot spot around 320Hz, it will vibrate whenever either of these E naturals are played. But what we’ll hear is a mix of 329 or 659 and 320. That’s going to have a detrimental effect on what we get to listen to.

Moving now to the V class guitar designs. The unwanted motion of the guitar (or certain parts) is restricted. Most notably, the front to back rocking in line with the strings is reduced, much like an electric guitar. Once this aspect has been toned down to a more manageable level, the inherent resonant hot spots of a body which react in weird ways can be evened out. What is left is a body which has little preference as to which exact frequencies it vibrates at. Rather than trying to move in its chaotic type of motion, it relies more simply on the speed it is vibrating at. Think of it as the time of motion instead of the type of motion. Just like the cone of a loudspeaker. The effect of this we hear as richer overtone and harmonic content (since those are allowed to be amplified instead of muffled by the body) and notes which have audible pitch closer to the intended one.

It's interesting to me, the overall effect is to impart more personality to each guitar and playing style, rather than less. Since all the nuances of tonewoods and performance (which are harmonic and overtone content) are reflected in higher degrees, we get to enjoy lots of different flavors.

I hope this is clear. If you need more information, I'm happy to help. You can see why when I explained this with even more detail to our marketing team who is tasked with introducing guitars to musicians, they felt we had better find a way to use descriptions and analogies to describe these effects.

-Andy