By its nature, building a guitar is an engineering project, but so is playing it – in a certain sense. So if you’re going to be successful at either, you have to know when to approach the subject as an intuitive artist and when to approach it as an analytical engineer. One of the things that draws me to instrument building is that it forces a discipline between art and science yet negates neither. Even for playing the guitar there are technical considerations which require analysis and disciplining of the hands despite that in the long run those technical aspects become habitual and transparent. In a sense, the building of each instrument is a performance of the art of instrument making, with no live audience but a recording of what happened at the end.

It is easy to get involved with the engineering of a part of the guitar but lose sight of its place in the artistic whole. Massive amounts of analysis have gone into the behavior and engineering of guitar tops recently, with elaborate schemes devised to measure their behavior at every frequency of vibration, as if some unrealized potential will be discovered to put the instrument on an even footing with the violin or piano. Certainly, some loud guitars have resulted which appeal to a segment of the market, but as yet I’m not at a point where I’m sufficiently satisfied musically to follow that course.

From a player’s point of view there are some considerations to be made of how the guitar operates. It was once described to me as ‘the original solid state amplifier – a wooden box with a hole in it’ ! Rather than attach a magnetic pickup to the string and amplify that electrically to a speaker cone, the strings attach directly to the ‘cone’. An oversimplification perhaps, but that is the basic reality. If you had taken the 12″ speaker from a guitar amp and eliminated the cabinet, you would find that no sound below about 500 Hz [cycles per second] would come out. The reason is that any sound wave coming forward from the cone would be sucked into the vacuum created on the back side – unless the cone reverses direction before it can get there. Thus, without some sort of baffle to isolate the pressures, the air around the speaker just churns about inaudibly under about 500 Hz . Given that the highest note on the guitar is about 500 Hz, in theory there should be no sound at all.

But there would be. While the fundamental frequency of, say, A at the 17th fret on the first string would be 440 like a tuning fork, the string divides itself into harmonic divisions which vibrate at the multiples 2, 3, 4, etc. to give 880, 1320, 1760, 2200 and so on. If we just take the first five, which are the critical ones anyway, we find that 880 is just another A an octave higher and blends in with the fundamental such that it isn’t very obvious. The next one is an E which is a fifth higher; 1760 is another A and 2200 is a C# which is a major third in an A major chord. Thus the harmonics or overtone series plays a major chord of divisions of the vibrating string. Air columns in trumpets do the same thing as do our vocal cords, so this aspect of music theory is a given fact of nature. We can find these harmonics on the open strings at the 12th, 7th, 5th and 4th frets.

Thus, the electric guitar with a ‘free range’ speaker would be quite audible, but all of the fundamental frequencies would be lost. The same thing would happen to a lesser degree to a guitar made without a back. In order to make an open cabinet guitar amplifier work down to 80 Hz the dimensions are about 30″ or so, which is why smaller ones are limited in bass fullness or made with a closed cabinet. A three foot long open backed guitar would be likewise impractical. Thus it utilizes the closed cabinet principle shown above.

At the other end of the guitar, a G on the sixth string would be 100 HZ with a series 200, 300, 400, 500 and so on. Thus only the fifth overtone – B in this case – would be audible, yet the note still identifies itself to the ear as a G at 100Hz. This is because the ear hears the series continuing through 600, 700, 800 and extrapolates back down to the missing fundamental regardless. If we look at how the ear hears at different fequencies, the actual sensitivity at low volumes is nowhere near linear.

The chart above shows the sensitivity of the ear to differing frequencies and volume levels. It’s an inverted scale in that it shows how much volume is required to be heard. If we take 60 Db as a typical speech volume we see that the ear hears well up to about 5000 Hz but at the low end is down about 15 Db at 80 Hz, the lowest note on the guitar. Considering that every 3 Db is a doubling of sound energy, 15 Db represents a reduction down to 1/32 of the sensitivity on an energy basis! This is why a tiny violin can drown out a huge bass fiddle; we hear the violin more efficiently. As the general sound level increases, the ear becomes more linear and the low frequencies become equally recognizable. This is why a guitar which sounds full up close can be less so at a distance. This is also why instruments such as the lute, harpsichord and early guitars, which concentrate on the high frequencies and overtones, can seem quite ‘present’ in a hall despite their seeming inadequacies up close.

Another factor, which presents itself in large halls, is directionality. If the radiating surface is smaller in diameter than one quarter of the wavelength of the sound, the sound will start becoming directional rather than following the usual ‘rock dropped in a puddle’ circular dispersion. The diagram below shows the approximate dispersion from a surface whose dimensions are progressively larger than the quarter wave of the sound. I have added the frequencies for the approximate dimensions of a guitar, thus at 250 Hz – about the second string – it is still quite omnidirectional and by the highest note is still only dropping by half in intensity towards the side. Once the full wave is contained on the top however, the sound is focussed rather narrowly and becomes almost comically so at high frequencies. This illustrates why the tweeter on a stereo speaker is never placed in the center of the cabinet but invariably at the upper edge.

While romantics might like to dismiss this as irrelevant to the guitar, exceptions are not made just for musicians and instrument makers. Several factors mitigate the directionality problem in practice. First, a reverberant room will reflect the directional components and scatter them about. Second, the bulk of the sound is still reasonably well spread and unaffected. But perhaps of greater significance is that shown by the lower plots; there is a secondary generation showing up to the side of the main cone of projection. Interestingly, the number of these increases as the dimension of the top becomes multiples of the wavelength. This diagram refers to the radiating pattern of a speaker cone but a guitar top has a major difference; it has a rather heavy bridge in the center. It is my contention that the mass of the bridge forces the higher frequencies to operate further out from the center, thus the secondary and tertiary patterns become more equal to the center. If the guitar top were more like a banjo with no significant central mass it would be more like what we see above, but it is my contention that one of the main roles of the bridge is to ensure this even radiation of the higher overtone frequencies.

At the low frequencies quite the opposite problem occurs. Not only does the ear hear these pitches poorly but they also are going backwards as well as forwards. While the back may serve to keep them from looping around and cancelling, it does not redirect them forward. Compared to a cello which shares a similar register, the guitar is rather small and short strung by comparison. A major increase in directionality can be had by placing a reflector behind or by playing in front of a wall or better yet in a corner. The reflector must be larger than the longest quarter wave and preferably the half wave, thus about six feet or more, and the optimum distance behind would be perhaps also no more than three feet.

Significant gains in low frequency audibility can be gained from this tactic which may not be easily ascertained at close range but brings better fullness and balance at a distance. However, despite the measurable gains, the actual music and tonality may not be much affected because so much of what we hear as complexity and richness is in the overtone series, for which the guitar is sufficiently directional to begin with. Besides, the low frequency power of a guitar is so limited by its stringing that even with better directionality it is still best at short range or in a quiet and lively room. I realize that for those not accustomed to thinking about sound in this manner it may be hard to understand all this at first reading. If we could actually see sound waves in action all this would be obvious, but like electricity, sound is transparent.