[ guitar aciton]Good fingerboards are not flat, good strings are not the same length, and a good action varies in height from treble to bass. If ever there was a subject to make Pythagoras turn in his grave, this is it. All the purity of divine perfect numbers is lost in the endless, murky compromise of trying to fit incompatible pieces together taken from several incomplete jigsaw puzzles.
Information on equal temperament and fretting intervals
To explain the above more fully we must look at why the fingerboard isn't flat. There are three very good reasons for this.
Firstly, if we look down the fingerboard following the line of the strings, the envelope of a vibrating string is not straight. Take the fundamental - the lowest vibration that a given string length is capable of producing (Fig 1). The basic pattern is always the same, but treble strings have higher pitched vibrations of smaller amplitude. Bass strings on the other hand, vibrate more slowly, but with a larger sweep. The aim of a good action is to keep the strings as low as possible over the surface of the fingerboard, especially towards the higher positions. It is easy to see what happens if a dead straight fingerboard is matched against the shape of the string envelope. (Fig 2). Where the two lines come together, this represents the string slapping on the fret - a particularly noisy and unpleasant business. One way round this would be simply to raise the string over the 12th fret (the action, measured at the 12th fret or half of the string length, is shown in red), but this is very uncomfortable to play. A much better solution is to shape the fingerboard into a curve to match the string. As we have seen, this curve is not the same for the bottom string and the top string. So the curve of the fingerboard is more shallow on the treble side than the bass side. NB the curves are greatly exaggerated for demonstration purposes.
Secondly, still looking down the line of the strings, we have seen that the bass strings need more room than the trebles because they have greater amplitude. Even though there is more curvature in the surface of the fingerboard, this is not enough to compensate for the difference. The bass strings need to be set higher than the trebles. This is the part of a set-up known as "the action" and refers to the height of the string over the octave fret (12th). As an accidental result of raising the bass strings, the string has to be bent further to reach the fret. This is simply bending in a vertical direction. Normally electric guitarists are used to bending notes sideways across the fret, but the result is just the same - the pitch goes up. So bass strings play sharper than treble strings as you approach the octave frets. The only way to make the guitar play in tune is to make the bass strings physically longer than the trebles. In fact, with the exception of the third string, each string gets slightly longer than its neighbour as you go from the first string down towards the sixth string. So, to return to the fingerboard shape, how do you give the bass strings more space? There are only two options - either the string goes up or the fingerboard goes down. On most guitars, the strings go up. You can see this by looking at the saddle. There is usually more saddle sticking out of the slot on the bridge on the bass side. This means that the leverage of the string on the soundboard is significantly different from one side to the other. There is a better, but far more complicated, way. The fingerboard can fall. In this case, as well as the curve of the string envelope, the surface skews like a propeller blade, winding its way downwards on the bass side towards the soundhole. This is a very complicated curve to visualise, but allows the strings to sit more or less equally high on the saddle and gives very good balance in sound.
Thirdly, just when you thought it couldn't get any worse, the frets are not flat! It is very hard for the hand to hold down a barr� across a totally flat fret. In the case of a full barr� , the finger joint falls across the third and fourth stings. In this hand position, it is often hard to get these strings to play clean. Flat frets require the player to use far more force, which can cause harm to the left hand. Convex frets, on the other hand, as long as they are not extreme, make the guitar far easier to play and suit the sweep of the fingers better as well. At this point, I will be merciful and avoid explaining why identically convex frets are often not the cleanest option. Suffice it to say that a slight conic section is often more preferable.
Oh no, a good fingerboard isn't flat!