playing in position pt. 9: fingerboard geometry

To simplify things, there’s basically three ways to change the pitch on a chordophone like a guitar: change the tension of the string, change the mass of the string, or change the effective vibrating length of the string. On the guitar the tension of the string is altered by ‘bending’ the strings or via mechanical means (e.g. tuning machines, a mechanical ‘detuner’ or whammy bar). In the context of position playing, however, it’s the latter two (mass and length of the vibrating string) that we’re interested in.You can view the fingerboard as a two dimensional space in which pitch is dependent on the position both longitudinally and transversally in relation to the strings. Pitch is altered by moving up and down the string (changing the vibrating length of the string) or by moving perpendicular to the string, across the fingerboard (selecting strings of different mass and, to some extent, tension).
In our exploration of playing in position, thus far, we’ve really only concentrated on the first of these dimensions, but we’re about to extend playing in position across the fingerboard. (Or, recalling my earlier metaphor of the guitar fingerboard as “a set of single-pole, multi-throw switches”, having concentrated our efforts on the individual switches, we are about to practice moving between the switches.)

One of the interesting side effects this 2-dimesional arrangement is that the same pitch may appear at multiple coordinates on the fingerboard:Another is that shapes derived from the comfortable hand shape (the diagonal fretting pattern that, from first to fourth finger, moves bass to treble across the strings, and bass to treble up the frets) tend to maximize the pitch interval available, while the reversed diagonal shape tends to minimize them. (These factors will become significant in, for example, the playing of clusters.)Keep these ideas in mind as you approach the 2-dimensional fingerboard: you’re about to take a step towards what some players describe as the fingerboard ‘lighting up’….