The String Dilemma: Tension vs Stiffness
The relationship of tension and stiffness has always been a major consideration in design of musical instrument strings. This became especially problematic for the electric guitar when very light gauge string sets with bare wire G strings became widely available in the 1950's. A combination of low tension with high stiffness results in a loss of upper harmonics. A .017 inch bare wire B string used on an acoustic guitar has 58.87 percent higher tension at pitch than the same string used as a G string on an electric guitar. Since B is four halftones from G, this can be calculated based on the fact that doubling the string's diameter is the equivalent of a fourfold increase in string mass, but we must also factor in the decrease of diameter from whatever stretching occurs at pitch which can be quite a bit.
The ideal for guitar strings is for each string to exert equal tension at pitch which requires an increase in mass as pitch decreases. For the three bare wire strings in a typical modern electric guitar set, this can be simplified via the 4 times mass = 2 times diameter rule with the following results:
With wound strings, the calculation
has to take into account that such strings are not solid cylinders, and
therefore, a simple mass-diameter ratio does not apply. We can generalize,
however, that increased string stiffness reduces the harmonic content
of a note. The further up the neck a string is fingered, the shorter and
stiffer it becomes. One can play an open E string, then E on the fifth
fret of the B string, or on the ninth fret of the G string -- offering
the very same pitch but each fingering has a different timbre due to decreasing
harmonic content. A savvy player can make use of this effect by deliberately
controlling timbre through fingering choices.
To give myself a full range
of such choices -- on my long scale and light-weight solid-body guitars,
I normally use a .009-.042 string set to avoid a stiff, large diameter
bare wire G string. By way of contrast, on my D'Angelico, I used a .016-.074
set which delivered a well-balanced timbre selection on that guitar; while
on my L-4, it took a .012-.056 set to do the job. Plainly, each guitar
requires a different set of strings for optimum timbre balance and to
match the resonance of the guitar.
The string industry could help with the bare G string problem by researching and adopting certain annealed steels to reduce stiffness. I often wonder – what are they waiting for?