Stringing

The frequency of a vibrating string is
1. Inversely proportional to the length
2. Directly proportional to the square root of the tension
3. Inversely proportional to the square root of the mass per unit length

On a harp, point 1 (length) appears to be fixed at the construction stage. In fact we have some control over the length of the string for a given note, as we can change the overall pitch of the harp - for example we may decide to use the same "notes" but to tune to "baroque pitch" (A=415) a semitone below standard pitch (A=440). Also the gamut of a harp is not standardised so given an ancient harp frame of 29 strings for example, there is no conventional note to set the lowest string to. To add even more complications the harp may not be strung to a simple diatonic progression; there is evidence for occasional chromaticism, such as the inclusion of both b natural and b flat, and of course on Gaelic harps there is the doubling of g in the tenor range (comhluige). Also we can choose which pin to string to which shoe; some old harps have a different number of pins and shoes, positively inviting us to try different configurations.

Point 2 (tension) is how we tune the harp on a day to day basis, by adjusting the tension on the tuning pin. However it has some natural limits. If the string is too slack it simply sounds bad; if it is too taught then either the string or the harp will break depending on which is the strongest. Instrument makers often aim to have the strings fairly close to their breaking tension, but this is a subjective area as the closer to breaking tension, the more frequently the string will snap at areas of stress in normal use. Because the strength of a monofilament wire string is proportional to its cross-sectional area, and so too is its density, we find that strings of the same material but different diameter nevertheless all break at approximately the same pitch. However the thickness does affect breakage, as thinner strings seem to snap less at the points of stress at each end, and wire work-hardens, becoming stronger, as it is drawn progressively thinner.

3. We can affect the mass per unit length of a string in two ways; by making the string thicker or by using a denser material. Note that making the string thicker also makes it stronger and stiffer thus adversely affecting the sound. Wound strings increase the density without causing stiffness problems, but they are not appropriate solutions for historical Gaelic harp stringing.

There are a number of other factors which do not affect the pitch of the string but do affect the tone quality. These are chiefly the hardness and the elasticity.

Having said that point 1 (length) does not constrain us in an absolute sense as we can shift the pitch of the entire instrument up or down, it nonetheless is the most important constraint on stringing practice as the profile of the neck or "harmonic curve" of the harp imposes a set of ratios on the length of the strings, known as the "scaling' of the instrument. The "ideal" harmonic curve has the string length increasing exponentially so that each string is twice the length of that an octave higher.

Consulting the illustrated comparison of surviving Gaelic harps will reveal that the historical instruments fall into three distinct groups. These have been described as "low-headed", "large low-headed" and "high-headed". Although originally used to describe the construction techniques used, I consider this threefold division to demonstrate real divisions in the ratios of string lengths.

References

Simon Chadwick