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An Introduction to Strings - Part 1

By Daniel Larson

Basic Physics of Musical Strings

A musical string is a cord stretched on an instrument which is struck, plucked, or bowed to produce tones.

There are three parameters that determine the properties of strings

  1. Length

  2. Pitch (frequency)

  3. Density

We can not do much about the first two, as most instruments are fixed in length and pitch. Although it is true that many viol players often change between two pitch standards — say, A=440 and A=415 — the general pitch for an instrument is usually fixed within a narrow range of musical frequencies. Therefore, the only element we change in any meaningful way is that of string density. String density is usually expressed as linear density; that is, weight (usually in grams) for a given length (usually meters), and this density is expressed as g/M (grams per meter). To ascertain this figure we can actually weigh a string and then divide this weight by the length to get g/M. It is this density that controls the tension of a string for a given length and frequency.

One aspect of viol strings that makes it easy to control tension is that there is only one material: gut. It is true that the density of a string can be changed by incorporating other materials into the construction, such as winding wire onto the gut (and we will consider multi-material strings later).

Because gut is one material, the only thing we can do to change the tension is to change the diameter, thereby changing the linear mass of the string. The following basic ideas are important to understanding the effects of changing a gut string diameter:

  1. The thicker the string, the more the mass, and therefore the heavier the string will be.

  2. A heavier string will have more tension for a given length and pitch.

  3. The thinner the string, the less the mass, and therefore the lighter the string will be.

  4. A lighter string will have less tension for a given length and pitch.

This table contains the weights of gut strings in g/M for diameters .38mm – 2.92mm

Since our string material is uniform, the only thing we can change is the diameter of the strings to change its weight. This is why it is important to be able to calculate the diameter of a string.

Next installment: Calculating String Diameters