Early music

I wanted to give you the external diameter of a wound string of my instrument thinking that it would be useful data for the calculation of the new string I need, but I was told that this data is useless: is this true?

Yes. The measurement of the outer diameter is only useful in strings made of only one material, such as those made of pure gut, Nylon, Nylgut, or metal only. Wound strings are composite strings, i.e. made of different materials combined together.

A wound string is characterised by these two parameters:

  • its ‘Gut Equivalent’
  • its ‘Metallicity Index’

Gut Equivalent

Since wound strings are the combination of heterogeneous materials, it has been agreed to characterise them in terms of equivalent gut: in practice, this refers to the diameter of a theoretical gut string with the same weight per unit length as the wound string under consideration. At the same pitch and vibrating length, both strings will have the same working tension. And this data is useful for calculating the required diameters.

How can we obtain the gut equivalent of a wound string that needs to be replaced and of which we know nothing?

Answer: the string must be weighed, using a precision scale that measures grams and decimals, and then the entire length is measured. The weight, expressed in grams, is then divided by the length expressed in meters. The square root of the resulting number is the ‘gut equivalent’ (expressed in mm).

Example: my wound string weighs 35.5 grams and it’s 98 cm long.

Therefore: 35.5 g / 0.98 m = 36.22 (whose square root is…) = 6,02 mm

In practice, the wound string under examination is equivalent to a theoretical gut string of approx. 6 mm in diameter.

Metallicity Index

For a given gut equivalent, a wound string can be made with innumerable ratios of metal / gut percentages.

It is obvious that as one component increases, the other decreases, in order to keep the total weight of the string, i.e. its gut equivalent, constant.

The greater the prevalence of gut over metal, the more opaque the sound will tend to be. The opposite is true if there is more metal. The correct ratio between the metal percentage to the gut core percentage is dictated purely by aesthetic taste, which refers to that particular timbral/dynamic mixture one has in mind, and which is subjectively judged ‘beautiful’.

In other words, there is no real formula that can tell us what proportion must be used. The intention here is to state that, once the value of a string’s equivalent gut (in other words, its correct working tension) has been established, the balance between metal and core can only be obtained through experience. The Metallicity Index is also related to the position occupied by the string within the instrument. In other words, the third wound string of the cello must have a lower Metallicity Index than the fourth. The latter string must in fact have a greater prevalence of the winding metal than the core (increase in Metallicity Index) in order to compensate for the natural loss of brightness due to the lower Acoustic Quality Index value (see this faq).

Two strings with the same equivalent gut value may well have completely different Metallicity Indices.

This is the case, for example, with the fourth string of the viola and the third string of the cello. In the first case – the C of the viola – there will be a clear prevalence of metal (higher Metallicity Index) than in the G of the cello. That’s why a G of a cello can’t be installed as a C of a viola: the working tension might be right, but the acoustic performance would be decidedly unsatisfactory.