The theoretical position of the frets on a guitar is determined by the notes in the equal tempered scale. The Swedish instrument maker D. P. Stråhle (1743) presented a simple geometric approximation to equal temperament. In the same issue of the Proceedings of the Swedish Academy, immediately following Stråhle’s paper, Faggot (1743) provided a trigonometric representation of Stråhle’s intuitive construction which suggested that it was not sufficiently accurate for the design of serious musical instruments. However, Barbour (1957) showed that Faggot’s work contained an error and that Stråhle’s construction has an accuracy which would be sufficient for guitar design.

The story is centred on three characters:

• Stråhle – an eighteenth century Swedish musical instrument maker.

• Faggot – an eighteenth century Swedish mathematician.

• Barbour – a twentieth century American mathematician.

SECONDARY: musical scales, equal temperament, Mersenne’s law, Stråhle’s construction.

SIXTH FORM: plus generalisations, perspective projection, interpolation and approximation.

Copyright Maths Discovery 2015