Sector (instrument)

In the context of musical instruments, a sector is a mathematical instrument used for performing proportional calculations, particularly useful in determining lengths for dividing musical intervals and constructing scales. It is typically a flat, two-legged ruler hinged at one end, resembling a protractor when opened.

The sector utilizes the principle of similar triangles. Different scales are marked on the legs of the instrument. By setting the distance between corresponding points on the scales to a specific length (e.g., the length of a string), one can then easily determine the length required for other proportional divisions (e.g., calculating fret positions for a guitar or mandolin).

Sectors are pre-cursors to more sophisticated computational devices, and were especially useful before the widespread adoption of calculators and computers. While less common today, they remain a valuable tool for understanding the mathematical principles underlying musical instrument design and tuning. They can also be used in other contexts such as surveying and architecture, applying the same principles of proportional calculation. Historically, sectors were produced in various materials, including brass, ivory, and wood, and often incorporated other mathematical scales or measuring tools.