Monochord
A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono) string (chord). The term monochord is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows. According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison.
A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (kanōn [Greek: law]) straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason." However, "music, mathematics, and astronomy were [also] inexorably linked in the monochord."
The monochord can be used to illustrate the mathematical properties of musical pitch and to illustrate Mersenne's laws regarding string length and tension: "essentially a tool for measuring musical intervals". For example, when a monochord's string is open it vibrates at a particular frequency and produces a pitch. When the length of the string is halved, and plucked, it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1) 
Play . Half of this length will produce a pitch two octaves higher than the original—four times the initial frequency (4:1)—and so on. Standard diatonic Pythagorean tuning (Ptolemy's Diatonic Ditonic) is easily derived starting from superparticular ratios, (n+1)/n, constructed from the first four counting numbers, the tetractys, measured out on a monochord. The mathematics involved include the multiplication table, least common multiples, and prime and composite numbers.
...
Wikipedia