A monochord is a one-stringed instrument that was used throughout the middle ages as a tool to explore the relationship between mathematics and sound. For instance, if a string is divided in half, it produces a tone one octave higher than the open string. Other ratios such as 3:2 (fifth), 4:3 (fourth), and 9:8 (whole tone) can be found on the monochord, at once clearly visible and audible. A section on how to ‘divide’ the monochord was a standard inclusion in medieval theoretical writings on music. In many instances, theorists described tuning systems to meet the priorities of the music of their time.

The monochord was also used as a practical tool for learning new music by plucking out the notes (as we might do today on a piano).

Instructions for dividing a monochord typically start by dividing the string into ninths or fourths, then marking certain of those points with note names. Then the distance between one of the new notes and the end of the string is divided and marked, producing more notes. The divisions are made by finding harmonics or by using a divider (a long-armed compass without the pencil). When the scale is laid out on the monochord, you set the moveable bridge to the note that you would like, and pluck the string.

See "The Monochord in the Medieval and Modern Classrooms" by Kate Buehler-McWilliams and Russell E. Murray, Journal of Music History Pedagogy, Vol 3, No 2.

See also my monochord theory blog at




A 12th century image of Boethius using dividers on a monochord.  Trinity College Cambridge R.15.22















Gaffurius is teaching his students about the relationship between numbers and sound.  There is no actual monochord in this image, but there is a useful pair of dividers hanging on the back wall.


The instrument consists of a basic long resonating box, approximately 100 cm long and 9 cm wide and high. The sides and bottom are made of maple or cherry, with a spruce soundboard with one soundhole. The string is brass harpsichord wire. The string is stretched over a fixed bridge at each end of the instrument, and the tuning peg is recessed within one endblock. Three moveable bridges as well as one handheld bridge are included for use with the divisions.

Historical accounts suggest that the division points were marked directly onto the soundboard or onto a strip of parchment on the soundboard. My monochord has a set of “division sticks” which can be slid into place on the edge of the soundboard. Two division sticks can be on the instrument at the same time, enabling direct comparison between the sound of different divisions. Any number of division sticks can be laid out on a table to visually compare the divisions.


The initial monochord purchase includes four marked divisions sticks. They represent a Pythagorean tuning (Guido), an anonymous just tuning, a chromatic Pythagorean tuning (Prosdocimo de Beldomandis), and equal temperament. The basic monochord division sticks are marked with inked lines, while the deluxe monochord division sticks are marked with wood inlay.

Blank division sticks allow the theorist to plot out his/her own divisions. Both sides can be used, and pencil marks can be erased to allow for multiple reuse.


Eagle heads on deluxe monochords


Decorative soundholes on deluxe dichords


Basic monochord -- $650

Deluxe monochord -- $900



Vincenzo Galilei, Dialogue on Ancient and Modern Music, 1581. Translated by Claude Palisca, 2003.

Jan Herlinger, “Medieval canonics,” in The Cambridge History of Western Music Theory, 2002.

Christian Meyer, Mensura Monochordi, 1996.

Kate Buehler-McWilliams and Russell E. Murray, "The Monochord in the Medieval and Modern Classrooms" Journal of Music History Pedagogy, Vol 3, No 2.