Monochord
Overview
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 theory. 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 my monochord theory blog at monochordtheory.blogspot.com.
Evidence
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.
Reconstruction
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 three marked divisions sticks. They represent a Pythagorean tuning (Guido), an anonymous just tuning, and a chromatic Pythagorean tuning (Prosdocimo de Beldomandis). 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
Pricing
Basic monochord -- $575
- Maple or cherry body, spruce soundboard with round soundhole.
- Three marked division sticks
- Bridges and dividers
- Tuning hammer for harpsichord string
- Cardboard tube shipping/carrying case
Deluxe monochord -- $775
- Maple or cherry body, spruce soundboard with decorative soundhole
- Eagle heads or other customized decoration
- Three inlaid and embossed division sticks
- Bridges and dividers
- Tuning hammer for harpsichord string
- Cardboard tube shipping/carrying case
Options
- Blank division sticks, $3 each
- Additional dividers, $8 each
- Dichord: Add an extra string to the monochord so you can compare intervals. Add $50 to the basic or deluxe price
Bibliography
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.