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Kate McWilliams of “Unprofitable Instruments“ demonstrates how to use a monochord to explore musical ratios. 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
