Digital Heritage Research Lab

The Kanon of Pythagoras: A single-string Sonometer (7th B.C.)

A monochord, also known as a single-stringed sonometer, is an ancient musical and scientific laboratory instrument, involving one (mono-) string (chord), upon which points may be delineated to signify where the string must be stopped to give certain notes, allowing comparisons. The string is fixed at both ends and stretched over a sound box. One or more movable bridges (tasta) are then manipulated to demonstrate mathematical relationships among the frequencies produced. “With its single string, movable bridge and graduated rule, the monochord (kanōn [Greek: rule]) straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason.” Music, Numeracy and Astronomy were inexorably linked to it, at the time.

This one-string zither finds its oldest known written trace in the Division of the Kanōn (probably by Euclid). It is described as a long hollow wooden box along the top of which is stretched one string, rigidly attached to the box at one end, with provision at the other for changing the tension. As such, it could be used for studying audible changes in pitch (fractions above/below some fixed original frequency), as well as showing that frequency varies inversely as the length (or as the square root of the mass per unit length) of the vibrating string, or directly as the square root of its tension. Although somewhat simple in its conceptualization, the intangibility aspect distinguishes this case study from the rest. No concrete evidence about the actual dimensions or materials has been found so far, however, a lot can be inferred from the way ancient Greeks managed to transform the auditory experience into visual perception; namely acoustical axioms, pure mathematical propositions, and a series of corollaries relating notes within the Greater Perfect System. This means we needed to trace manufacturing trends back to Pythagorean Era, and collect evidence from third-party descriptions whenever the Kanon is mentioned (keeping an eye out for human biases, accounting for the Pythagoreanism evolving into a cosmology theory with religious and cult extensions.).

The team intends to apply an innovative (user-driven) approach for the first time. That is, build an EdTech interactive software tool with an open (customizable) frontend configuration, where the user essentially becomes the designer. In the first instance, our interface will allow for controlled parametrization, allowing the user to tune several adjustable metrics (such as dimensions, materials, etc.) and come up with their version of the monochord (along with some estimated probability measure of confidence in its description accuracy). Afterward, the resulting 3D model will be capable of offering highly engaging (non-immersive) digital experiences, relying on sensory stimuli to bring DCH to life. This means emphasis will be placed on adaptation/personalization of the learning experience (LX) fueled by drive-time calculations.

The specialty of this Case Study lies in the fact that it is an ancient object for which we only have basic information from the Ancient Greek Grammar, but not of the physical object nor the corresponding drawings. Based only on written information from ancient times and information from modern literature expressing various opinions about the Kanon, one of the main goals is to design the possible structure of the object (digital 3D geometry).

Another goal is to find out how such an object can be used as a tool in education. For example, with the implementation of the appropriate application that can be used for teaching purposes. In this manner, the Kanon can be used as an educational tool in the areas of Music, Mathematics, and Physics.

Graphical User Interface for the setting of the simulator parameters (History Tab).

Indicative visualization of Combined Magnitude Response (y-axis) vs Frequency (x-axis) from the simulation app using the Audio ToolBox


User centred approach of the Pythagorean monochords’ digitization

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