File:FMC00.680.jpg

Image caption

FMC00.680 shows,

on the left, Raphael's fresco painting 'The School of Athens' with a detail of the tablet held up before Pythagoras (ca. 570 to ca. 490 BC).

The tablet shows the tetractys below (see Schema FMC00.556 and variants), and above the U-bow representation of musical harmonic ratios.

In the middle, in colour, a legend with the greek and modern terms for what we know as the octave, fourth and fifth in music.

On the right is an example of the corresponding illustration from a 14th century book by Jean des Murs (ca 1291-1344) who revisited Boethius (ca 480-524) work in Latin on ancient Greek knowledge and ideas about music (including Pythagorean numerical ratios)

This example shows the lineage tradition of the U-bow representation shown on Raphael's work for showing ratios.

Many such illustrations can be found in the centuries that followed, when also other visualizations were used, ao with concentric circles and arc-based structured such as Robert Fludd's monochord and others.