The School of Athens

In Raphael's famous fresco a boy holds a small tablet up to Pythagoras. On it is the tetractys, together with the music theory of the Pythagoreans.

Between 1509 and 1511 Raphael painted The School of Athens in the Vatican. The fresco gathers the thinkers of antiquity in a vast hall: Plato and Aristotle at the centre, around them Socrates, Euclid, Heraclitus, Diogenes and many others.

Raphael's fresco The School of Athens: an assembly of ancient philosophers in a hall with high arches — Raphael, *The School of Athens*, 1509–1511, Stanza della Segnatura, Vatican. Pythagoras sits in the lower left foreground.

Pythagoras and the tablet

In the lower left of the picture Pythagoras sits writing in a book. In front of him a boy holds a small black tablet. It is easily overlooked, but carefully inscribed:

Detail: Pythagoras writes in a book while a boy holds up a black tablet with numbers and a triangle — Detail with Pythagoras. The tablet at lower right shows the numbers VI, VIII, IX and XII with arcs at the top and a triangle with the number X below.

At the top is the Greek word ΕΠΟΓΔΟΩΝ, epogdoon, “an eighth over”. It means the ratio 9 : 8, the whole tone.
Below it are the numbers VI, VIII, IX and XII, linked by arcs. These four numbers contain all the basic intervals of Pythagorean music theory: 6 : 12 is the octave, 6 : 9 and 8 : 12 are fifths, 6 : 8 and 9 : 12 fourths, and 8 : 9 is the whole tone.
At the bottom is a triangle of strokes with the number X beneath it. This is the tetractys with its sum of ten.

So Raphael did not show Pythagoras with the theorem of the right triangle for which he is known today, but with music and the tetractys. In his time, the Renaissance, precisely this counted as the heart of Pythagorean teaching: the insight that harmony rests on ratios of numbers. You can hear how these ratios sound on the page Number and sound.