Pythagoras

Pythagoras was a Greek philosopher and religious teacher of the second half of the 6th century BC, born on Samos. His figure belongs to Magna Graecia, and his influence on Western music theory has proved enduring, although much of what is known about him comes through later authors and is mixed with legend.

According to the sources, Pythagoras emigrated to Croton in 531 BC and later settled in Metapontum, in southern Italy. Both moves may have been motivated by political or religious persecution, although the text presents this as a possibility rather than a confirmed fact. In Croton he probably acted as a religious leader, and from his community emerged doctrines such as the transmigration of souls and a regulated way of life known as the bios. His thought insisted that the natural world can be explained through numerical relationships.

In the most radical Pythagorean doctrine, the physical world would be a material representation of a numerical truth perceived immediately, though superficially, in the elementary consonant intervals. His ideas were disseminated by Philolaus in the 5th century BC and by Archytas of Tarentum in the first half of the 4th century BC, and were known to Plato and Aristotle, for whom Pythagoras was already a legendary figure. During the 5th century the community split into a scientific branch, the mathematikoi, and a more conservative and religious one, the akousmatikoi.

In Late Antiquity, authors such as Nicomachus, Iamblichus and Proclus revived his teachings and combined them with those of Plato. His music theory is known from later treatises, such as the Divisio canonis attributed to Euclid, Nicomachus of Gerasa's Manual of Harmonics, and Gaudentius's Introductio harmonica, as well as from commentaries by Ptolemy, Porphyry, Theon of Smyrna and Aristides Quintilianus. Boethius and other Latin authors transmitted this knowledge to the medieval Western world.

His best-known achievement is the geometric theorem that bears his name, but his musical relevance lies in the numerical basis of acoustics attributed to him. According to an anecdote transmitted by Nicomachus, he supposedly observed that hammers of different weights produced consonant and dissonant intervals when striking, which the text itself considers a traditional tale. What is indeed associated with his school is the relationship between consonances and simple ratios derived from the tetractys 1, 2, 3, 4, applied to string lengths or frequencies.

His legacy is above all conceptual: the idea that musical harmony follows mathematical proportions sustained music theory for centuries. This conception reached as far as the harmony of the spheres, which Kepler developed in complex form in Harmonices mundi, published in 1619.