Archytas of Tarentum, according to Aristoxenus, was the ‘last of the Pythagoreans’ in the continuous tradition stretching back to the founder. The precise dates of his birth and death are not known, but his life seems to have spanned almost exactly the same period as Plato's (427–347 bc), and if the seventh Platonic letter is genuine they were personal friends. Certainly there are close connections between their writings on harmonics, though the evidence about the relation is not always easy to interpret.

Archytas was by all accounts a remarkable man, distinguished simultaneously as a philosopher, a mathematician, an inventor of ingenious gadgets, a statesman and a military commander, and admired also for his personal qualities, his kindness, resourcefulness, self-control and affection for children. He counts as a heroic figure in the early history of mathematical harmonics, which he raised to new levels of conceptual and technical sophistication and channelled in unprecedented directions. Only a few fragments of his writings survive, along with reports in various (and variously reliable) later sources, but they are enough to allow us to reconstruct a coherent general outline of his approaches and ideas, and to piece certain parts of his work together in some detail.

Half a millennium later, in the most accomplished of all Greek essays in the mathematical style of harmonics, Ptolemy speaks of Archytas with evident admiration.