Archytas (fl. 400–350 B.C.), Greek Pythagorean philosopher from Tarentum in southern Italy. He was elected general seven times and sent a ship to rescue Plato from Dionysius II of Syracuse in 361. He is famous for solutions to specific mathematical problems, such as the doubling of the cube, but little is known about his general philosophical principles. His proof that the numbers in a superparticular ratio have no mean proportional has relevance to music theory, as does his work with the arithmetic, geometric, and harmonic means. He gave mathematical accounts of the diatonic, enharmonic, and chromatic scales and developed a theory of acoustics. Fragments 1 and 2 and perhaps 3 are authentic, but most material preserved in his name is spurious. See also PYTHAGORA. C.A.H.