Pythagoras and the Pythagoreans are regarded as the discoverers of harmony. Their definition is based on music: octave, fifth, and fourth are components of harmony and, according to many researchers, were defined by Pythagoras and his students in their mathematical ratios of 2:1, 3:2, and 4:3. Texts from the Pythagorean Philolaus, Archytas, and the Pythagorean sympathizer Plato are cited as evidence for this view. In particular, Plato's work Timaeus serves as proof of Pythagoras's significance in the mathematical definitions in music. A thorough examination of the original texts of ancient Greek and early Roman philosophers, natural scientists, and musicologists leads to a critical reassessment of common statements and the formulation of four theses. These concern the definition of the three modes of tonality in antiquity.