 No list of Archytas’ works has come down to us from antiquity, so that we don’t know how many books he wrote. In the face of the large mass of spurious works, it is disappointing that only a few fragments of genuine works have survived. Most scholars accept as genuine the four fragments printed by Diels and Kranz (B1–4). Burkert (1972a, 220 n.14 and 379 n. 46) raised some concerns about the authenticity of even some of these fragments, but see the responses of Bowen (1982) and Huffman (1985 and 2005). Our evidence for the titles of Archytas’ genuine writings depends largely on the citations given by the authors who quote the fragments. Fragments B1 and B2 are reported to come from a treatise entitled Harmonics, and the major testimonia about Archytas’ harmonic theory are likely to be ultimately based on this book (A16–19). This treatise began with a discussion of the basic principles of acoustics (B1), defined the three types of mean which are of importance in music theory (B2), and went on to present Archytas’ mathematical descriptions of the tetrachord (the fourth) in the three main genera (chromatic, diatonic, and enharmonic – A16-A19). B3 probably comes from a work On Sciences, which may have been a more general discussion of the value of mathematics for human life in general and for the establishment of a just state in particular. New support for its authenticity has been provided by Schofield (2009). B4 comes from a work entitled Discourses (Diatribai). The fragment itself asserts the priority of the science of calculation (ha logistika, “logistic”) to the other sciences, such as geometry, and thus suggests a technical work of mathematics. The title Diatribai would more normally suggest a treatise of ethical content, however, so that in this work the sciences may have been evaluated in terms of their contribution to the wisdom that leads to a good life.