 A second strand of Neopythagoreanism, while maintaining connection to these metaphysical speculations, emphasizes Pythagoras’ role in the mathematical sciences. Nicomachus of Gerasa (modern Jerash in Jordan) was probably active a little before Numenius, in the first half of the second century CE. Unlike Neopythagoreans such as Eudorus, Moderatus and Numenius, whose works only survive in fragments, two complete works of Nicomachus survive, Introduction to Arithmetic and Handbook of Music. More than anyone else in antiquity he was responsible for popularizing supposed Pythagorean achievements in mathematics and the sciences. The Handbook of Music gives the canonical but scientifically impossible story of Pythagoras’ discovery of the whole number ratios, which correspond to the basic concordant intervals in music: the octave (2:1), fifth (3:2), and fourth (4:3); he supposedly heard the concords in the sounds produced by hammers of varying weights in a blacksmith’s shop, which he happened to be passing (Chapter 6 — translation in Barker 1989, 256 ff.). In the next century, Iamblichus took this chapter over virtually verbatim and without acknowledgement in his On the Pythagorean Life (Chapter 26) and it was repeated in many later authors. The harmonic theory presented by Nicomachus in the Handbook is not original and is, in fact, somewhat retrograde. It is tied to the diatonic scale used by Plato in the Timaeus (35b-36b), which was previously used by the Pythagorean Philolaus in the fifth-century (Fr. 6a) and shows no awareness of or interest in the more sophisticated analysis of Archytas in the fourth century BCE. Nicomachus is not concerned with musical practice but with “what pure reasoning can reveal about the properties of a rationally impeccable and unalterable system of quantitative relations” (Barker 2007, 447). Nicomachus also relies heavily and without acknowledgement on a non-Pythagorean treatment of music, Aristoxenus’ Elementa Harmonica, many of the ideas of which he assigns to the Pythagoreans (e.g., in Chapter 2; see Barker 1989, 245 ff.).