 The question remains whether or not Pythagoras had adumbrated any sort of cosmology and what the relation of that cosmology was to Philolaus’ later system. It is certainly true that the discovery that the primary musical concords of the octave, fourth and fifth are governed by the simple whole number ratios 2 : 1, 4 : 3 and 3 : 2 occurred before Philolaus. Most of the traditions connecting this discovery to Pythagoras himself, however, are unreliable; Hippasus is the earliest Pythagorean connected to a scientific demonstration of these phenomena, but the actual discovery probably antedates him and may not be specifically Pythagorean (Huffman 1993, 147–8). It is also true that number plays a significant symbolic role in the acousmata that go back to the time of Pythagoras. Thus one of the acousmata asserts that number is the wisest thing (Iamblichus, On the Pythagorean Life 82). Pythagoreans took oaths in the name of Pythagoras as “the one who gave the tetraktys”—tetraktys being a name for the first four numbers, whose total is ten, which was the perfect number for the Pythagoreans. Our evidence for the oath is late, but the acousmata refer to the tetraktys as “the harmony in which the Sirens sang” (Iamblichus, On the Pythagorean Life 82), which may indicate an awareness of the role of the first four numbers in the whole-number ratios which determine the musical concords. The harmony in which the Sirens sing could be a reference to the famous doctrine of the harmony of the spheres, according to which the heavens make music by their motions. The acousmata also adumbrate a cosmology which is tied to a religious doctrine of reward and punishment. The planets are described as the avenging hounds of the goddess Persephone (Porphyry, Life of Pythagoras 41), the sun and the moon are the isles of the blessed, where the good may be sent as a reward (Iamblichus, On the Pythagorean Life 82), and thunder is a warning to souls in Tartarus (Aristotle, Posterior Analytics II, 11 94b33). It appears then that Pythagoras had presented a vision of the cosmos which was ordered according to symbolic numbers and which reinforced certain religious ideas (West 1971, 213–18). Philolaus continues in this tradition by arguing that there are ten celestial bodies arranged around the central fire, because ten is the perfect number, and also by perhaps endowing some of the parts of his cosmos with mythological and religious significance, e.g., by equating the central fire with the fire guarded by Zeus and stolen by Prometheus (see 4.2 above). On the other hand Philolaus’ attempt to save astronomical phenomena by including the five planets in correct order according to their periods, by giving an explanation of night and day and by responding to concerns about how parallax might affect the way the heavenly bodies appear to move has no apparent precedent in the cosmology of the acousmata. It would thus appear that Pythagoras promulgated a cosmology that was largely of mythic and religious significance and that Philolaus, while maintaining some of this religious import, significantly reworked these ideas in order to produce a system that could account for basic astronomical phenomena (Huffman 2013). Graham has thus recently argued that Philolaus is not the mere transmitter of the earlier philosophy of Pythagoras but rather was the inventor of “Pythagorean” philosophy, the figure who brought Pythagoreanism out of the shadowy world of Pythagorean lore into the light of Greek philosophical conversation (Graham 2014: 48).