Os princípios cosmológicos de Filolau e a música - Oliveira, Guilherme Magalhães (2010)
Our object of study is the relation between music and cosmology in Pythagoreanism, specifically in the fragments by Philolaus of Croton (470-385 b.C.), a pythagorean philosopher who influenced both Platonic and Aristotelian philosophy. This investigation is divided into four parts: (1) Music in Ancient Greece, where we briefly examine the meaning of the word mousike and its relation to Greek culture, from Homer up until the Lyrical Poets. (2) Pythagoras and Pythagoreanism, where we discuss who was Pythagoras and his community. (3) Philolaus Pythagoreanism, where we analyze Philolaus fragments and explain the principles of his cosmology. Here, the meaning of limited (peras) and unlimited (apeira), his two cosmological principles, are discussed. Then we investigate the concept of harmony, understood here as a third principle, which serves the purpose of uniting in good proportion the first two principles in order to form an ordered whole (kosmos). As we look into the meaning of harmony, we also analyze the importance of the number, or arithmos, in Philolaus philosophy, since it is directly related to the concept of harmony. (4) In Music and the Cosmos, after we have explained Philolaus fundamental concepts, we demonstrate how they are linked to music, i.e. to the numeric ratios that are considered to be musical (or sound) intervals and the formation of the diatonic scale. According to Philolaus and the Pythagoreans, this scale presents a specific mathematical/musical structure, which is an image or imitation of the structure of the kosmos. Finally, we show that Philolaus diatonic scale is also used by Plato, on his Timeu