(fl c450–400 bce ). Pythagorean philosopher. A contemporary of Socrates and teacher of Democritus, he came from Croton (southern Italy), famous for its religious community associated with Pythagoras. After the destruction of the community in about 450 bce, he escaped to Thebes, a leading musical centre, where he taught some of the Pythagoreans whom Plato knew. He was the first to commit the precepts of Pythagoras to writing. Fragments from two of his works survive: the Bacchae (Diels, 44b17–19), and On Nature (Peri physios; Diels, 44b1–16), originally a multi-volume work, according to Nicomachus of Gerasa who quoted from it (Diels, 44b6). The authenticity of these fragments (written in the Doric dialect) has been disputed, but most scholars now regard them as genuine.
The fragments, together with the accounts of Aëtius (Diels, 44a9–13, 15–21) and Boethius (44a26), embrace a variety of subjects. In the fragment on music (44b6), Philolaus begins as a traditional Pythagorean philosopher with an explanation of harmonia, whose function is to bring into accord all the principles of opposition of which the cosmos is composed; but his own concluding analysis of the structural components of harmonia suggests a stronger link with musical practice (Philolaus himself was active as an aulos player; Diels, 44a7) than with Pythagorean doctrine.
Philolaus’s nomenclature in effect adumbrates the tuning techniques of musicians: thus, harmonia, his term for octave (diapasōn: the concord running ‘through all the notes’), denotes the harmonic framework or ‘fitting together’ of the octave’s components; the 5th (diapente: the concord running ‘through five notes’), he called dioxeian – ‘through the high-pitched notes’; and the 4th (diatesserōn: ‘through four notes’) is syllaba – the first ‘grab’ of the fingers on the strings of the tilted lyre. What the Pythagoreans and Plato called leimma (limma) – the semitone ‘left over’ after the subtraction of two whole tones from the 4th – Philolaus named diesis (‘passing through’), a term reserved by later theorists for the quarter-tone.
In his analysis of intervals smaller than a whole tone, Philolaus departed radically from Pythagorean doctrine, the hallmark of which is the treatment of musical intervals as numerical ratios. Using the numbers constituting these ratios as addable, not correlated, entities, Philolaus (as reported by Boethius) posited an array of micro-intervals, computed in units of 14 – apotomē (large semitone), 13 – diesis (small semitone), 1 – komma (comma; the difference between the large and small semitones) and ½ – schisma (half of a comma). This process of bisecting musical intervals is so mathematically unsound (the proper method being the multiplication and division of ratios) that scholars have judged Philolaus’s analysis unworthy of a Pythagorean thinker. It is possible, however, that he was treating musical intervals not as mathematically expressible proportions but, after the practice of musicians, as units in a tonal continuum governed solely by the capacities of the human voice and ear.
H. Diels, ed.: Die Fragmente der Vorsokratiker (Berlin, 1903, rev. 6/1951–2/R by W. Kranz; Eng. trans., 1948, 2/1959)
A. Barker, ed.: Greek Musical Writings, ii: Harmonic and Acoustic Theory (Cambridge,1989), 36–9, 261–2
J. Burnet: Early Greek Philosophy (London, 1892, 4/1945), 277ff
E. Frank: Plato und die sogennanten Pythagoreer (Halle, 1923/R), 263ff
W. Burkert: Weisheit und Wissenschaft: Studien zu Pythagoras, Philolaos und Platon (Nuremberg, 1962; Eng. trans., rev., 1962, as Lore and Science in Ancient Pythagoreanism)
C.J. de Vogel: Pythagoras and Early Pythagoreanism (Assen, 1966)
K. von Fritz: ‘Philolaos’, Paulys Real-Encyclopädie der klassischen Altertumswissenschaft, suppl.xiii (Munich, 1973), 453–83
C.A. Huffman: Philolaus of Croton: Pythagorean and Presocratic (Cambridge,1993) [incl. commentary on the fragments]
FLORA R. LEVIN