(fl Smyrna [now Izmir], early 2nd century bce). Greek philosopher and mathematician. His work was dependent on that of Thrasyllus of Alexandria (d 36 ce), Tiberius's court astrologer, and Adrastus, a member of the (Aristotelian) Peripatetic School (fl 1st–2nd century ce), but not on the Almagest (i.e. the Mathēmatikē suntaxis) of Ptolemy. Besides two treatises about Plato, now lost, Theon wrote a dissertation On Mathematics Useful for the Understanding of Plato (Tōn kata to mathēmatikon chrēsimōn eis tēn Platōnos anagnōsin). This mathematical introduction to the study of Platonic philosophy survives in two separate sections, one concerned with the study of numbers and harmony, the other with astronomy. Part of the work seems to have been lost, for Theon in his preamble promises discussions of five numerical sciences: arithmetic, geometry, stereometry, astronomy and music (ed. Hiller, 1.13ff; 16.24ff).
The second main section of this work is devoted to music, which Theon divides into three main categories: the ‘noetic’, or intelligible, music of numbers (hē en arithmois mousikē), deduced from arithmetical theorems; the ‘aesthetic’ music of instruments (hē en organois mousikē), perceived through the senses; and the music of the cosmos (hē en kosmō harmonia kai hē en toutō harmonia), or harmony of the spheres. Although he regarded the music of the cosmos, rather than the music of instruments, as the proper subject for consideration, he deals with instrumental music first on the grounds that the music of numbers is thereby made easier to grasp.
The section on instrumental music represents chapters from a mathematical treatise on musical intervals following the tradition of the Pythagoreans, rather than a discussion of melody or scale in the manner of the disciples of Aristoxenus. In it he quotes Thrasyllus (47.18ff) concerning notes, harmonic sounds, intervals and harmonia. The consonances (sumphōniai) are graded according to the simplicity of their ratios, or their ability to blend, first as antiphōnia (the octave or double octave) and paraphōnia (4th and 5th) – the cornerstones of the tonal system, and then as consonances ‘according to proximity’, that is, indirectly related (whole tone, diesis). Theon quotes Adrastus (49.6ff; 61.18ff), also using excerpts from Thrasyllus dealing with physical experiments (56.9ff), concerning the analogy between speech and music; the requirements for the production of notes; the principal consonances, whole tones and semitones; the three genera; and the diesis, the combination and categorization of the consonances, the whole tone and the limma.
His section on the music of numbers, or computable music, is purely arithmological, and again draws on Thrasyllus and Adrastus. It gives an account of ratios (74.15ff), proportions, with a digression on the division of the monochord (82.16ff), and finally of means (106ff).
Only in the third main section, on astronomy (120–205), does Theon touch upon the music of the cosmos. In a fragment of a didactic poem by Alexander of Ephesus quoted by Adrastus, the planets are for the first time assigned specific pitches in a nine-degree chromatic scale, an organization to which Greek and Roman authors would later return.
There are striking correspondences between Theon's sources and those parts of the writings of the Latin Neoplatonists Chalcidius, Favonius and Macrobius that deal with the theory of number, even discounting the Pythagorean and Platonic tradition common to all of them. Possible connections between Theon's musical classification and that of Boethius, which was to become authoritative in the Latin Middle Ages, have yet to be investigated; but like the similar categorization of Ptolemy, Theon's categorization of the intervals according to their degree of consonance, which he had derived from Thrasyllus, continued to exert an influence for a further millennium, especially through the works of Byzantine theorists such as Psellus and Bryennius.
See also Greece, §I, 6.
E. Hiller, ed.: Expositio rerum mathematicarum ad legendum Platonem utilium (Leipzig, 1878/R)
J. Dupuis, trans.: Théon de Smyrne, philosophe Platonicien: Exposition des connaissances mathématiques utiles pour la lecture de Platon (Paris, 1892/R)
R. and D. Lawlor, trans.: Theon of Smyrna: Mathematics Useful for Understanding Plato (San Diego, 1979)
A. Barker, ed.: Greek Musical Writings, ii: Harmonic and Acoustic Theory (Cambridge, 1989), 209–29
only works concerned with music
C. Stumpf: ‘Geschichte des Konsonanzbegriffes, I: Die Definition der Konsonanz im Altertum’, Abhandlungen der Bayerischen Akademie der Wissenschaften, Philosophisch-philologische Klasse, xxi (1897), 1–78; pubd separately (Munich, 1901)
L. Schönberger: Studien zum 1. Buch der Harmonik des Claudius Ptolemäus (Augsburg, 1914)
F.E. Robbins: ‘Posidonius and the Sources of Pythagorean Arithmology’, Classical Philology, xv (1920), 309–22
F.E. Robbins: ‘The Tradition of Greek Arithmology’, Classical Philology, xvi (1921), 97–123
K. von Fritz: ‘Theon (14)’, Paulys Real-Encyclopädie der classischen Altertumswissenschaft, 2nd ser., x (1934), 2067–75
W. Burkett: ‘Hellenistische Pseudopythagorica, II: Ein System der Sphärenharmonie’, Philologus, cv (1961), 226–43
L. Richter: Zur Wissenschaftslehre von der Musik bei Platon und Aristoteles (Berlin, 1961), 74–5
J. Flamant: Macrobe et le néoplatonisme latin, à la fin du IVe siècle (Leiden, 1977)
I. Hadot: Arts libéraux et philosophie dans la pensée antique (Paris, 1984), 65–73, 78–80, 254 [on Thrasyllus]
P. Moraux: Der Aristotelianismus bei den Griechen (Berlin, 1986)
LUKAS RICHTER