(b Tarentum, Magna Graecia, c375–360 bce; d ?Athens). Greek music theorist, philosopher and writer. According to the Suda he was the son of a musician called Mnesias or Spintharus who gave him his early musical education. It is not known to which philosophical or musical school Mnesias belonged, but he may have been one of the Pythagoreans whose political influence had been dominant in Magna Graecia, particularly in Tarentum, with which Archytas had long been associated. Mnesias could have known a number of prominent figures both in Magna Graecia and in Athens: the musicians Archytas, Damon and Philoxenus, as well as Socrates and perhaps even the Theban general Epaminondas. Aristoxenus himself followed the teachings of Lampros of Erythrae, and then, in Athens, of Xenophilus the Pythagorean. He spent most of his life in Greece. A fragment of one of his works indicates that he lived for some time at Mantinea in Arcadia, where music, which was held in high esteem, was subject to the kind of conservative laws that appealed to his austerity and love of ancient traditions.
At some unspecified date Aristoxenus renounced Pythagorean doctrines, although he retained his admiration for Archytas, whose biography he wrote. He then followed the teachings of Aristotle and seems to have become one of the master’s most eminent disciples, for Aristotle apparently considered appointing him his successor as head of the Lyceum. When Theophrastus gained the post instead, Aristoxenus broke with the school entirely and began teaching on his own account, concentrating mainly on music. However, he evidently did not reject the Aristotelian doctrines, because authors in antiquity consistently described him as a ‘follower of Aristotle’. As a pure first-generation Peripatetic, Aristoxenus brought the new science of music into the Lyceum, the ‘studio of all the arts’.
Aristoxenus was a prolific author with many interests: as well as writing on education and music he also produced biographies and histories of institutions. The Suda credits him with 453 works, although this is surely an exaggeration. Only 139 fragments of his memoranda, miscellanea and other small works have survived (ed. Wehrli); these reveal his interest not only in the theory of harmonics and rhythm, but also (unusually for a Greek theorist) in the history of music, musicians and musical institutions.
Aristoxenus’s principal work, the one that gained him the reputation of supreme mousikos throughout antiquity, was the treatise On Harmonics, which has come down to us under the probably erroneous title Harmonic Elements (Harmonika stoicheia). It is the oldest work of music theory written in Greek to have been preserved in substantial fragments, and was the first part of a larger work On Music, in which the author studied the various branches of the subject, in particular rhythm. Only fragments of the Rhythmic Elements have survived, either through quotations by later authors (Aristides Quintilianus and more particularly Michael Psellus, an 11th-century Byzantine writer), or through papyri; it is possible that POxy 9 + 2687 contains part of the Rhythmic Elements.
In so far as the history of musical thought in ancient times is concerned, the doctrines of Aristoxenus represent an epistemological revolution whose importance was acknowledged by all later theorists, whether they agreed with him or not. Before him, the Pythagoreans (such as Philolaus and Archytas) and the Platonists had regarded the science of music as part of mathematics. Aristoxenus, on the other hand, believed that music should be an autonomous discipline, one entirely separate from arithmetic and astronomy. No longer could music be a matter of calculating intervals expressed by the relationship of two numbers, for its concern is not mathematical entities but sound, and musical sound as distinct from noise or the sounds of spoken language. Its tools are rational thought (dianoia) and auditory sensation (akoē and aisthēsis). Reason establishes musical principles through the investigation of theorems (problēmata), some of which are also the subject of demonstrations. As for auditory sensation, Aristoxenus was the first musical theorist to insist on the necessity of training the ear to make hearing more precise, and on the control to be exercised over it by rational thought. On this basis he constructed a science of music whose methods, terminology and principles derive directly from Aristotelian scientific doctrines.
The first part of the Harmonic Elements is an examination by Aristoxenus of the doctrines of his predecessors; he proves to be highly critical, less on points of detail than on the actual foundations of their teachings. He criticized the Pythagoreans (without naming them) for regarding intervals not as pure musical entities but as numerical ratios, which are superparticular when they ‘define’ consonant intervals: octave (2:1), 5th (3:2), 4th (4:3) and tone (9:8). For Aristoxenus, music consisted of sounds structurally organized within a sound-space, and the function of the science of harmonics was to describe and regulate their spatial and dynamic relations. Unlike the Pythagoreans, he postulated and demonstrated that the tone can be divided into two equal semitones, not a limma (leimma) in the ratio 256:243 and an apotomē in the ratio 2187:2048. He also took the exact semitone as the unit of measurement for all musical intervals, and he differed from the Harmonicists, whose diagrams exhibit 28 consecutive dieses, which are devoid of any musical reality since more than two quarter-tones are never heard in succession.
Aristoxenus himself endeavoured to describe the musical system in all its coherence and complexity, setting out from the simplest of entities (musical sound) and proceeding to increasingly complex combinations of intervals and ‘systems’, envisaged simultaneously according to their ‘range’, ‘disposition’ and ‘function’. The last part of the treatise is a set of theorems setting out the laws of harmonics. Aristoxenus was the first to formulate the concept of the genus (genos), defined by the position of the two movable notes within a tetrachord (spanning the interval of a 4th), which divide it into three intervals of varying sizes. He described three genera: the enharmonic (‘the oldest and finest’), the chromatic and the diatonic. The enharmonic tetrachord consists of a ditone followed by two quarter-tones, moving from top to bottom; the chromatic – a tone-and-a-half, a semitone and a semitone; and the diatonic – a tone, a tone and a semitone. The chromatic and diatonic genera permit ‘coloration’ or ‘nuances’ (chroai) in which the extent of the intervals varies within limits set out by Aristoxenus.
Finally Aristoxenus defined the tonoi, a term probably of his own coining and destined to replace the old concept of harmonia. On approaching this important subject he rejected all the classifications and dispositions advanced by his predecessors and proceeded ‘from basics’, with a view to bringing order to the confusion then prevalent in music. The tonoi are related to the positions of the voice ‘in which each of the systēmes is placed in singing a melody’. In other words, the tonoi represent transpositions of the scales.
Unfortunately the passage in which Aristoxenus enumerated the tonoi has not survived. Their names as given by Cleonides are: Hypermixolydian (also called Hyperphrygian), high and low Mixolydian (also respectively called Hyperiastian and Hyperdorian), high and low Lydian (the low also called Aeolian), high and low Phrygian (the low also called Iastian), Dorian, high and low Hypolydian (the low also called Hypoaeolian), high and low Hypophrygian (the low also called Hypoiastian) and Hypodorian. They are grouped on the principle of the ‘affinity’ of their tones, allowing modulation from one to the other with more or less ease. They are not, therefore, modes, as has so often been thought, but transposition scales rising from semitone to semitone.
Aristoxenus excluded musical practice and in particular musical composition from the science of harmonics, and consequently anything to do with musical notation, on the grounds that such subjects involve skill (technē) and not science (epistēmē).
Many Greek and Latin writers on music, including Cleonides and Gaudentius, were directly inspired by the writings of Aristoxenus. Those theorists belonging to schools of philosophy opposed to the Aristoxenian musical doctrines tried either to refute them or, like Theon of Smyrna and Ptolemy, to integrate certain of the demands of Aristoxenus into their own theories. However, such a reconciliation of doctrines constructed on irreconcilable principles could never be entirely successful.
From what has survived of the Rhythmic Elements, it seems that Aristoxenus had adopted the same approach to rhythm as to harmonics: the determination of a small number of basic ‘principles’, the choice of a unit of measurement (the ‘primary time’ – prōtos chronos), the choice of criteria (hearing and judgment), and the articulation of the constituent elements of rhythm. Aristoxenus was the first to distinguish rhythmics from metrics, and he seems also to have been the first to write on the mutual relationship of musical durations, fundamentally distinct from words, melody or gesture, which were things that can be ‘set in rhythm (ta rhuthmizomena)’.
See also Greece, §I, 6(iii).
H.S. Macran, ed. and trans.: The Harmonics of Aristoxenus (Oxford, 1902/R)
F. Wehrli, ed.: Die Schule des Aristoteles: Texte und Kommentare, ii (Basle, 1945, 2/1967)
R. da Rios, ed. and trans.: Aristoxeni Elementa harmonica (Rome, 1954)
G.B. Pighi, trans.: Aristoxenus: Rhythmica (Bologna, 1959)
A. Barker, ed.: Greek Musical Writings, ii: Harmonic and Acoustic Theory (Cambridge, 1989), 119–89
L. Pearson, ed. and trans.: Elementa rhythmica: the Fragment of Book II and the Additional Evidence for Aristoxenian Rhythmic Theory (Oxford, 1990)
A. Bélis, ed. and trans.: Aristoxène de Tarente: le Traité d’harmonique (forthcoming)
R. Westphal: Aristoxenus von Tarent: Melik und Rhythmik des classischen Hellenentums (Leipzig, 1883–93/R)
R. Westphal: ‘Die Aristoxenische Rhythmuslehre’, Vierteljahrsschrift für Musikwissenschaft, vii (1891), 74–107
L. Laloy: Aristoxène de Tarente, disciple d’Aristote et la musique d’antiquité (Paris, 1904)
R.P. Winnington-Ingram: ‘Aristoxenus and the Intervals of Greek Music’, Classical Quarterly, xxvi (1932), 195–208
R.P. Winnington-Ingram: Mode in Ancient Greek Music (Cambridge, 1936/R)
M. Vogel: Die Enharmonik der Griechen (Düsseldorf, 1963)
F.R. Levin: ‘Synesis in Aristoxenian Theory’, Transactions of the American Philological Association, ciii (1972), 211–34
A. Barker: ‘Music and Perception: a Study in Aristoxenus’, Journal of Hellenic Studies, xlviii (1978), 9–16
A. Bélis: ‘Les “nuances” dans le Traité d’harmonique d’Aristoxène de Tarente’, Revue des études grecques, xcv (1982), 54–73
A. Barker: ‘Aristoxenus’ Theorems and the Foundations of Harmonic Science’, Ancient Philosophy, iv (1984), 23–64
J. Solomon: ‘Towards a History of Tonoi’, JM, iii (1984), 242–51
A. Bélis: ‘La théorie de l’âme chez Aristoxène de Tarente’, Revue de philologie, lix (1985), 239–46
A. Bélis: Aristoxène de Tarente et Aristote: le ‘Traité d’harmonique’ (Paris, 1986)
L.E. Rossi: ‘POxy9 + POxy 2687: trattato ritmico-metrico’, Aristoxenica, Menandrea, fragmenta philosophica, ed. A. Brancacci and others (Florence, 1988), 11–30
A. Barker: ‘Aristoxenus’ Harmonics and Aristotle’s Theory of Science’, Science and Philosophy in Classical Greece, ed. A.C. Bowen (New York, 1991), 188–226
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