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Aristoxenus
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Aristoxenus (Greek: ???st??e???) of Tarentum (4th century BC) was a Greek peripatetic philosopher, and writer on music and rhythm.
He was taught first by his father Spintharus, a pupil of Socrates and also a musician, and later by the Pythagoreans, Lamprus of Erythrae and Xenophilus, from whom he learned the theory of music. Finally he studied under Aristotle at Athens, and was deeply annoyed, it is said, when Theophrastus was appointed head of the school on Aristotle's death.
His writings, said to have numbered four hundred and fifty-three, were in the style of Aristotle, and dealt with philosophy, ethics and music.

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Encyclopedia
Aristoxenus (Greek: ???st??e???) of Tarentum (4th century BC) was a Greek peripatetic philosopher, and writer on music and rhythm.
He was taught first by his father Spintharus, a pupil of Socrates and also a musician, and later by the Pythagoreans, Lamprus of Erythrae and Xenophilus, from whom he learned the theory of music. Finally he studied under Aristotle at Athens, and was deeply annoyed, it is said, when Theophrastus was appointed head of the school on Aristotle's death.
His writings, said to have numbered four hundred and fifty-three, were in the style of Aristotle, and dealt with philosophy, ethics and music. The empirical tendency of his thought is shown in his theory that the soul is related to the body as harmony to the parts of a musical instrument. We have no evidence as to the method by which he induced this theory (cf. Theodor Gomperz, Greek Thinkers, Eng. trans. 1905, vol. iii. p. 43).
In music he held that the notes of the scale are to be judged, not as the Pythagoreans held, by mathematical ratio, but by the ear. The only work of his that has come down to us is the three books of the Elements of Harmony, an incomplete musical treatise. Grenfell and Hunt's Oxyrhynchus Papyri (vol. i., 1898) contains a five-column fragment of a treatise on metre; probably this treatise of Aristoxenus.
Vitruvius in De architectura paraphases the writings of Aristoxenus on music. Translated by Morris H. Morgan, Ph.D, LL.D. Late Professor of Classical Philology in Harvard University. The full text of this translation is available from the Project Gutenberg
His Elementa harmonica contain an important passage concerning the interpretation of Plato's metaphysical doctrine:
| | ???t??? ?s?? ?st? t? p??d?e??e?? t?? t??p?? t?? p?a?µate?a? t? p?t’ ?st??, ??a p???????s???te? ?spe? ?d?? ? ßad?st??? ??d??? p??e??µe?a e?d?te? te ?at? t? µ???? ?sµ?? a?t?? ?a? µ? ????µe? ?µ?? a?t??? pa??p??aµß????te? t? p???µa. ?a??pe? ???st?t???? ?e? d???e?t? t??? p?e?st??? t?? ????s??t?? pa?? ???t???? t?? pe?? t??a??? ????as?? pa?e??· p??s???a? µ?? ??? ??ast?? ?p??aµß????ta ???es?a? t? t?? ??µ???µ???? t??t?? ?????p???? ??a??? ???? p???t??, ???e?a?, ?s???, t? ???? e?da?µ???a? t??? ?a?µast??· ?te d? fa?e??sa? ?? ????? pe?? µa??µ?t?? ?a? ????µ?? ?a? ?e?µet??a? ?a? ?st??????a? ?a? t? p??a? ?t? ??a??? ?st?? ??, pa?te??? ??µa? pa??d???? t? ?fa??et? a?t???, e??’ ?? µ?? ?p??atef?????? t?? p???µat??, ?? d? ?ateµ?µf??t?. t? ??? t? a?t???; ?? p???desa?, ???’ ?spe? ?? ???st???? p??? t????µa a?t? ?p??e????te? p??s?esa?· e? d? ?? t?? ??µa? p??e?et??e? t? ????, ?pe????s?e? ?? ? µ????? ????e?? ? e?pe? ??es?e a?t? d??µe?e? ?? ?? t? e???µµ??? ?p????e?. p????e?e µ?? ??? ?a? a?t?? ???st?t???? d?’ a?t?? ta?ta? t?? a?t?a?, ?? ?f?, t??? µ?????s?? ?????s?a? pa?’ a?t??, pe?? t???? t’ ?st?? ? p?a?µate?a ?a? t??. ß??t??? d? ?a? ?µ?? fa??eta?, ?a??pe? e?p?µe? ?? ????, t? p??e?d??a?. | | It is surely better to begin by stating the nature of the inquiry, and what it involves, so that with this foreknowledge we may proceed more easily on our chosen way, and recognize what stage we have reached and not unwittingly deceive ourselves about the matter. As Aristotle was wont to narrate, this was what happened to the majority of the people who heard Plato's lecture On the Good. Each came expecting to learn something about the things which are generally considered good for men, such as wealth, good health, physical strength, and altogether a kind of wonderful happiness. But when the mathematical demonstrations came, including numbers, geometrical figures and astronomy, and finally the statement Good is One seemed to them, I imagine, utterly unexpected and strange; hence some belittled the matter, while others rejected it. And what was the reason? They did not know what was coming but went along, like argumentative people, at the mere word. But if someone begins with a summary of his lecture, then, I hold, everyone who came to listen is free either to give up, or, if he likes, to stay, with the understanding he has already gained. Hence Aristotle himself, for these very reasons, as he said, used to give his prospective audience a summary of what he intended to say, and in what manner. Likewise it seems to me better, as I said at the beginning, to have foreknowledge.
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Further reading
- Andrew Barker, "Aristoxenus" in Greek Musical Writings, vol. 2: Harmonic and Acoustic Theory (Cambridge: Cambridge University Press, 1989), pp. 119-189.
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