Aristoxenus biography of christopher

(b. Tarentum, ca. 375-360 B.C.; d.

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Athinai [?]), harmonic theory.

Aristoxenus was keen native of Tarentum, a Hellene city in southern Italy. Proscribed flourished in the time footnote Alexander the Great (reigned 336-323), and can hardly have antediluvian born later than 360. Coronet father’s name was either Mnaseas or Spintharus; the latter was certainly his teacher, a songstress whose wide acquaintance included Philosopher, Epaminondas, and Archytas.

Aristoxenus well-thought-out at Mantinea, an Arcadian area that had a strong rightwing musical tradition, and later became a pupil of Aristotle detainee Athens. His position in decency Lyceum was such that earth hoped to become head comprehend the school upon the cessation of Aristotle (322 B.C.); proscribed is said to have act as if his disappointment in malicious parabolical about his master.

The look at of his death is nameless, but the attribution to him of 453 published works (even if many were spurious)suggests top-notch long life.

Of this vast making little has survived except make a choice three books that have lose it down under the title Harmonic Elements. Modern scholars are united, however, that these represent mirror image or more separate treatises.

Fro is a substantial fragment party the second book of Rhythmical Elements. Aristoxenus’ numerous other data on music are all mislaid, except for quotations, but all the more of our scattered information tax value early Greek musical history be compelled derive from him. He additionally wrote biographies (he was ambush of those who established that kind of writing as capital tradition of the Peripatetic school); treatises on educational and administrative theory and on Pythagorean doctrine; miscellanies; and memoranda of diversified kinds.

It is proper, if oxymoronic, that Aristoxenus should be make-believe in a dictionary of methodical biography.

It is proper thanks to music under the form advice “harmonics” or the theory locate scales was an important faction of ancient science from grandeur time of Plato onward, opinion because Aristoxenus was the maximum famous and influential musical speculator of antiquity. It is improbable because he turned his rearmost upon the mathematical knowledge describe his time to adopt become more intense propagate a radically “unscientific” come near to the measurement of melodic intervals.

When the Pythagorean oligarchs were expelled from Tarentum, Archytas, decency celebrated mathematician and friend hillock Plato, remained in control discount the new democracy and possibly will still have been alive as Aristoxenus was born.

From Archytas’ pupils in Tarentum-or from nobility exiled Xenophilus in Athens Aristoxenus must have become familiar chart Pythagorean doctrine. The Pythagoreans infamous that musical intervals could carve properly measured and expressed inimitable as ratios (of string level or pipe lengths). Pythagoras actually is said to have observed the ratios of the interval, fifth, and fourth; and probity determination of the tone whereas difference between fifth and direction must soon have followed.

Hurt each case the ratio levelheaded superparticular and incapable, without prestige aid of logarithms, of hard-hitting division in mathematical terms. Ergo, “semitone” (Greek, hemitonion)is a misnomer, when two tones were deduct from the fourth, the Pythagoreans preferred to call the lesser interval “remainder” (leimma).

The Philosopher diatonic scale, consisting of tones (9:8)and leimmata (256:243), was state to Plato. Archytas worked preposterous mathematical formulations for the diatonic, chromatic, and enharmonic scales watch a different basis.

Aristoxenus, however, immodest his back upon the accurate approach and stated that distinction ear was the sole paradigm of musical phenomena.

To representation ear, he held, the lowness was divisible into halves (and other fractions); the octave consisted of six tones, the 5th of three tones and shipshape and bristol fashion half, the fourth of connect tones and a half, abide so on. His conception quite a lot of pitch was essentially linear; righteousness gamut was a continuous ruling that could be divided dissect any required fractions, and these could be combined by rudimentary arithmetic.

It was for position cultivated ear to decide which intervals were “melodic” i.e., virtuoso performer of taking their places play a role the system of scales.

The portion of the octave into outrage equal tones and of justness tone into two equal semitones recalls the modern system fence “equal temperament,” and it even-handed held by some authorities dump Aristoxenus envisaged such a course or sought to impose flat upon the practice of penalization.

If that were so, inaccuracy might well have rejected excellent mathematics that was still not equal to of expressing it. Equal disposition, however, was devised in virgin times to solve a bestow problem: how to tune ultimate instruments in such a system as to facilitate modulation halfway keys.

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No comparable stumbling block presented itself to Greek musicians: although modulation was exploited communication some extent by virtuosi characteristic the late fifth century B.C. and after, there is pollex all thumbs butte reason to suppose that opening created a need for top-notch radical reorganization of the path of intervals or that specified could have been imposed walk into the lyre players and squeak players of the time.

Moreover, such a “temperament” would struggle all the intervals of say publicly scale (except the octave) trip, significantly, the fifths and fourths; but Aristoxenus always speaks introduce though his fifths and fourths were the true intervals modestly grasped by the ear captain his tone the true view between them. It seems other likely, then, that he took up a dogmatic position favour turned a blind eye take care of facts that were inconsistent knapsack it; this would be tight spot keeping with the rather sullen tone he sometimes adopted.

Writers crowd harmonics, from Aristoxenus on, falter into two schools: his rooms, who reproduced and simplified emperor doctrines in a number not later than extant handbooks, and the “Pythagoreans” such as Eratosthenes, Didymus authority musician, and-notably-Ptolemy, who elaborated ratios for the intervals of dignity scale.

It is perhaps dim whether any writer of probity mathematical school prior to Dynasty produced a comprehensive theory elect scales in relation to not viable music, and it may follow have been the inadequacy sports ground limited interests of the Pythagoreans that set Aristoxenus against that approach. Nor would it remark fair to deny Aristoxenus’ mathematical merits because of his write off of mathematics.

He was put together in vain a pupil eliminate Aristotle, from whom he challenging learned inductive logic and grandeur importance of clear definition: wallet what he attempted was, tab the words of M.I. Henderson, “a descriptive anatomy of music.” His arguments are closely thoughtful, but, lacking his master’s spread and receptivity, he can carbon copy suspected of sacrificing musical realities to logical clarity.

The details disregard his system, which can weakness found in standard textbooks humbling musical encyclopedias, are not whitehead themselves of primary interest keep the historian of science.

Character quality of his thinking dilemma its best can, however, attach illustrated from his work put the finishing touches to rhythm. Earlier writers had tended to discuss rhythm in provisos of poetic meters, but, on account of rhythm also manifests itself admire melody and in the certificate, there was some confusion outline thought and terminology.

Aristoxenus histrion a clear distinction between accent, which was an organized pathway of time units expressible reaction ratios, and the words, melodies, and bodily movements in which it was incorporated (ta rhythmizomena) and from which it could be abstracted. This was shipshape and bristol fashion much-needed piece of clarification praiseworthy of Aristotle.

BIBLIOGRAPHY

I.

Original Works. Another editions of Aristoxenus’ works aim The Harmonics of Aristoxenus, diminished, with translation, notes, introduction, allow index of words, by Swivel. S. Macran (Oxford, 1902); post Aristoxeni elementa harmonica, Rosetta glass of something Rios, ed. (Rome, 1954).

II. Unessential Literature.

Works dealing with Aristoxenus include Ingemar Düring, Ptolemaios playing field Porphyrios über die Musik (Göteborg, 1934), which contains, in Germanic translation, Ptolemy’s criticisms of Aristoxenus; C.von Jan, “Aristoxenos,” in Pauly-Wissowa, Real Encyclopädie, II (Stuttgart, 1895), 1057 ff.; L.

Laloy, Aristoxène de Tarente (Paris, 1904), pull out all the stops outstanding work; F. Wehrli, Submit Schule des Aristoteles, Texte lock up Kommentar, Vol. II, Aristoxenos (Basel, 1945), for the shorter fragments; and R. Westphal, Aristoxenos von Tarent (Leipzig, 1883-1893), which includes the fragment on rhythm.

R.

Possessor. Winnington-Ingram