NMSAT :: Networked Music & SoundArt Timeline

ca - 400 BC __ Acoustics
Archytas of Tarentum (Ἀρχύτας / Arkhytas) (ca 428-350 BC)
Comment : Archytas of Tarentum was active in the first half of the fourth century BCE as a mathematician and a philosopher in the Pythagorean tradition. More texts have been preserved in Archytas's name than in that of any other Pythagorean, but the majority of these texts are spurious. The pseudo-Pythagorean treatises of the first century BCE and later were often written in his name, considering him the latest of the three great early Pythagoreans (following Pythagoras himself and Philolaus). The spurious works on categories in Archytas's name were regarded as genuine by the commentators on Aristotle's "Categories" and were frequently cited. Four fragments survive from Archytas's genuine works, of which "Harmonics" was the most important, and there is a relatively rich set of testimonia. The beginning of Archytas's "Harmonics", is the earliest text to identify a quadrivium of four sciences (the science of number, geometry, astronomy, and music). Archytas praises the sciences for beginning by distinguishing the universal concepts relevant to the specific science, but he regards their ultimate goal as an account of individual things in the world in terms of number, thus building on Philolaus's insight that all things are known through number. Archytas's own "Harmonics" begins by distinguishing important general conceptions in acoustics. His mistaken view that pitch depends on the speed with which a sound travels.it depends, in fact, on the frequency of impacts in a given period.was adopted with modifications by both Plato and Aristotle and was the most common view in antiquity. Archytas provided an important proof that the basic musical intervals such as the octave, which correspond to ratios of the form (n+1)/1, cannot be divided in half. The goal of Archytas's harmonics, however, was the description of a particular set of phenomena.in this case the musical scales in use in his day.in terms of specific numerical ratios. Plato complained that such a science of harmonics sought numbers in the sensible world rather than ascending to more abstract problems, which were independent of the phenomena (Rep. 531c). For Archytas, however, there was no split between the intelligible and sensible world. Logistic, the science of number and proportion, was the master science for Archytas, because all other sciences ultimately rely on number to provide knowledge of individual things. Just as his science aimed at mathematical description of concrete phenomena, so Archytas also developed a theory of definition that earned Aristotle's praise (Metaph. 1043a14–26) for taking into account not just the limiting (formal) aspect of the definiendum but also the unlimited (material) aspect. (from "Encyclopedia of Philosophy". Copyright © 2001-2006 by Macmillan Reference USA)
French comment : Archytas s'est intéressée aux applications des sciences, intérêt dont Platon le blâmait. On attribue ainsi à Archytas plusieurs inventions dont une colombe en bois capable de voler (Favorinus d'Arles, cité par Aulu-Gelle, Nuits attiques, X, XII, 8). On lui attribue également l'invention de la crécelle, du hochet, de la poulie et de la vis . « Considérons donc comme une heureuse invention la crécelle d'Archytas, qu'on donne aux petits enfants pour les occuper ; cela leur évite de tout casser dans la maison, car la jeunesse n'est pas capable de rester en place. » (Politiques, VIII, VI, 1340 b 26).Archytas de Tarente [en grec ancien Ἀρχύτας / Arkhytas] est né probablement une douzaine d'années avant Platon, vers la fin du Vème siècle. [...] On le considère de nos jours comme le premier acousticien, du moins celui dont on peut lire quelques écrits fiables. Il s'agit principalement d'extraits transmis plus ou moins fidèlement par Porphyre au IIIème siècle de notre ère, dans ses Commentaires sur l'harmonique de Ptolémée (Ces extraits ont été traduits par Diels, à partir du Commentaire sur les Harmoniques de Ptolémée, écrit par Porphyre au IIIème siècle. Hermann Diels, "Die Fragmente der Vorsokratiker", trad. française par J.P. Dumont, Les présocratiques, Gallimard, Paris, 1988, p 533-535. Une étude approfondie sur Archytas est parue récemment : Carl A. Huffman: "Archytas of Tarentum. Pythagorean, Philosopher and Mathematician King", Cambridge University Press 2005. Huffman exprime quelques doutes sur l'exactitude du texte transmis par Porphyre, mais le passage cité ici semble correct). Voici l'extrait essentiel de la théorie de la production des sons chez Archytas : « [..] Ils [les mathématiciens] ont ainsi découvert les premiers qu'il ne peut se produire de son que si des corps se heurtent entre eux. Selon eux, le heurt se produit au moment de la rencontre et de la collision de corps en mouvement. Il y a son, tantôt quand des corps, animés de mouvements contraires, se freinent mutuellement en se heurtant, et tantôt quand des corps, emportés dans une même direction, mais à des vitesses inégales, sont heurtés par ceux qui les suivent en voulant les dépasser. Or beaucoup de ces bruits sont tels que notre nature ne nous permet pas de les percevoir, soit en raison de la faiblesse du choc, soit parce qu'une grande distance nous en sépare, soit encore en raison de l'excès d'amplitude de ces bruits (car les bruits de forte amplitude ne pénètrent pas en notre ouïe, de la même façon que rien ne pénètre à l'intérieur d'un vase à l'embouchure étroite, quand on veut y verser une [trop] grande quantité [de liquide]). » Archytas parle des 'mathématiciens ‘dont il cite l'explication de la production des sons. Il s'agit sans doute de Pythagore et de ses disciples, mais nous n'en avons pas trace. Bien entendu cette définition est insuffisante, puisque nombre de bruits sont produits sans qu'il y ait un choc manifeste qui en soit la source, et réciproquement. C'est pourquoi Archytas propose que certains chocs soient silencieux, soit parce qu'ils sont trop faibles, soit au contraire trop intenses. C'est ici la première approche du son, et le paramètre immédiatement perceptible, avant la hauteur, c'est son intensité. Et Archytas énonce la première loi de propagation, l'accroissement de la distance entre l'auditeur et le lieu de production du son diminue son intensité. Pas de mesure ici, pourtant il aurait été facile d'en pratiquer, en évaluant, de façon relative par l’audition, l'intensité de sons produits par un ou plusieurs chocs simultanés, et en mesurant la distance de perception. On ne voit pas bien quels sont ces bruits trop intenses pour être perçus, si ce n'est l'allusion, qui réapparaîtra plus tard, aux sons des astres en mouvement. Pour Archytas le choc est consécutif à la collision de deux corps en mouvement, mais il ne développe pas l'idée de la nécessité du mouvement pour produire un son. En particulier Archytas ne dit rien de la voix ou des instruments à vent, dans lesquels les chocs ne sont pas évidents, quand bien même certains de ses successeurs y verront des ébranlements de l'air consécutifs à un choc. Par ailleurs, Archytas use du terme Ψόφος, qui signifie bruit ou son d'une façon très générale, alors que dans les textes concernant l'acoustique qui vont suivre, on trouve le mot φϑόγγος, qui est un son inarticulé, différent de la voix (φονή), mais qui suppose une certaine musicalité, au sens d'une constance de la note. (François BASKEVITCH, p. 49)
Original excerpt : « [...] Well then, first they [the Mathematicians] reflected that it is not possible that there be sound, if an impact of some things against one another does not occur ; they said that an impact occurred whenever things in motion came upon and collided with one another. Some moving in opposing directions, when they meet, make a sound as each slows the other down, but others moving in the same direction but not with equal speed, being overtaken by the ones rushing upon them and being struck, make a sound. Indeed many of these sounds cannot be recognized beacuse of our nature, some because of the weakness of the blow, others because of the distance of separation from us and some because of the excess of the magnitude. For the great sounds do not steal into our hearing, just as nothing is poured into narrow-mouthed vessels, whenever someone pours out a lot. Well then, of the sounds reaching our perception those which arrive quickly and strongly from impacts appear high in pitch, but those which arise slowly and weakly seem to be low in pitch. For if someone should pick up a stick and move it sluggishly and weakly, he will make a low sound with his blow, but if quickly and strongly, high. Not only by this would we recognize the fact, but also whenever either speaking or singing we wish to voice something loud and high, since we speak with a violent breath. But further this also happens just as with missiles. Those which are hurled strongly are carried far, those weakly, near. For to those moving vigorously the air yields more and to those moving weakly less. The same thing will also happen with vocal sounds. The one carried be a strong breath will turn out to be loud and high, the one by a weak one, soft and low. But indeed we can also see this fact from this strongest sign, that we can hear the same man speaking loudly from far off but speaking softly not even from near at hand. But indeed also in flutes, the breath moving from the mouth and falling into the openings near the mouth produces a higher sound because of the great force, but that falling into the holes further away, produces a lower sound. So that it is clear that quick motion makes a high sound and slow motion a low sound. But indeed the same thing also happens to the rhomboi which are whirled in the mysteries. If they are moved calmly, they produce a low sound but, if forcefully, a high sound. But also indeed, a reed, if someone, having blocked the lower part of it, blows in it, he will, you know, produce a low sound. But if he blows into the half of whatever part of it, it will sound high. For the same breath is carried weakly through a long distance and strongly through a shorter distance. Having said other things about the motion of voice being according to intervals he summarizes the argument thus : It has become clear to us from many things that high notes move more quickly and low ones more slowly. Through this text and those cited still earlier, I have shown sufficiently that this was an ancient Pythagoran doctrine, which Ptolemy championed, having worked out some aspects himself, while running over other aspects highly, since they were in general circulation. » (Archytas the Pythagorean, "On Mathematics", In Carl A. Huffman, "Archytas of Tarentum: Pythagorean, philosopher, and mathematician king", pp. 106-107, Cambridge University Press, 2005)
Source : Baskevitch, François (2008), "Les représentations de la propagation du son, d’Aristote à l’Encyclopédie", Thèse de Doctorat, Université de Nantes, U.F.R. Lettres et Langages, Ecole doctorale : « Connaissance, Langages, Cultures ».
Source : Carl A. Huffman (2005), "Archytas of Tarentum: Pythagorean, philosopher, and mathematician king", Cambridge University Press.
Urls : http://tel.archives-ouvertes.fr/tel-00423362/en/ (last visited )

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