principais teorias acerca do som musical na Antiguidade grega, entre o final do século VI a.C. e o início do século III a.C. O estudo analisa, em primeiro lugar, as circunstâncias históricas e materiais que propiciaram o desenvolvimento da teoria musical grega, chamada harmônica, e a sua relação com a prática musical do período em questão. A primeira teoria analisada está inserida no contexto da escola pitagórica, em que a cosmologia é o referencial de uma visão de mundo que se expande conectando todas as áreas do pensamento, e um dos pontos de origem é a harmônica matemática. São apresentadas a seguir as demonstrações feitas a partir do cálculo das médias proporcionais e sua relação com o princípio da coesão harmônica da oitava. No segundo capítulo são estudadas as teorias acústicas da Antiguidade, que se originaram das razões pitagóricas e se desenvolveram no âmbito das ciências naturais, aprofundando-se com a filosofia aristotélica. No terceiro capítulo, são analisados os principais pontos de confronto promovidos pela corrente aristoxeniana, que se insere no quadro epistemológico aristotélico, e que foram levantados contra os pitagóricos. Nessa nova forma de pensamento, a harmônica é estudada como uma tékne, que tem uma linguagem especializada particular e um objeto específico, o mélos. Ganha importância especial o conceito de aisthésis e, para colocá-lo em prática, a idéia de dynamis torna-se central. Por fim, é apresentada a persistência da concepção pitagórica nos cálculos dos intervalos musicais a partir da divisão do cânone. / This work presents the central ideas related to two main theories about musical sound in greek Antiquity between the end of VI century and the beginning of III B.C. First, the historical and material contexts that lead to the development of greek musical theory, called Harmonics, are investigated, and its relationship with the musical practice of the period. The first theory analyzed comes from the pythagorean school, in which cosmology is the framework of a world view that expands connecting all areas of thought and one of its departure point is mathematical Harmonics. Afterwards, I discuss the demonstrations that are done from the calculations of proportional medias and their relations with the octave harmonic cohesion principle. In the second chapter, its exposed the acoustic theories of Antiquity which originated from the musical ratios and had developed in the branch of natural sciences, deepening by the Aristotelian Philosophy. In the third chapter, I presented the most important issues concerning the differences between the aristoxenian current, which belongs to the aristotelian epistemological framework, against the pythagoreans. In this new way of thought, Harmonics is studied as a tékne that has a particular range of specialized terms and a specific object, the mélos. The concept of aisthésis assumes relevance and to put it into practice, the idea of dynamis becomes central. At last, the persistency of the pythagorean conception it is presented in the calculations of the musical intervals in the division of the canon.

principais teorias acerca do som musical na Antiguidade grega, entre o final do século VI a.C. e o início do século III a.C. O estudo analisa, em primeiro lugar, as circunstâncias históricas e materiais que propiciaram o desenvolvimento da teoria musical grega, chamada harmônica, e a sua relação com a prática musical do período em questão. A primeira teoria analisada está inserida no contexto da escola pitagórica, em que a cosmologia é o referencial de uma visão de mundo que se expande conectando todas as áreas do pensamento, e um dos pontos de origem é a harmônica matemática. São apresentadas a seguir as demonstrações feitas a partir do cálculo das médias proporcionais e sua relação com o princípio da coesão harmônica da oitava. No segundo capítulo são estudadas as teorias acústicas da Antiguidade, que se originaram das razões pitagóricas e se desenvolveram no âmbito das ciências naturais, aprofundando-se com a filosofia aristotélica. No terceiro capítulo, são analisados os principais pontos de confronto promovidos pela corrente aristoxeniana, que se insere no quadro epistemológico aristotélico, e que foram levantados contra os pitagóricos. Nessa nova forma de pensamento, a harmônica é estudada como uma tékne, que tem uma linguagem especializada particular e um objeto específico, o mélos. Ganha importância especial o conceito de aisthésis e, para colocá-lo em prática, a idéia de dynamis torna-se central. Por fim, é apresentada a persistência da concepção pitagórica nos cálculos dos intervalos musicais a partir da divisão do cânone. / This work presents the central ideas related to two main theories about musical sound in greek Antiquity between the end of VI century and the beginning of III B.C. First, the historical and material contexts that lead to the development of greek musical theory, called Harmonics, are investigated, and its relationship with the musical practice of the period. The first theory analyzed comes from the pythagorean school, in which cosmology is the framework of a world view that expands connecting all areas of thought and one of its departure point is mathematical Harmonics. Afterwards, I discuss the demonstrations that are done from the calculations of proportional medias and their relations with the octave harmonic cohesion principle. In the second chapter, its exposed the acoustic theories of Antiquity which originated from the musical ratios and had developed in the branch of natural sciences, deepening by the Aristotelian Philosophy. In the third chapter, I presented the most important issues concerning the differences between the aristoxenian current, which belongs to the aristotelian epistemological framework, against the pythagoreans. In this new way of thought, Harmonics is studied as a tékne that has a particular range of specialized terms and a specific object, the mélos. The concept of aisthésis assumes relevance and to put it into practice, the idea of dynamis becomes central. At last, the persistency of the pythagorean conception it is presented in the calculations of the musical intervals in the division of the canon.

Les Épîtres des Frères en Pureté forment une encyclopédie des sciences philosophiques (au sens hégélien) composée par Aḥmad b. aṭ-Ṭayyib as-Saraḫsī vers 280/894 à partir des travaux effectués par les Frères en Pureté, héritage du « cercle d’al-Kindī ». Le système trouve ses fondations dans l’arithmétique de Nicomaque de Gérase, est composé de la science kindienne, et s’élève sur les préoccupations politiques d’al-Ǧāḥiẓ, mais réalise une construction philosophique originale. Historiquement, une fois démontrée l’unicité du rédacteur, établi qu’Abū Ḥātim puise sa réfutation d’Abū Bakr ar-Rāzī dans la doctrine rasaélienne de l’héritage scientifique des prophètes, compris que les Rasāʾil sont alimentées par le kindisme, repéré que le seul héritier d’al-Kindī apte à cette entreprise est as-Saraḫsī, la comparaison des fragments saraḫsiens avec les épîtres révèle l’identité de style et de doctrine. L’identification de surcroît d’as-Saraḫsī au réviseur de l’Introduction arithmétique de Nicomaque autorise à postuler un système philosophique fondé mathématiquement. Préoccupées par le problème ontologique de la diversité du réel sous l’unité du Créateur, par le problème épistémologique de la divergence des méthodes et des doctrines scientifiques et religieuses malgré l’unité de la vérité et par le problème politique de la discorde malgré l’interdépendance des hommes, les Rasāʾil Iḫwān aṣ-Ṣafā entreprennent d’unifier la multiplicité empirique des êtres, de coordonner les savoirs et de réconcilier les hommes en une communauté vertueuse au moyen de trois concepts mathématiques : par leur origine dans l’émanation des êtres à partir du Créateur exprimée par la suite arithmétique, dans leur structure par la compréhension des analogies et des puissances entre les choses que révèle le rapport harmonique, et dans leur finalité au moyen de l’abstraction géométrique des formes hors de la matière constituée en modèle initiatique des âmes à la séparation d’avec le corps. / The Epistles of Brethren in Purity are an encyclopedia of philosophical sciences (in the Hegelian meaning) and were composed by Aḥmad b. aṭ-Ṭayyib as-Saraḫsī around 280/894. They are based on the work of the Brethren in Purity, which are the social inheritance of the “circle of al-Kindī.” The system itself is based on the arithmetic works of Nicomaque of Gerase. It is full of kindian science and erected on al-Ǧāḥiẓ political concerns. But as-Saraḫsī builds a very particular philosophical object. At the historical level, once we determine that the author is unique, that his views on the scientific heritage of the prophets is largely used by Abū Ḥātim ar-Rāzī to dispute with Abū Bakr, that the epistles are full of kindian elements, that the only al-Kindī’s student able to write such a book is Aḥmad b. aṭ-Ṭayyib as-Saraḫsī, we can compare the text with his fragments and reveal that they both share a particular style and philosophical ideas. So, because as-Saraḫsī is also the corrector of Nicomaque’s Introduction on Arithmetics, we can assume that he gives great importance to mathematics and base his system on it. The Epistles are focused on the ontological problem of the diversity of reality under the reign of the Creator’s unity, on the epistemological problem of contrariety of sciences and religions in methods and beliefs, and on the political problem of adversity of men in spite common interdependence. So they unify the effective multiplicity of beings, order the different disciplines of knowledge and build human reconciliation in the virtuous city, thanks to three mathematical concepts: they rewrite the emanation of beings from the Creator’s spring with the arithmetical sequence, they unify the actual structure of the world with the harmonic relation that rationalizes the different analogies and the mutual powers of their parts, and they educate the soul to its spiritual end with the geometric abstraction of forms from the material.