Witkowska-Zaremba, Elżbieta2023-11-272023-11-271987Roczniki Teologiczno-Kanoniczne, 1987, T. 34, z. 7, s. 285-292.0035-7723http://theo-logos.pl/xmlui/handle/123456789/11789The Pythagorean system i.e. the bases of the Pythagorean tune and its theoretical argumentation was presented by J. de Muris in his first musical treatise "Notitia artis musicae" in 1321. He developed his ideas in the treatise "Musica speculativa" published in two versions in 1323 and in 1325. "Musica speculative" became, especially in Central Europe, one of the best known music manuals of the Late Middle Ages and the Pythagorean system as formulated by de Muris for nearly two centuries provided a presentation of the problems related to the "artis muslcae" among the "artes liberales". All three above mentioned approaches to the Pythagorean system by the author "are based on the treatise "De institutione musica" by Boethius. The differences which exist between them result from the fact that various methodological assumptions were made. In the first book titled "Notitiae" de Muris exposed the relation between music and physics. In the first version of "Musica speculativa" written in 1323 he discussed only the mathematical aspects of music. The second version of this treatise (1325) presented a kind of intermediary approach. This approach is the fullest reflection of an idea very popular at that time, according to which music is something half-way between mathematics and physics, and in consequence has the status of a "scientiae mediae". De Muris is perhaps the first theoretician of music who was ever known by name and who used the terms "musica speculativa" and "musica practica" in the titles of his treatises. He did not, however, formulate any definition of those terms and any criterion for the classification. An undeniable achievement of this theoretician is the definition of the theory of interval, described in the Pythagorean system as "musica speculativa". Thus, in contradistinction to the "Speculum muslcae" by J. de Liege or the "De muslcae speculations" by W. Odington - which were comprehensive late medieval syntheses of the whole of the musical knowledge of those times - (with regerad to both theory and practice) - "Musica speculativa" by de Muris covers only one branch of the science of music. The reasons for which, this branch represented music among the "quadrivium disiclplines" are obvious: It was a kind of "normative acoustic" which investigated the reality of sound with the help of mathematics and at the same time discovered the very nature of objective and rational beauty deducing the rules of the art of music from it.plAttribution-NonCommercial-NoDerivs 3.0 Polandhttp://creativecommons.org/licenses/by-nc-nd/3.0/pl/Jehan des MursJohannes de MurismuzykologiamusicologyśredniowieczeMiddle Agessystem pitagorejskiPythagorean systemmuzykafizykamusicphysicsmatematykamathematicsArticle