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首页> 外文期刊>International journal of mathematics, game theory and algebra >MATHEMATICAL MEANS IN MUSIC AND ARCHITECTURE UP TO THE RENAISSANCE
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MATHEMATICAL MEANS IN MUSIC AND ARCHITECTURE UP TO THE RENAISSANCE

机译：音乐和建筑的数学手段，到了文艺复兴

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摘要

This chapter aims at showing the importance of mathematical means associated with the role of Pythagorean musical tradition in mathematical and architectural contexts up to the Renaissance. It comprises theoreticians such as Pythagoras and Archytas, the Roman Vitruvius, as well as Alberti, Zarlino and Palladio in Italian Renaissance. Pythagoras' discovery concerning the monochord represents the beginning of a science oriented toward mathematics. In theoretical music contexts, Archytas handled with what we call arithmetic, geometric and harmonic means. Nowadays, means are basically known in their algebraic representation, whilst, in Antiquity, theoreticians such as Archytas handled with them as geometric objects, namely, as proportions. Such a tradition was transmitted to the Roman architect Vitruvius, whose architectural treatise was related to the Pythagorean musical theory. In the Renaissance, both Alberti and Palladio followed the tradition handed down by Vitruvius. At last, this chapter focus on Palladio's text, which explains the three means used in calculating heights of rooms' domes, presenting also designs of some of his famous villas, whose measures are related to Zarlino's diatonic tuning.
机译：本章旨在展示与毕达哥拉斯音乐传统在数学和建筑环境中的作用相关的数学手段的重要性。它包括理论管理员，如Pythagoras和Archytas，罗马vitruvius，以及意大利文艺复兴时期的Alberti，Zarlino和Palladio。毕达哥拉斯关于单色的发现代表了对数学的科学的开始。在理论音乐背景下，Archytas处理了我们所谓的算术，几何和谐波手段。如今，手段基本上是在他们的代数表示中已知的，同时在古代，理论管理员如archytas与它们处理为几何物体，即作为比例。这种传统被传送到罗马建筑师Vitruvius，其建筑论文与毕达哥拉斯音乐理论有关。在文艺复兴时期，Alberti和Palladio都遵循了Vitruvius的传统。最后，本章侧重于Palladio的文本，该文本解释了计算房间圆顶高度的三种手段，也是他的一些着名别墅的设计，其措施与Zarlino的Diatonic调整有关。

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