演绎完美-数学与音乐的巧妙结合1.doc

xx大学毕业设计（论文） 题 目：演绎完美——数学与音乐的巧妙结合 指导教师： 职称： 学生姓名： 学号： 专 业： 院 （系）： 完成时间： 年 月 日 演绎完美——数学与音乐的巧妙结合 摘要 主要介绍了音乐与数学之间的联系、数学知识在音乐中的应用。包括：音乐理论中的数学推导，乐谱书写时的数学知识，音乐中出现的的数学变换、比例、黄金分割和数列等知识。结合物理声波的叠加原理，揭示了乐器制造中的一些数学计算过程和计算方法。讲述了一些数学家与音乐的故事，以及音乐家在作曲时对数学知识的应用，让我们对数学与音乐的结合有一个全新的理解。通过研究会发现，音乐和数学之间的联系并不是偶然而是很自然的结合。这是一种感性与理性的完美结合，一种美与另一种美之间的融通！ 关键词 乐理、乐律、乐器、数学原理 Deduction perfect — unique combination of mathematics and music Abstract This paper mainly introduces the relationship between music and mathematics and the application of mathematics to music. The application includes: using mathematics to analyze some theories on music; mathematical knowledge required to compose a concerto; and mathematical transformations, golden ration and numerical sequence and the like. This paper also tells some stories about mathematicians who have a special interest in music. Whats more, in order to compose a piece of music in an elegent way, some world-class musicians always have to have a understanding on mathematics. The stories of mathematicians and musicians mentioned above, would offer us a brand new insight into the close link between music and mathematics. In a word, this is a perfect combination of sensitivity and rationality and of two different kinds of ethereal beauties! Keywords Music Theory, Temperament, Musical Instruments, Principia Mathematica 目 录 中英文摘要及关键词··················································（1） 1引言·······················································（3） 2基础乐理与数学··················································（3） 3数学知识在音乐中的综合应用···············································（9） 4乐器制作中的数学原理···················································（13） 5数学家与音乐···························································（17） 6结论···························································（18） 致谢·············