演绎完美数学与音乐的巧妙结合1.doc

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1、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

2、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Deductionperfect—uniquecombinationofmathematicsandmusicAbstractThispapermainlyintroducestherelationshipbetweenmusicandmathematicsandtheapplicationofmathematicstomusic.Theapplic

3、ationincludes:usingmathematicstoanalyzesometheoriesonmusic;mathematicalknowledgerequiredtocomposeaconcerto;andmathematicaltransformations,goldenrationandnumericalsequenceandthelike.Thispaperalsotellssomestoriesaboutmathematicianswhohaveaspecialinteres

4、tinmusic.What'smore,inordertocomposeapieceofmusicinanelegentway,someworld-classmusiciansalwayshavetohaveaunderstandingonmathematics.Thestoriesofmathematiciansandmusiciansmentionedabove,wouldofferusabrandnewinsightintothecloselinkbetweenmusicandmathema

5、tics.Inaword,thisisaperfectcombinationofsensitivityandrationalityandoftwodifferentkindsofetherealbeauties!KeywordsMusicTheory,Temperament,MusicalInstruments,PrincipiaMathematica目录中英文摘要及关键词··················································（1）1引言·······

6、················································（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··

7、·························································（17）6结论···························································（18）致谢··································································（19）参考文献················································

8、·············（19）1引言2500年前的一天，古希腊哲学家毕达哥拉斯外出散步，经过一家铁匠铺，发现里面传出的打铁声响，要比别的铁匠铺更加协调、悦耳。他走进铺子，量了又量铁锤和铁砧的大小,发现了一个规律，音响的和谐与发声体体积的一定比例有关。之后，他又在琴弦上做了许多试验，进一步发现只要按比例去划分一根振动着的弦，就可以产生悦耳的音程。如1:2产生八度，2:3产生五度，3:4产生四度等等。就这样，毕达哥拉斯在世界上第一次发现了音乐和数学的联系。若干世纪以来，音乐和数学一