目录
摘要I
关键词I
AbstractⅡ
引言
引言1
1高等数学在吉他制作中的应用1
1.1吉他的构成 1
1.2吉他发声的基本原理1
1.2.1弦的波速公式2
1.2.2弦的驻波解2
1.3弦振动发声的数学模型2
1.4实际应用2
1.4.13
1.4.23
1.3.33
2 高等数学在吉他音乐演奏中的应用4
2.1声音之间的高等数学关系4
2.2更小的音程 & 八度的分割5
2.3十二平均律 & 半音 5
2.4几种音程6
2.5实际应用7
3 高等数学在吉他音乐创作中的应用7
3.1音阶中的数学原理 7
3.2万能和弦 8
3.3黄金比例 9
4讨论 9
致谢10
参考文献12
高等数学在吉他音乐中的应用
摘 要
早在古希腊时期就有人提出了“数学”音乐思想, 这个思想一直影响着西方音乐的发展。其实，数学本就是音乐的基石，可以说是数学产生了音乐，当我们去深度挖掘音乐的本质与基础时，就会发现许多高等数学的知识。无论是在音乐理论方面还是在音乐创作方面, 数学都与其有着千丝万缕的联系。国内外早已有数学音乐的理念与理论，但多数都是对宏观音乐的概述，很少有针对一种乐器的全面分析与研究。本课题以吉他这种乐器为例，从吉他制作、吉他音乐演奏、吉他音乐创作三个方面探究高等数学在其中的应用。采用理论联系实际的方法，总结出吉他音乐中的数学基础，提炼出吉他音乐中的数学法则。充分展示出高等数学对吉他音乐的指导作用，让高等数学与吉他音乐更好的结合起来，使吉他音乐变得数学化。在探究出高等数学在吉他中的应用后，进而更加科学的制造吉他、更加简易的学习吉他、降低吉他音乐创作的门槛，同时可以影响目前的音乐教育模式和方法，使学习吉他音乐更加科学高效。
APPLICATION OF ADVANCED MATHEMATICS IN GUITAR *51今日免费论文网|www.51jrft.com +Q: ￥351916072￥ 
MUSIC
ABSTRACT
As early as the ancient Greece time some people proposed "the mathematics" music thought, this thought has been influencing the western music development. In fact, mathematics is the cornerstone of music, can be said to produce music, when we go deep into the nature and basis of music, we will find a lot of knowledge of higher mathematics. No matter in the aspect of music theory or in the aspect of music creation, mathematics has a lot to do with it. The concept and theory of mathematical music have existed at home and abroad for a long time, but most of them are the summary of macroscopic music. Taking Guitar as an example, this paper explores the application of advanced mathematics from three aspects: Guitar Making, Guitar Music playing and Guitar Music Creation. With the method of combining theory with practice, the mathematical basis of guitar music is summarized, and the Mathematical Rules of guitar music are abstracted. Fully show the guidance of advanced mathematics to guitar music, so that the better combination of advanced mathematics and Guitar Music, Guitar Music Become Mathematical. After exploring the application of higher mathematics in Guitar, we can make guitar more scientifically, learn guitar more easily, lower the threshold of guitar music creation, and at the same time influence the present music education mode and method, make Learning Guitar music more scientific and efficient.

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