从泛音的发现到傅立叶级数理论的建立

The Course from the Discovery of Harmonics to the Establishment of the Theory of Fourier Series

对协和音程的较低音调中存在较高音调这一现象的剖析引出了泛音概念。对基音与泛音共存现象的深入研究提出了简单模式叠加观念。傅立叶在简单模式叠加观念的启发下建立了其级数理论。从泛音的发现到傅立叶级数理论的建立是一个漫长的历史过程,对此过程的历史考察是研究傅立叶级数理论的起源、实质及内核的重要方面,同时也是揭示数学与音乐之间联系的重要视角。

Through analyzing the phenomenon of higher pitch existing in lower pitch in consonance,the concept of harmonics was put forward.Then the notion of superposition of simple modes emerged from the thorough study on the phenomenon of fundamental tone coexisting with overtone.With the enlightenment of the notion of superposition of simple modes,Fourier set up the theory of trigonometric series.From the discovery of harmonics to the establishment of the theory of Fourier series,it was a long historical process.The historical exploring on this process was not only important to the study on the origin,essence and core of the theory of Fourier series,but also a significant perspective to reveal the links between mathematics and music.