Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Membrane Vibrational Modes

膜振动模式

Stretched membranes have many vibrational modes, some of which are harmonically related to the lowest pitch and some not. The theoretical case of a rectangular membrane begins to show the complexity of membranes.

拉伸的膜具有许多振动模式，其中一些与最低音调谐波相关，而另一些则不相关。矩形膜的理论情况开始显示出膜的复杂性。

The musically more useful circular membranes have even greater complexity.

在音乐上更有用的圆形膜甚至具有更大的复杂性
 Index

Percussion instruments

Musical instruments

Reference
Berg & Stork
索引 鼓类乐器 音乐乐器 参考 Berg & Stork
 
HyperPhysics***** Sound
HyperPhysics ***** 声音
R Nave
 Go Back
返回








Rectangular Membrane

矩形膜

The resonant vibrational modes of an ideal membrane with length equal to 1.41 times its width are shown. The membrane produces harmonics, but also produces non-harmonic overtones. Where there are multiple segments, adjacent segments are moving in opposite directions during vibration.

理想膜片的共振振动模式如图所示，其长度为宽度的1.41倍。该膜片会产生谐波，同时也产生非谐波泛音。当有多个段时，相邻的段在振动时方向相反。

No, I haven't seen a rectangular drum either, but it is a useful mathematical model to show that resonant systems often have overtones which are not harmonics. This is true also in the more useful circular membranes used in drum heads, but the overtones are much more complex there.

不，我也没见过矩形鼓，但这是一个有用的数学模型，用以说明共振系统往往有非谐波的泛音。这一点在更实用的圆形鼓膜上也成立，但那里的泛音更为复杂。
 Index

Percussion instruments

Musical instruments

Reference
Backus
索引打击乐器 音乐乐器 参考 Backus
 
HyperPhysics***** Sound
HyperPhysics ***** 声音
R Nave
 Go Back
返回