Why can one ancient bell produce two tones?
一口古钟，为什么能敲出两个音？
同一口古钟，换个位置敲击，听到的可能不是同一个音变响，而是另一个高低不同的音。
Striking the same ancient bell in a different place may produce a tone of a different pitch, rather than simply make the same tone louder.
这件事出现在一些中国古代青铜钟上。
This happens with some ancient Chinese bronze bells.
钟没有换，大小也没有变，为什么音高却能改变？
The bell has not been replaced or resized, so why can the pitch change?
先看看钟口：这类钟的横截面不是圆形，而接近两端较尖的杏仁形。
First, look at the bell's opening: its cross section is not circular but resembles an almond with somewhat pointed ends.
这种外形不只是装饰，也影响钟身怎样振动。
This shape is more than decoration; it also affects how the bell vibrates.
敲钟时，我们听到的声音来自钟身的振动。
When a bell is struck, the sound we hear comes from its vibrations.
钟身可以按多种不同的方式振动，而不是整体只用一种方式来回动。
The bell can vibrate in several different patterns, rather than move back and forth as a whole in just one way.
研究者把这些有规律的振动方式叫作“振动模态”。
Researchers call these regular patterns of vibration vibrational modes.
在这种不圆的结构中，一些模态成对出现，两个成员的振动频率并不相同。
In this noncircular structure, some modes occur in pairs whose two members have different vibration frequencies.
频率就是振动快慢的量度；它与声音的高低有关。
Frequency measures how fast something vibrates; it is related to the pitch of a sound.
敲击不同部位，会让不同的振动成分更明显，于是可以突出不同的音。
Striking different places makes different vibration components more prominent, allowing different tones to stand out.
所以，关键不只是“敲得有多重”，还有“敲在什么地方”。
The key is therefore not only how hard the bell is struck, but also where it is struck.
为了观察这种机制，研究者曾研究一口苏州制造的现代双音钟。
To investigate this mechanism, researchers studied a modern two-tone bell made in Suzhou.
他们用仪器测量钟身的振动，并用全息干涉的方法观察振动模态。
They used instruments to measure the bell's vibrations and holographic interferometry to observe its vibrational modes.
研究者认为，这两种音的音高，似乎主要取决于两个最低的振动模态。
The researchers suggest that the pitches of these two tones appear to depend largely on the two lowest-frequency modes.
不过，钟声包含更多振动成分，不能把整个声音都简化成只有两个模态。
However, the bell's sound contains more vibration components, so the whole sound cannot be reduced to just two modes.
现代实验能够帮助解释古钟的声音，却不能单凭这口现代钟，就还原古代工匠的全部制作方法。
Modern experiments can help explain the sound of ancient bells, but this modern bell alone cannot reconstruct all the methods used by ancient craftspeople.
同样，也不能把所有古钟的两个音都看成完全相同的音程。
Likewise, the interval between the two tones cannot be assumed to be exactly the same for all ancient bells.
原来，一口钟不必改变大小，也能靠自身的结构和敲击位置，让两个不同的音显现出来。
It turns out that a bell need not change size to reveal two different tones: its structure and the place where it is struck can do that.
形状、振动和手下的落点，合在一起，才是这个“两音秘密”的线索。
Shape, vibration, and the point of the strike together provide the clues to this two-tone secret.
