内容概述
毕达哥拉斯发现音程取决于简单的数字比：在相同张力下，同种琴弦的长度比为 2:1 时产生八度，3:2 时产生五度，4:3 时产生四度。这些结果被认为是最早记录在案的数学物理事实，并促使毕达哥拉斯学派开始用科学方法研究音阶。故事还记述了一个广为流传的传说：毕达哥拉斯路过铁匠铺，被铁锤敲击铁砧的和谐声响吸引，借锤回家称重后挂在同样粗细的琴弦上验证；但作者指出，这个故事在物理学上有重大漏洞，因为铁锤敲击铁砧的音调并不取决于铁锤的重量。
中文正文
36° 数学物理的第一个记录
据说毕达哥拉斯有一个关于数字的惊人发现：音程依赖于简单的数字比。就是说，毕达哥拉斯发现，在相同张力下的同样的琴弦，8 度音程的长度应该是 2 比 1，5 度音程为 3 比 2，4 度音程为 4 比 3。这些结果显然是最早的数学物理事实，据说，它们启发了毕达哥拉斯对音阶的研究。
13 中国人似乎更早就发现了音律与弦长的关系。成书于战国时期的《管子·地员篇》记载了“三分损益法”，即根据一基本音高的弦长，然后通过损（乘以 2/3）或益（乘以 4/3）递次得出其他四度音。这与毕氏的五度相生律不完全相同。
毕达哥拉斯的那个发现已经流传了千百年。事情是这样的：一天，毕达哥拉斯路过一家五金店，被一阵“叮当”声吸引了。四个奴隶正挥着锤轮番打击一块火红的铁。有一只铁锤的声音特别悦耳。经过一番考察，毕达哥拉斯发现，音调的高低区别在于铁锤的不同重量。他向店老板借来铁锤。他把铁锤带回家，称了重量，然后把它们悬挂在四根一样长、一样粗的铁丝上。拨动铁丝，他听出那声音原来跟铁锤打铁的声音是一样的。然后，他在铁锤上粘一小把土，让声音走调，发出跟其他三个铁锤和谐的声音。
然而，这流传多年的故事有一个大问题：铁锤打击铁砧所产生的音调与铁锤的重量无关。只要在铁匠铺多站几分钟，那些向后辈传播故事的饱学之士就会明白，整个故事在物理上是多么荒谬。
英文正文
36° The first recorded facts in mathematical physics. A remarkable discovery about numbers, claimed to have been made by Pythagoras, is the dependence of musical intervals upon simple numerical ratios. Thus Pythagoras is said to have found that for like strings under the same tension, the lengths should be 2 to 1 for the octave, 3 to 2 for the fifth, and 4 to 3 for the fourth. These results, apparently the first recorded facts in mathematical physics, are said to have led the Pythagoreans to initiate the scientific study of musical scales.
The manner of the above discovery by Pythagoras has been told repeatedly over the ages and runs as follows. While passing a blacksmith's shop one day, Pythagoras was arrested by the clang of four hammers swung in succession by four slaves pounding a piece of red-hot iron. All but one of the hammers clanged in harmony. Upon investigation, Pythagoras found that the differences in pitch of the four sounds were due to the different weights of the hammers. He persuaded the blacksmith to let him borrow the hammers for a short time. Taking the hammers home, he weighed them and then hung them individually to four strings of the same length and thickness. On plucking the strings, he noted that the emitted sounds corresponded to those made by the hammers striking the red-hot iron. By sticking a small lump of clay on the hammer responsible for the dissonance, he brought the emitted note for this hammer into harmony with the other three.
Now, curiously enough, there is a grave flaw in this often-repeated story, namely: the tone of a hammer striking a given anvil is independent of the weight of the hammer. A couple of minutes in a blacksmith's shop would have convinced any one of the erudite scholars who passed this legend on to their successors that the whole story is physically absurd.
英语学习拓展
常用词汇
mathematical physics音标/ˌmæθəˈmætɪkl ˈfɪzɪks/
数学物理。
原文用法：apparently the first recorded facts in mathematical physics.
interval音标/ˈɪntəvl/
音程；间隔。
原文用法：the dependence of musical intervals upon simple numerical ratios.
numerical ratio音标/njuːˈmerɪkl ˈreɪʃiəʊ/
数字比；数值比。
原文用法：simple numerical ratios.
tension音标/ˈtenʃn/
张力。
原文用法：for like strings under the same tension.
octave音标/ˈɒktɪv/
八度音程。
原文用法：2 to 1 for the octave.
fifth音标/fɪfθ/
五度音程。
原文用法：3 to 2 for the fifth.
fourth音标/fɔːθ/
四度音程。
原文用法：4 to 3 for the fourth.
scale音标/skeɪl/
音阶。
原文用法：initiate the scientific study of musical scales.
blacksmith音标/ˈblæksmɪθ/
铁匠；铁匠铺。
原文用法：While passing a blacksmith's shop one day...
clang音标/klæŋ/
叮当声；发出叮当声。
原文用法：Pythagoras was arrested by the clang of four hammers.
dissonance音标/ˈdɪsənəns/
不和谐的音；不和谐。
原文用法：the hammer responsible for the dissonance.
erudite音标/ˈerudaɪt/
博学的。
原文用法：any one of the erudite scholars...
同义词与近义词
对应核心词汇：interval
对应核心词汇：interval。
辨析：interval 侧重音程（两个音之间的距离），pitch difference 强调音高差异，frequency gap 强调频率差。
对应核心词汇：numerical ratio
对应核心词汇：ratio。
辨析：ratio 泛指两个量的比；proportion 强调成比例关系；fraction 强调分数形式。
对应核心词汇：dissonance
对应核心词汇：dissonance。
辨析：dissonance 为音乐术语，指不协和音；discord 为日常用语，指不一致；harshness 强调刺耳。
常用短语与固定搭配
- depend upon：依赖于。原文用法：the dependence of musical intervals upon simple numerical ratios.
- be said to have done：据说曾经做过。原文用法：Pythagoras is said to have found...
- under the same tension：在相同张力下。原文用法：like strings under the same tension.
- run as follows：内容如下。原文用法：runs as follows.
- arrested by：被……吸引住（注意此处为文学化用法，非“逮捕”）。原文用法：Pythagoras was arrested by the clang...
- in succession：依次；接连地。原文用法：swung in succession by four slaves.
- bring ... into harmony with：使……与……和谐。原文用法：he brought the emitted note for this hammer into harmony with the other three.
常用句式
- Pattern: A remarkable discovery about ... is ...：关于……的惊人发现是……。原文例句：A remarkable discovery about numbers, claimed to have been made by Pythagoras, is the dependence of musical intervals upon simple numerical ratios.
- Pattern: These results, apparently ..., are said to have led ...：这些结果显然是……，据说它们促使……。原文例句：These results, apparently the first recorded facts in mathematical physics, are said to have led the Pythagoreans to initiate the scientific study of musical scales.
长难句解析
Now, curiously enough, there is a grave flaw in this often-repeated story, namely: the tone of a hammer striking a given anvil is independent of the weight of the hammer.
- 主干：there is a grave flaw in this often-repeated story.
- 修饰与从句：
- Now, curiously enough 为评注性状语，引出转折； - namely 后接同位语，具体说明 flaw 的内容； - of a hammer striking a given anvil 为介词短语修饰 the tone，其中 striking a given anvil 为现在分词短语； - of the hammer 修饰 the weight。
- 逻辑关系：前半句指出故事有严重漏洞，后半句用 namely 解释漏洞的具体内容，说明铁砧音调与铁锤重量无关。
语言使用特点
- 用被动语态和“be said to have done”表达传说性质，暗示信息来源不确定；
- 用 “apparently” 等副词缓和断言语气，体现学术写作的谨慎；
- 结尾用反讽语气揭示故事在物理上的荒谬性。
迁移练习
- 用 “A remarkable discovery about ... is ...” 写一句话，描述一个你学过的科学发现。
- 解释为什么铁匠铺传说在物理上是荒谬的。
- 翻译：在相同张力下，琴弦长度为 2 比 1 时产生八度音程。
点击展开参考答案
- （示例）A remarkable discovery about sound is that pitch depends on the frequency of vibration.
- （示例）Because the tone made by a hammer striking a given anvil depends on the anvil and the way it is struck, not on the weight of the hammer.
- for like strings under the same tension, the lengths should be 2 to 1 for the octave.