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钢琴为什么不能调音? – 译学馆
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钢琴为什么不能调音?

Why It's Impossible to Tune a Piano

啊哈 动物肠子震动的声音 我的意思是 传统的琴弦
Aah, the sound of shaking animal intestines.. I mean, strings which are traditionally
是由猫的肠子做成的 但是不管琴弦是由什么制成的 一根琴弦是连接在琴上震动的
made out of cat gut but regardless of what it’s made out of when a string
这意味着它只能
vibrates it does so with the ends fixed to the instrument. This means that it can only
以一定的波长震动 。正弦波,像一个跳动的绳索,有一个或两个波峰,或者是
vibrate in certain waves, sin waves. Like a jump rope with one bump or two bumps or
三个,四个或者是很多波峰的组合。波峰越多
three or four or some combination of these bumps. The more bumps the higher
琴弦音调越高和振动越快。事实上,琴弦振动
the pitch and the faster the string has to vibrate. In fact, the frequency of a
频率等价于波动的次数,琴弦的基本
strings vibration is exactly equal to the number of bumps times the strings
频率就是在一个波动范围内的振动次数。
fundamental frequency that is, the frequency of vibrations for a single bump.
因为大多数乐器不管是采用琴弦振动,还是空气振动,
And since most melodious instruments use either strings or air vibrating
管线都有一个相同的正弦曲线,所以一点也不奇怪你会听到
pipes which has the same sinusoidal behavior it won’t surprise you to hear
音乐家为不同的管线的比率命名不同!在
that musicians have different names for the different ratios between these pitches. In
传统的西方标准下,1到2之间的波动称为一个八度音程,2到3之间为完整的五度音程;
the traditional Western scale, 1 to 2 bumps is called an octave; 2 to 3 is a perfect fifth;
3到4之间为完整的四度音程音符,然后是大小三度音程以及其他
3 to 4 is a perfect fourth, then a major third, minor third some other things that
没有度量的东西,8到9之间的波动是大二音度或者是全音阶。如果你
aren’t on the scale and from 8 to 9 bumps is a major second or whole step. If you play a few of these
注意到了这些,就会演奏的完美和谐的声音。所以这个
notes together you get the nice sound of perfect harmony. Hence the name for this band of
音高被成为和声。事实上一个与和声相匹配的声音
pitches, harmonics. In fact a sound that matches one of the harmonics of a string can cause
可以使琴弦振动产生共鸣。一个喇叭
that string to start vibrating on its own with their resonant tuning sound. And a bugle
吹号角时只能使用单一
playing taps uses only the notes in a single
系列的和声,这就是为什么号角的旋律
series of harmonics which is part of why the melody of taps rings
如此纯粹的部分原因,也是你能够用单一的吉他琴弦演奏和声的原因。
so purely and why you can play taps with the harmonics of a single guitar string.
和声也可以用来优化弦乐器。例如,
Harmonics can also be used to tune string instruments. For example, on a
在大,中,小提琴上,第三和声在一个弦上和
violin, viola or cello, the third harmonic on one string should be equal to the
下一个弦的第二和声相同。贝斯手和吉他手可以调节
second harmonic on the next string up. Bassists and guitarists can compare the fourth
第四谐音同第三谐音相同,但是我们再谈谈钢琴
harmonic to the third harmonic on the next string up but then we come to the piano or
或者历史上的大键琴,古钢琴它们都有一个共同问题是
historically the harpsichord or clavichord but either way the problem is
有太多的琴键。一个琴弦对应每十二个半音符,在
this: it has too many strings. There’s a string for each of the 12 semi tones of
西方中的标准是:7次。如果你想用这些琴键作曲
the Western scale: times seven. If you wanted to tune these strings using
用和声你可以试着用整个调子,也就是说你可以
harmonics you could for example try using whole steps that is you could
用一个键表示第九和声也可以用两个键的第八和声,那种方法好呢取决于
compare the ninth harmonic on one key to the eighth harmonic two keys up which works fine for the
最初的几个键;但是如果你重复
first few keys; but if you do it
六次,你将会得到最初应该得到的一个八度,
six times, you’ll get to what’s supposed to be the original note an octave up
这应该是两倍的频率。
which should have twice the frequency.
除了我们的谐波变音乘以频率的一个因素是
Except that our harmonic tuning method multiplied the frequency by a factor of
每次9/8和9/8到9/6之间不是2而是2.027286529541等等。如果你尝试过
nine eighths each time and 9 over 8 to the 6th is not two, its 2.027286529541 etcetera. If you tried
用钢琴的大三音阶谐音化,你需要增加
harmonically tuning a piano using major thirds instead, you’d multiply the
频率为5/4三次或者是1.953125,但也不是2.
frequency by five fourths three times or 1.953125, still not two. Using fourths
使用四次会得到1.973不是2.五次的话是2.027。而且不要考虑
you’d get 1.973 not two. Fifths gives 2.027 again. And don’t even try
使用半拍。你将失去百分之十,这就是问题的所在。
using half steps; you will be off by almost 10 percent and this is the problem. It’s
从数学的角度来讲,给钢琴调音不可能始终用
mathematically impossible to tune a piano consistently across all keys using
完美的谐波,所以我们也不这样做。大多数钢琴钢琴现在使用的方式叫做
perfect beautiful harmonics, so we don’t. Most pianos these days use what’s called
平衡调优,每个键的频率是2的12次根
equal tempered tuning where the frequency of each key is the 12th root of two
琴键的频率小于它。2的12次根是无理数。
times the frequency of the key below it. The 12th root of 2 is an irrational number
你永远也不可能得到一个简单的频率调优。
something you never get using simple ratios of harmonic tuning;
但是好处就是一旦你增加到12键
but its benefit is that once you go up 12 keys you end up
以2的12次根的12次方结束或者是频率的两倍,就是一个完美的八度音阶!
with exactly the 12th root of 2 to the 12th or, twice the frequency. Perfect octave!
然而,八阶音度是唯一一个完美的间隔对于一个平衡调优过的钢琴。五度音阶
However, the octave is the only perfect interval on an equally tuned piano. Fifths
略轻;平四度略尖锐;大三音阶太尖锐,小三音阶
are slightly; flat fourths are slightly sharp; major thirds are sharp, minor thirds are
太平缓等等。你可以听到类似于wawawa的声音,
flat and so on. You can hear a kind of "wawawawawa" effect
这就是平衡调优的效果;使用和弦这种情况就会消失。但是,如果你调乐器时
in this equal tempered chord; which goes away using harmonic tune. But, if you tuned an instrument
使用的是2的12次根作为大多数钢琴,数字调音器和电脑工具,你可以弹奏任何
using the 12th root of 2 as most pianos, digital tuners and computer instruments are, you can play
歌曲,用任意键,那么它们都是一样的只是有些走调。
any song, in any key, and they will all be equally and just slightly out of tune.
这一刻物理视频来自于audible网站,
This Minute Physics video is brought to you in part by audible.com, the leading
音响书籍的领先提供者,包含了所有种类的文献,包括小说
provider of audio books across all types of literature including fiction
非小说和期刊。如果你进入audible网站或者物理一分钟,你可以在这儿
non-fiction and periodicals. If you go to audible.com/minute physics you can try audible
根据自己的选择下载免费的有声读物。
out by downloading a free audiobook of your choice. I just read
我只是看过Patrick Rothfuss的“风的名字”。这是个奇幻小说,
‘The Name of the Wind’ by Patrick Rothfuss. It’s a fantasy novel with a very music
有个很爱音乐和科学的主角,我特别喜欢。
and scientifically oriented protagonist and I thoroughly enjoyed it. You can
你可以下载这个有声书籍,或者由你自己选择免费的有声书籍在audible网站或者
download this audiobook or a free audiobook of your choice at audible.com/minutephysics
物理一分钟上,我想感谢audible网站帮助我继续
and I’d like to thank audible for helping me continue to make these
制作这些视频。
videos

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