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Aah, the sound of shaking animal intestines..
啊，动物肠子震动的声音…
I mean, strings which are traditionally made out of cat gut
我的意思是，弦传统上是用肠线做的，
but regardless of what it's made out of when a string vibrates it does so with the ends fixed to the instrument.
但不管它是由什么材料制成的，当一根弦振动时，它的末端都固定在乐器上。
This means that it can only vibrate in certain waves, sin waves.
这意味着它只能以特定的波中振动，也就是正弦波。
Like a jump rope with one bump or two bumps or three or four or some combination of these bumps.
就像跳绳有一个凸起，两个凸起，三个或四个凸起，或者这些凸起的组合。
The more bumps the higher the pitch and the faster the string has to vibrate.
凸起越多，音高越高，琴弦振动的速度也越快。
In fact, the frequency of a strings vibration is exactly equal to the number of bumps times the strings fundamental frequency that is,
事实上，弦振动的频率等于凸起的次数乘以弦的基本频率，
the frequency of vibrations for a single bump.
一次凸起的振动频率。
And since most melodious instruments use either strings or air vibrating pipes which has the same sinusoidal behavior
因为大多数旋律乐器要么使用弦，要么使用空气振动管，它们具有相同的正弦行为，
it won't surprise you to hear that musicians have different names for the different ratios between these pitches.
当你听到音乐家们对这些音高的不同比例有不同的叫法时，你不会感到惊讶。
In the traditional Western scale, 1 to 2 bumps is called an octave; 2 to 3 is a perfect fifth; 3 to 4 is a perfect fourth,
在传统的西方音阶中，1到2个音阶被称为八度音阶；2到3是完美的五度音阶；3到4是完美的四度音阶，
then a major third, minor third some other things that aren't on the scale and from 8 to 9 bumps is a major second or whole step.
然后是大三度，小三度还有其他一些不在这个范围里的东西。从8到9个突起是大二度或全音阶。
If you play a few of these notes together you get the nice sound of perfect harmony.
如果你一起演奏几个这样的音符，你会得到完美和谐的美妙声音。
Hence the name for this band of pitches, harmonics.
因此这支音高乐队的名字，泛音。
In fact a sound that matches one of the harmonics of a string can cause that string to start vibrating on its own with their resonant ringing sound.
事实上，如果一根弦发出的声音与其中一个泛音相匹配，就会导致弦自己开始振动，发出共振的振铃声。
And a bugle playing taps uses only the notes in a single series of harmonics
而军号只使用单一的一系列泛音中的音符，
which is part of why the melody of taps rings so purely and why you can play taps with the harmonics of a single guitar string.
这就是为什么军号的旋律如此纯粹的部分原因，也是为什么你可以用一根吉他弦的泛音来演奏的部分原因。
Harmonics can also be used to tune string instruments.
泛音也可以用来给弦乐器调音。
For example, on a violin, viola or cello, the third harmonic on one string should be equal to the second harmonic on the next string up.
例如，在小提琴、中提琴或大提琴上，一根弦上的三次泛音应该等于下一根弦上的二次泛音。
Bassists and guitarists can compare the fourth harmonic to the third harmonic on the next string up
贝斯和吉他手可以比较四次泛音和下一弦的三次泛音，
but then we come to the piano or historically the harpsichord or clavichord but either way the problem is this: it has too many strings.
然后我们谈到钢琴，或者历史上的拨弦古钢琴或击弦古钢琴，但无论哪种方式，问题都是：它有太多的弦。
There's a string for each of the 12 semi tones of the Western scale times seven.
西方音阶的每一个12个半音调都有七根弦。
If you wanted to tune these strings using harmonics you could for example try using whole steps
如果你想用泛音来调整这些弦，你可以尝试使用整个步骤，
that is you could compare the ninth harmonic on one key to the eighth harmonic two keys up which works fine for the first few keys;
你可以比较一个键上的九次泛音和两个键上的八次泛音，这对前几个键来说是可以的，
but if you do it six times, you'll get to what's supposed to be the original note an octave up which should have twice the frequency.
但如果你这样做六次，你会得到原本应该是一个高八度的音，频率应该是原来的两倍。
Except that our harmonic tuning method multiplied the frequency by a factor of nine eighths each time
但是我们的泛音调谐方法每次都会将频率乘以八分之九，
and 9 over 8 to the 6th is not two, its 2.027286529541 etcetera.
而八分之九的6次方不是2，而是2.027286529541等等。
If you tried harmonically tuning a piano using major thirds instead, you'd multiply the frequency by five fourths three times or 1.953125, still not two.
如果你试着用三大调来给钢琴调音，你会把频率乘以四分之五3次，或者是1.953125，但仍然不是2次。
Using fourths you'd get 1.973 not two. Fifths gives 2.027 again.
用四调，结果会是1.973，而不是2。用五调还是2.027。
And don't even try using half steps; you will be off by almost 10 percent and this is the problem.
不要尝试用半音；你会差10%，这就是问题所在。
It's mathematically impossible to tune a piano consistently across all keys using perfect beautiful harmonics, so we don't.
从数学上讲，我们不可能用完美优美的泛音让一架钢琴在所有的琴键上一致地调音，所以我们没有这样做。
Most pianos these days use what's called equal tempered tuning
现在大多数钢琴都使用所谓的平均律音阶调音，
where the frequency of each key is the 12th root of two times the frequency of the key below it.
其中每个键的频率是它下面键频率的2的12次方根。
The 12th root of 2 is an irrational number something you never get using simple ratios of harmonic tuning;
2的12次方根是一个无理数，你永远不会用简单的比率来得到它；
but its benefit is that once you go up 12 keys you end up with exactly the 12th root of 2 to the 12th or, twice the frequency.
但它的好处是一旦你上升12个键你最终得到2的12次方的12次方根，或者2倍的频率。
Perfect octave! However, the octave is the only perfect interval on an equally tuned piano.
完美的八度！然而，在一个同等调音的钢琴，八度是唯一完美的音程。
Fifths are slightly flat; fourths are slightly sharp; major thirds are sharp, minor thirds are flat and so on.
五度略平；四度稍尖锐；大三度音是尖的，小三度音是平的，等等。
You can hear a kind of "wawawawawa"; effect in this equal tempered chord; which goes away using harmonic tune.
你可以听到一种“wawawawawa”的声音；在这和谐的和弦中产生效果；用和声就消失了。
But, if you tuned an instrument using the 12th root of 2 as most pianos, digital tuners and computer instruments are,
但是，如果像调大多数钢琴一样，你用2的12次方根，数字调音器和电脑工具给乐器调音，
you can play any song, in any key, and they will all be equally and just slightly out of tune.
你就可以用任何音调演奏任何歌曲，它们都是一样的，只是稍微走调。
