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  • Aah, the sound of shaking animal intestines.. I mean, strings which are traditionally


  • made out of cat gut but regardless of what it's made out of when a string

    傳統上是用羊腸線製成的。 但不管是何種材料,當琴弦振動時

  • vibrates it does so with the ends fixed to the instrument. This means that it can only


  • vibrate in certain waves, sin waves. Like a jump rope with one bump or two bumps or

    這意味著它只能用特定方式振動,即正弦波。 像跳繩一樣,它可以有一次、兩次

  • three or four or some combination of these bumps. The more bumps the higher


  • the pitch and the faster the string has to vibrate. In fact, the frequency of a


  • strings vibration is exactly equal to the number of bumps times the strings


  • fundamental frequency that is, the frequency of vibrations for a single bump.


  • And since most melodious instruments use either strings or air vibrating


  • pipes which has the same sinusoidal behavior it won't surprise you to hear


  • that musicians have different names for the different ratios between these pitches. In


  • the traditional Western scale, 1 to 2 bumps is called an octave; 2 to 3 is a perfect fifth;

    在傳統西方音樂中,一次諧波到二次諧波稱為「八度」 二到三次稱為「完全五度」

  • 3 to 4 is a perfect fourth, then a major third, minor third some other things that

    三到四次叫「完全四度」 再來是「大三度」、「小三度」

  • 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

    還有些不在音階裡的東西, 八次到九次稱為「大二度」或「一個全音」。

  • notes together you get the nice sound of perfect harmony. Hence the name for this band of

    如果你把一些音同時彈奏,會得到完美的和諧。 這就是「諧波」名稱的由來。

  • pitches, harmonics. 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. And a bugle


  • playing taps uses only the notes in a single


  • series of harmonics 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.


  • Harmonics can also be used to tune string instruments. For example, on a

    泛音列也可以用來校準弦樂器 比如在小提琴、中提琴或大提琴,

  • violin, viola or cello, the third harmonic on one string should be equal to the


  • second harmonic on the next string up. Bassists and guitarists can compare the fourth

    貝斯和吉他手可以比較一根弦的第四泛音 和上一弦第三泛音,

  • harmonic to the third harmonic on the next string up 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. There's a string for each of the 12 semi tones of


  • the Western scale times seven. If you wanted to tune these strings using


  • harmonics you could for example try using whole steps that is you could


  • compare the ninth harmonic on one key to the eighth harmonic two keys up which works fine for the

    也就是比較某一鍵的第九泛音 和它高兩個鍵的第八泛音

  • first few keys; 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.


  • Except that our harmonic tuning method multiplied the frequency by a factor of


  • nine eighths each time and 9 over 8 to the 6th is not two, its 2.027286529541 etcetera. If you tried

    用9/8乘6並不等於二, 而是2.027286529541......

  • harmonically tuning a piano using major thirds instead, you'd multiply the


  • frequency by five fourths three times or 1.953125, still not two. Using fourths

    那八度下來就會是5/4乘3 等於1.953125......,仍舊不是2

  • you'd get 1.973 not two. Fifths gives 2.027 again. And don't even try

    用完全四度得到1.973......而非2。 完全五度又得到2.027......

  • using half steps; you will be off by almost 10 percent and this is the problem. It's


  • mathematically impossible to tune a piano consistently across all keys using

    數學上絕無可能使用完美的泛音 精確校正每一根弦,

  • perfect beautiful harmonics, so we don't. Most pianos these days use what's called


  • equal tempered tuning where the frequency of each key is the 12th root of two

    現今鋼琴大多使用「十二平均律」 每根弦的頻率都是低半音的12√2倍

  • times the frequency of the key below it. The 12th root of 2 is an irrational number


  • something you never get using simple ratios of harmonic tuning;


  • 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. Perfect octave!


  • However, the octave is the only perfect interval on an equally tuned piano. Fifths

    然而在十二平均律的鋼琴上, 八度卻是唯一精確的比例。

  • are slightly; flat fourths are slightly sharp; major thirds are sharp, minor thirds are

    完全五度比正常稍窄,完全四度略寬 大三度略寬,小三度略窄等等。

  • flat and so on. You can hear a kind of "wawawawawa" effect


  • in this equal tempered chord; which goes away using harmonic tune. But, if you tuned an instrument


  • using the 12th root of 2 as most pianos, digital tuners and computer instruments are, you can play


  • any song, in any key, and they will all be equally and just slightly out of tune.


  • This Minute Physics video is brought to you in part by, the leading


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  • non-fiction and periodicals. If you go to physics you can try audible

    前往 physics

  • out by downloading a free audiobook of your choice. I just read


  • 'The Name of the Wind' by Patrick Rothfuss. It's a fantasy novel with a very music

    我剛才看了Patrick Rothfuss寫的The Name of the Wind。

  • and scientifically oriented protagonist and I thoroughly enjoyed it. You can


  • download this audiobook or a free audiobook of your choice at


  • and I'd like to thank audible for helping me continue to make these


  • videos

Aah, the sound of shaking animal intestines.. I mean, strings which are traditionally



影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

B1 中級 中文 鋼琴 頻率 使用 樂器 讀物 調整

為什麼不可能給鋼琴調音? (Why It's Impossible to Tune a Piano)

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    簡簡哲 發佈於 2021 年 01 月 14 日