Placeholder Image

字幕列表 影片播放

已審核 字幕已審核
  • So what makes a piece of music beautiful?

    是什麼讓音樂如此美妙呢?

  • Well, most musicologists would argue

    大多數音樂理論家都會說

  • that repetition is a key aspect of beauty.

    重復是美的關鍵

  • The idea that we take a melody, a motif, a musical idea,

    我們寫一段旋律、一個主題、一個音樂想法

  • we repeat it, we set up the expectation for repetition,

    我們重復它 讓人有重複的期待

  • and then we either realize it or we break the repetition.

    接著要麼我們或者滿足這種期待 或者打破這種重復

  • And that's a key component of beauty.

    這就是組成美的關鍵部分

  • So if repetition and patterns are key to beauty,

    所以如果重復和模式是美的關鍵

  • then what would the absence of patterns sound like

    那麼要是我們把模式 都拿去會怎麼樣呢?

  • if we wrote a piece of music

    如果我們寫一段樂曲

  • that had no repetition whatsoever in it?

    任何重復都沒有?

  • That's actually an interesting mathematical question.

    這實際上是個很有意思的數學問題

  • Is it possible to write a piece of music that has no repetition whatsoever?

    寫一段完全沒有重復的樂曲 有這種可能嗎?

  • It's not random. Random is easy.

    這並不是隨意來寫 隨意寫很簡單

  • Repetition-free, it turns out, is extremely difficult

    事實證明 做到無重復是極其困難的

  • and the only reason that we can actually do it

    而我們能做到無重復的唯一原因

  • is because of a man who was hunting for submarines.

    要歸咎於一個搜尋潛水艇的人

  • It turns out a guy who was trying to develop

    原來一個努力開發

  • the world's perfect sonar ping

    世界上最完美的聲納音的人

  • solved the problem of writing pattern-free music.

    解決了譜寫無重復樂曲的難題

  • And that's what the topic of the talk is today.

    這就是我們今天要談論的話題

  • So, recall that in sonar,

    那麽 回想一下聲納

  • you have a ship that sends out some sound in the water,

    你有一艘船在水裡發出聲音

  • and it listens for it -- an echo.

    並且聆聽這個聲音──一個回聲

  • The sound goes down, it echoes back, it goes down, echoes back.

    發出聲音 回聲傳回來 再發出聲音 回聲再傳回來

  • The time it takes the sound to come back tells you how far away it is.

    你通過聲音回傳的時間來判斷距離

  • If it comes at a higher pitch, it's because the thing is moving toward you.

    如果傳回來的音調變高 那說明前方的物體正向你靠近

  • If it comes back at a lower pitch, it's because it's moving away from you.

    如果音調變低 是因為那物體離你越來越遠

  • So how would you design a perfect sonar ping?

    所以你會怎樣設計出完美的聲納音呢?

  • Well, in the 1960s, a guy by the name of John Costas

    在20世紀60年代 一個名叫約翰·科斯塔斯的人

  • was working on the Navy's extremely expensive sonar system.

    當時正在研發海軍極其昂貴的聲納系統

  • It wasn't working,

    沒有成功

  • and it was because the ping they were using was inappropriate.

    原因是他們使用的聲納音不合適

  • It was a ping much like the following here,

    聽起來就像下面這聲音

  • which you can think of this as the notes

    你可以把這看作是音符

  • and this is time.

    把這看作時間

  • (Music)

    (音樂)

  • So that was the sonar ping they were using: a down chirp.

    這就是他們當時使用的聲納音:一串降調

  • It turns out that's a really bad ping.

    結果是這段聲音很糟糕

  • Why? Because it looks like shifts of itself.

    為什麼?因為它聽起來就像自身的變換

  • The relationship between the first two notes is the same

    頭兩個音符的關系跟

  • as the second two and so forth.

    後兩個音符的關系一樣 其它的也是

  • So he designed a different kind of sonar ping:

    所以他設計了另外一種不同的聲納音

  • one that looks random.

    這種聲音看起來是隨意的

  • These look like a random pattern of dots, but they're not.

    這些看起來像隨意編寫的音符 但其實它們並非如此

  • If you look very carefully, you may notice

    如果你們仔細看 就會發現

  • that in fact the relationship between each pair of dots is distinct.

    事實上 每對音符之間的關系都是不同的

  • Nothing is ever repeated.

    沒有任何重復

  • The first two notes and every other pair of notes

    頭兩個音符及其它每對的音符之間

  • have a different relationship.

    關系是不同的

  • So the fact that we know about these patterns is unusual.

    所以我們了解這些格式的事實是很不平常的

  • John Costas is the inventor of these patterns.

    約翰·科斯塔斯發名了這些格式

  • This is a picture from 2006, shortly before his death.

    這是2006年的照片 在他去世不久之前

  • He was the sonar engineer working for the Navy.

    他是海軍的聲納工程師

  • He was thinking about these patterns

    他研究這些格式

  • and he was, by hand, able to come up with them to size 12 --

    而且他能親手將這些格式制作成12號的 ──

  • 12 by 12.

    12乘12大小

  • He couldn't go any further and he thought

    他再也做不了比那更大的了 所以他想

  • maybe they don't exist in any size bigger than 12.

    它們可能不會以 大於12乘12的大小出現

  • So he wrote a letter to the mathematician in the middle,

    所以他給中間的那位數學家寫了一封信

  • who was a young mathematician in California at the time,

    那是個年輕的數學家 當時住在加裡福尼亞

  • Solomon Golomb.

    索羅門·哥隆

  • It turns out that Solomon Golomb was one of the

    索羅門·哥隆是我們時代

  • most gifted discrete mathematicians of our time.

    最具天賦的離散數學家

  • John asked Solomon if he could tell him the right reference

    約翰問索羅門能否告訴他

  • to where these patterns were.

    這些格式在哪的正確參照

  • There was no reference.

    並沒有什麼參照

  • Nobody had ever thought about

    以前從沒有人曾想到過會有

  • a repetition, a pattern-free structure before.

    一個無重復、無格式的結構

  • Solomon Golomb spent the summer thinking about the problem.

    索羅門·哥隆花了一夏天來思考這個問題

  • And he relied on the mathematics of this gentleman here,

    他還依靠了這位數學家的幫助

  • Evariste Galois.

    埃瓦裡斯特· 伽羅瓦

  • Now, Galois is a very famous mathematician.

    現在 伽羅瓦是位家喻戶曉的數學家

  • He's famous because he invented a whole branch of mathematics,

    他的出名源於他發明了數學中一整個分支

  • which bears his name, called Galois Field Theory.

    並以他的名字命名為伽羅瓦理論

  • It's the mathematics of prime numbers.

    這就是素數數學

  • He's also famous because of the way that he died.

    他出名還因為他的死因

  • So the story is that he stood up for the honor of a young woman.

    事情是這樣的 為了一個年輕姑娘的名譽

  • He was challenged to a duel and he accepted.

    他被要求決斗挑戰 他接受了

  • And shortly before the duel occurred,

    決斗開始前不久

  • he wrote down all of his mathematical ideas,

    他把他所有數學的理念寫了下來

  • sent letters to all of his friends,

    寄給了他所有的朋友

  • saying please, please, please --

    信上說 請一定,一定,一定──

  • this is 200 years ago --

    ──這是200年以前──

  • please, please, please

    請一定,一定,一定

  • see that these things get published eventually.

    要把這些東西出版

  • He then fought the duel, was shot, and died at age 20.

    之後他進行了決斗 中槍身亡 終年20歲

  • The mathematics that runs your cell phones, the Internet,

    你手機的運轉、實現我們交流的網絡

  • that allows us to communicate, DVDs,

    DVD,運用於這些的那些數學理念

  • all comes from the mind of Evariste Galois,

    都來源於埃瓦裡斯特· 伽羅瓦的思想

  • a mathematician who died 20 years young.

    一個 20 歲便去世的年輕數學家

  • When you talk about the legacy that you leave,

    當你們談論你們 死後留下的遺產的時候

  • of course he couldn't have even anticipated the way

    當然他不會想到人們會這樣

  • that his mathematics would be used.

    使用他的數學理念

  • Thankfully, his mathematics was eventually published.

    謝天謝地 他的理論最終被出版了

  • Solomon Golomb realized that that mathematics was

    索羅門·哥隆意識到那些數學理念

  • exactly the mathematics needed to solve the problem

    正是解決這個問題所需要的理念

  • of creating a pattern-free structure.

    來創造一段無格式的節構

  • So he sent a letter back to John saying it turns out you can

    所以他回信給約翰說 其實你可以自己

  • generate these patterns using prime number theory.

    運用素數理論生成那些格式

  • And John went about and solved the sonar problem for the Navy.

    之後約翰著手解決了海軍的聲納問題

  • So what do these patterns look like again?

    那麼這些新格式又長什麼樣呢?

  • Here's a pattern here.

    這裡有一個格式

  • This is an 88 by 88 sized Costas array.

    這就是88乘88大小的科斯塔斯陣列

  • It's generated in a very simple way.

    它生成方式很簡單

  • Elementary school mathematics is sufficient to solve this problem.

    小學數學就足以解決這個問題

  • It's generated by repeatedly multiplying by the number 3.

    反復乘以3便生成了這組陣列

  • 1, 3, 9, 27, 81, 243 ...

    1,3,9,27,81,243……

  • When I get to a bigger [number] that's larger than 89

    當我得到一個大於 89 的數字時

  • which happens to be prime,

    而且恰好又是素數

  • I keep taking 89s away until I get back below.

    我減掉 89 直到數字比 89 小

  • And this will eventually fill the entire grid, 88 by 88.

    這最終會填滿整個 88 乘 88 的格子

  • And there happen to be 88 notes on the piano.

    恰好鋼琴有 88 個鍵

  • So today, we are going to have the world premiere

    所以今天 我們即將看到世界首支

  • of the world's first pattern-free piano sonata.

    無格式鋼琴奏鳴曲的全球首演

  • So, back to the question of music.

    好了,我們回到音樂的問題上

  • What makes music beautiful?

    是什麼讓音樂如此美妙?

  • Let's think about one of the most beautiful pieces ever written,

    我們來想一段世界上最美的樂曲

  • Beethoven's Fifth Symphony.

    貝多芬第五交響樂

  • And the famous "da na na na" motif.

    和那著名的“噠吶吶吶”的主旨

  • That motif occurs hundreds of times in the symphony --

    這支交響樂中這個主旨出現了幾百次──

  • hundreds of times in the first movement alone,

    僅在第一樂章就出現了幾百次

  • and also in all the other movements as well.

    在其它樂章裡也是如此

  • So this repetition, the setting up of this repetition

    這種重復 這樣一種重復的設定

  • is so important for beauty.

    對美來說太重要了

  • If we think about random music as being just random notes here,

    如果我們說這邊是隨機音樂 就是隨意的一些音符

  • and over here is somehow Beethoven's Fifth in some kind of pattern,

    這邊貝多芬第五交響樂 有一定的格式

  • if we wrote completely pattern-free music,

    如果我們寫下完全無格式的音樂

  • it would be way out on the tail.

    那它就會在這邊的最尾端

  • In fact, the end of the tail of music

    事實上 在音樂的最尾端

  • would be these pattern-free structures.

    就是這些無格式的結構

  • This music that we saw before, those stars on the grid,

    我們之前看到的那段曲子 那點格子裡的點

  • is far, far, far from random.

    遠遠不是隨意為之

  • It's perfectly pattern-free.

    它是完美的無格式之作

  • It turns out that musicologists --

    原來,一位音樂理倫家──

  • a famous composer by the name of Arnold Schoenberg --

    一位著名的曲作者 名叫阿諾德·勛伯格──

  • thought of this in the 1930s, '40s and '50s.

    在20世紀30年代、40年代、 50年代就想到了這點

  • His goal as a composer was to write music that would

    他作為一名曲作者的目標 便是要把寫出的曲子

  • free music from total structure.

    完完全全從結構中解放出來

  • He called it the emancipation of the dissonance.

    他把這稱作不諧和音的解放

  • He created these structures called tone rows.

    他創造的這些結構被叫作音列

  • This is a tone row there.

    大屏幕上顯示的就是一組音列

  • It sounds a lot like a Costas array.

    聽起來很像科斯塔斯陣列

  • Unfortunately, he died 10 years before Costas solved the problem of

    遺憾的是 在科斯塔斯解決了

  • how you can mathematically create these structures.

    如何用數學方法創造 這些結構之前十年他就去世了

  • Today, we're going to hear the world premiere of the perfect ping.

    今天 我們將聽到完美聲吶音的世界首演

  • This is an 88 by 88 sized Costas array,

    這是88乘88的科斯塔斯陣列

  • mapped to notes on the piano,

    把它繪制成鋼琴的88個音符

  • played using a structure called a Golomb ruler for the rhythm,

    用一種名為哥隆韻律尺的結構來彈奏

  • which means the starting time of each pair of notes

    也就是說每對音符開始的時間

  • is distinct as well.

    也都是不同的

  • This is mathematically almost impossible.

    這在數學上是近乎不可能的

  • Actually, computationally, it would be impossible to create.

    其實 在運算上 這是不可能實現的

  • Because of the mathematics that was developed 200 years ago --

    因為數學200年的發展──

  • through another mathematician recently and an engineer --

    並且最近通過另外 一位數學家和一名工程師

  • we are able to actually compose this, or construct this,

    我們現在能夠使其完成 或者說 將其構建成形

  • using multiplication by the number 3.

    運用持續乘以 3 的運算

  • The point when you hear this music

    我想說的是 當你們聽到這段音樂

  • is not that it's supposed to be beautiful.

    它不會是美妙動聽的

  • This is supposed to be the world's ugliest piece of music.

    它應該是世界上最難聽的一段曲子

  • In fact, it's music that only a mathematician could write.

    事實上 只有數學家才能寫出這種曲子

  • When you're listening to this piece of music, I implore you:

    當你們聽這段曲子的時候 我懇求各位

  • Try and find some repetition.

    嘗試著找出一些重復

  • Try and find something that you enjoy,

    嘗試著找到讓你們感學愉悅的地方

  • and then revel in the fact that you won't find it.

    之後 你就可以陶醉在 你們根本找不到這個事實中了

  • Okay?

    好嗎?

  • So without further ado, Michael Linville,

    閑話少說 有請邁克爾·裡恩維爾

  • the director of chamber music at the New World Symphony,

    新世界交響樂團室內音樂的指揮

  • will perform the world premiere of the perfect ping.

    將為各位帶來完美音的世界首演

  • (Music)

    (音樂)

  • Thank you.

    謝謝

  • (Applause)

    (掌聲)

So what makes a piece of music beautiful?

是什麼讓音樂如此美妙呢?

字幕與單字
已審核 字幕已審核

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 美國腔 格式 音符 數學 數學家 隨意 曲子

【TEDx】如何創造出一段難聽的音樂?解析音樂的秘密 The world's ugliest music: Scott Rickard at TEDxMIA

  • 14867 437
    阿多賓 發佈於 2014 年 06 月 03 日
影片單字