未登录,请登录后再发表信息
最新评论 (0)
播放视频

音乐与数学:天才贝多芬

Music and math: The genius of Beethoven - Natalya St. Clair

It may sound like a paradox, or some cruel joke,
这听起来也许像谬论 或是残忍的玩笑
but whatever it is, it’s true.
但无论如何 这就是事实
Beethoven, the composer of some of the most celebrated music in history,
贝多芬 这位谱写了许多流传百世作品的作曲家
spent most of his career going deaf.
在他音乐生涯的大部分时间里却双耳失聪
So how was he still able to create such intricate and moving compositions?
那么他是如何创作出如此复杂感人的乐曲的呢?
The answer lies in the patterns hidden beneath the beautiful sounds.
答案就藏在这些美妙声音背后的模式中
Let’s take a look at the famous “Moonlight Sonata,”
我们来看下著名的《月光奏鸣曲》
which opens with a slow, steady stream of notes grouped into triplets:
这首乐曲以一连串缓慢稳定的三连音开始:
One-and-a-two-and-a-three-and-a.
一哒哒 二哒哒 三哒哒
But though they sound deceptively simple,
虽然听起来好像很简单
each triplet contains an elegant melodic structure,
但每组三连音都包含了优雅的旋律性的结构
revealing the fascinating relationship between music and math.
这揭示了音乐与数学之间的奇妙关系
Beethoven once said,
贝多芬曾说
“I always have a picture in my mind when composing and follow its lines.”
“作曲时 我的脑中总会有个图像 然后我依照图像谱写出来”
Similarly, we can picture a standard piano octave consisting of thirteen keys,
类似地 我们也可以想象一个 由13个键组成的标准钢琴八度
each separated by a half step.
每个琴键距是一个半音
A standard major or minor scale uses eight of these keys,
标准的大调或小调音阶使用其中的8个琴键
with five whole step intervals and two half step ones.
8个琴键中5个是全音程 2个是半音程
And the first half of measure 50, for example,
例如第50节的前半段
consists of three notes in D major,
由D大调的三个音符组成
separated by intervals called thirds, that skip over the next note in the scale.
每个音符被三度音程分开 然后在这个音阶中跳过下一个音符
By stacking the scale’s first, third and fifth notes, D, F-sharp and A,
把音阶中的第一 第三及第五个音符 即D F#A 叠起来
we get a harmonic pattern known as a triad.
我们就会听到被称为三和弦的和声
But these aren’t just arbitrary magic numbers.
但这些不是随意的魔术数字
Rather, they represent the mathematical relationship
它们其实代表不同音符音高频率的数学关系
between the pitch frequencies of different notes which form a geometric series.
而其关系形成等比数列
If we begin with the note A3 at 220 hertz,
如果我们以音符A3 频率220赫兹开始
the series can be expressed with this equation,
这个序列可以用这个方程式表达
where “n” corresponds to successive notes on the keyboard.
这里的“n” 对应键盘上的连续音符
The D major triplet from the Moonlight Sonata uses “n” values five, nine, and twelve.
《月光奏鸣曲》的D大调三连音其n值分别为5 9 12
And by plugging these into the function, we can graph the sine wave for each note,
把这些数字放进方程式中 我们能用正弦波图表示每个音符
allowing us to see the patterns that Beethoven could not hear.
此图使我们看到贝多芬听不见的波形图
When all three of the sine waves are graphed,
当三个正弦波都画出来时
they intersect at their starting point of 0,0 and again at 0,0.042.
在坐标原点(0,0)以及(0,0.042)点重合
Within this span, the D goes through two full cycles,
在这段区间 D会贯穿两个周期
F-sharp through two and a half, and A goes through three.
F#跨越两个半 A则跨越三个
This pattern is known as consonance, which sounds naturally pleasant to our ears.
这种模式称为和弦 其声音自然悦耳
But perhaps equally captivating is Beethoven’s use of dissonance.
但贝多芬使用的不和谐音也同样迷人
Take a look at measures 52 through 54,
来看看52至54小节
which feature triplets containing the notes B and C.
主要包含B和C音符的三连音
As their sine graphs show, the waves are largely out of sync,
正如其正弦波图 两者的波在大部分时间都不同步
matching up rarely, if at all.
即使有同步的地方 也很少
And it is by contrasting this dissonance
也就是通过这样的不和谐音
with the consonance of the D major triad in the preceding measures
与前几小节D大调的协和三和弦形成鲜明的对比
that Beethoven adds the unquantifiable elements of emotion and creativity
贝多芬把不可量化的情绪和创意元素
to the certainty of mathematics,
融入数学的必然性中
creating what Hector Berlioz described as
创作出了埃克托·柏辽兹所描述的
“one of those poems that human language does not know how to qualify.”
“人类难以言喻的一首诗”
So although we can investigate the underlying mathematical patterns of musical pieces,
虽然我们能研究音乐作品中暗含的数学规律
it is yet to be discovered why certain sequences of these patterns
却仍未发现这些图形的特定顺序
strike the hearts of listeners in certain ways.
能以某种形式打动听者心灵的原因
And Beethoven’s true genius lay
而贝多芬真正的天赋
not only in his ability to see the patterns without hearing the music,
不仅在于他无需听到音乐就能看到图形的能力
but to feel their effect.
还在于他感受音效的能力
As James Sylvester wrote,
正如数学家詹姆斯·希尔维斯所写:
“May not music be described as the mathematics of the sense,
“难道音乐不能被描述为感官的数学
mathematics as music of the reason?”
数学不能被描述为理性的音乐吗?”
The musician feels mathematics. The mathematician thinks music.
音乐家感受数学 数学家思考音乐
Music, the dream. Mathematics, the working life.
音乐 是梦想 数学 是工作上的生活

发表评论

译制信息
视频概述

这位天才音乐家是怎么使音乐和数学联系起来的?一起来看看吧

听录译者

收集自网络

翻译译者

...琼楼

审核员

审核员 V

视频来源

https://www.youtube.com/watch?v=zAxT0mRGuoY

相关推荐