Pachelbel's Canon in D

[chengjun wang]

用Mathematica演奏卡农 Pachelbel's Canon in D http://t.cn/zWX1YcU，之前，有介绍用matlab演奏卡农的：http://t.cn/zWX1Yc4 

Best regards.                         

                                       

Chengjun Wang

Web Mining Lab
Department of Media and Communication

City University of Hong Kong.

Room 5008, 18 Tat Hong Avenue, Run Run Shaw Creative Media Centre

Kowloon. Hong Kong

Email: wang...@gmail.com; cheng...@student.cityu.edu.hk

Mobile: +852-96442905

[chengjun wang]

音乐是数学的奇迹来源： 于悦的日志

前一阵校内上流行一个matlab演奏《卡农》的帖子，写法蛮帅的，用的还是纯律而非平均律。回想起我初中时候在少科站无聊也用Turbo Pascal编过《亚洲雄风》来着，当时就觉得一串数字转化成音乐是件很神奇的事情。来聊聊音乐和数学哈~

音乐之所以和谐美妙，很大程度上得益于两个数学上的约等式同时成立：

1)  2 ^ (7/12) = 1.4983 ≈ 3/2，误差 0.1% 
2)  2 ^ (4/12) = 1.2599 ≈ 5/4，误差 0.8%

听起来很邪乎吧？详见http://blog.renren.com/share/280633000/13739927797 

Best regards.                         

                                       

Chengjun Wang

Web Mining Lab
Department of Media and Communication

City University of Hong Kong.

Room 5008, 18 Tat Hong Avenue, Run Run Shaw Creative Media Centre

Kowloon. Hong Kong

Email: wang...@gmail.com; cheng...@student.cityu.edu.hk

Mobile: +852-96442905

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[王雄]

有人看懂了这个吗  虽然不懂 但看似很厉害的样子。。。

2012/7/22 chengjun wang <wang...@gmail.com>

[lingfei wu]

我以前用mathematica 写过一个钢琴曲，叫e。附件可以播放。

其实就是把e表达成钢琴曲。网上有人做过pi的，我觉得不好听，做了一个e的，感觉好一点。

mathematica代码很简单，如下

f = Sound@Flatten[Table[(SoundNote[#, 0.2, "Piano"] & /@ ((Mod[#, 10] & /@First[RealDigits[E, 10, 108]]) /. {0 -> None})), {y, 1}], 1]

2012/7/22 chengjun wang <wang...@gmail.com>

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Wu  Lingfei
wlf8...@gmail.com
Dept. of Media & Communication

[王雄]

音乐之所以和谐美妙，很大程度上得益于两个数学上的约等式同时成立：

1)  2 ^ (7/12) = 1.4983 ≈ 3/2，误差 0.1%
2)  2 ^ (4/12) = 1.2599 ≈ 5/4，误差 0.8%

 

这个到底啥意思?

2012/7/22 lingfei wu <wlf8...@gmail.com>

[wang pianpian]

今儿竟然讨论到了音乐，我跳出来说两句吧。

而数学是纯理性的东西，而大部分音乐都是感性的东西，两者之间看似没有太大的联系。但是从巴赫赋格的音乐中，人们似乎看到了某种神奇的数学精确性。在哥德尔，艾舍尔和巴赫（GEB）那本书里面就有利用巴赫的音乐来做对比示例，贯通逻辑和感官的关系来讲解哥德尔的不完备定理。赋格曲（Fugue）的创作就像中国古诗一样是要符合一定的谱曲规律的，比如模仿对位法等。用数学来“描述”或说“创造”音乐就是将那些规则数字化，所谱写的曲子体现了一定的理性逻辑，也许也算是音乐中的冷静理性派吧。

2012/7/22 王雄 <wangxi...@gmail.com>

--

Wang Pianpian

PhD Candidate 

City University of Hong Kong

Media and Communication Department

[chengjun wang]

Coda

With a somewhat ironic smile, Pallas said, "On my next visit to Earth, I will check with you to see if ideas on nonequilibrium statistical mechanics have progressed in the direction you indicated. But for now let us leave this discussion. Would you like to listen to some music?"

"Well . . . there are relations between nonequilibrium and music, but is that the real reason you ask?"

"It is something else. You know how unnatural the tampered scale is−−brutally cut by human musicians into 12 equal half−tones, every interval slightly wrong. Because of your imperfect human hearing, you do not realize it, but the result is truly abominable. And the funny thing is that I have come to enjoy it! Isn't that very perverse?"

"Tempered scale," I said weakly, "not tampered. And Johann Sebastian Bach is neither truly abominable nor very perverse." This time I was really upset.

But Pallas just smiled sweetly. "Ready to listen to some preludes and fugues from the Well−Tempered Clavier?" 

Conversations on Nonequilibrium Physics With an Extraterrestrial Nonequilibrium systems come in many varieties, and a number of not−yet−reconciled mathematical approaches can be applied to them.

David Ruelle

Best regards.                         

                                       

Chengjun Wang

Web Mining Lab
Department of Media and Communication

City University of Hong Kong.

Room 5008, 18 Tat Hong Avenue, Run Run Shaw Creative Media Centre

Kowloon. Hong Kong

Email: wang...@gmail.com; cheng...@student.cityu.edu.hk

Mobile: +852-96442905

[lingfei wu]

和非平衡态物理一样，音乐中和绘画中也存在某种标度对称性，正如这篇文章指出的。

其中的插图2用了三个数据，Holst的“The Planets”， Beethoven的“Fifth Symphony” 和Alice Cooper的 “Billion Dollar Babies”.

插图3用了两个数据，Klee的画Flora on the sand，和Kandinsky的画 Several Circles 。

美就是真，真就是美。

2012/7/22 chengjun wang <wang...@gmail.com>

[wang pianpian]

一些简单的音乐与数学常识.

才知道巴赫的十二平均律指的是什么——十二个音程的几何平均。而和音的和谐与否从数学上来看就是频率比的分母，越小的有理数越好。好了数学家们，你们下次再“创造”音乐的时候可以做出一些感觉好一点的音乐了。

2012/7/22 lingfei wu <wlf8...@gmail.com>

--

Wang Pianpian

PhD Candidate 

City University of Hong Kong

Media and Communication Department

[王雄]

虽不明但觉厉

2012/7/22 wang pianpian <pianpi...@gmail.com>

[chengjun wang]

这里有一篇音乐基础知识的介绍：跟我和一曲阿卡贝拉

>> 悠扬 发表于 2009-10-04 10:49

http://songshuhui.net/archives/20632


悠扬现在也在我们组中。欢迎。



Best regards.

Chengjun Wang


【和专题】跟我和一曲阿卡贝拉Comments>>

悠扬 发表于 2009-10-04 10:49

Web Mining Lab
Department of Media and Communication
City University of Hong Kong.
Room 5008, 18 Tat Hong Avenue, Run Run Shaw Creative Media Centre
Kowloon. Hong Kong
Email: wang...@gmail.com; cheng...@student.cityu.edu.hk
Mobile: +852-96442905





On Mon, Jul 23, 2012 at 2:30 PM, 王雄 <wangxi...@gmail.com> wrote:
>
> 虽不明但觉厉
>
>
> 2012/7/22 wang pianpian <pianpi...@gmail.com>
>>
>> 一些简单的音乐与数学常识.

>> 才知道巴赫的十二平均律指的是什么----十二个音程的几何平均。而和音的和谐与否从数学上来看就是频率比的分母，越小的有理数越好。好了数学家们，你们下次再"创造"音乐的时候可以做出一些感觉好一点的音乐了。

>>
>>
>>
>> 2012/7/22 lingfei wu <wlf8...@gmail.com>
>>>
>>> 和非平衡态物理一样，音乐中和绘画中也存在某种标度对称性，正如这篇文章指出的。
>>>
>>> 其中的插图2用了三个数据，Holst的"The Planets"， Beethoven的"Fifth Symphony" 和Alice Cooper的 "Billion Dollar Babies".
>>>
>>> 插图3用了两个数据，Klee的画Flora on the sand，和Kandinsky的画 Several Circles 。
>>>
>>> 美就是真，真就是美。
>>>
>>>
>>>
>>>
>>>
>>> 2012/7/22 chengjun wang <wang...@gmail.com>
>>>>>
>>>>> Coda
>>>>>
>>>>> With a somewhat ironic smile, Pallas said, "On my next visit to Earth, I will check with you to see if ideas on nonequilibrium statistical mechanics have progressed in the direction you indicated. But for now let us leave this discussion. Would you like to listen to some music?"
>>>>>
>>>>> "Well . . . there are relations between nonequilibrium and music, but is that the real reason you ask?"
>>>>>

>>>>> "It is something else. You know how unnatural the tampered scale is--brutally cut by human musicians into 12 equal half-tones, every interval slightly wrong. Because of your imperfect human hearing, you do not realize it, but the result is truly abominable. And the funny thing is that I have come to enjoy it! Isn't that very perverse?"

>>>>>
>>>>> "Tempered scale," I said weakly, "not tampered. And Johann Sebastian Bach is neither truly abominable nor very perverse." This time I was really upset.
>>>>>

>>>>> But Pallas just smiled sweetly. "Ready to listen to some preludes and fugues from the Well-Tempered Clavier?"
>>>>
>>>>
>>>> Conversations on Nonequilibrium Physics With an Extraterrestrial Nonequilibrium systems come in many varieties, and a number of not-yet-reconciled mathematical approaches can be applied to them.

>>>>
>>>> David Ruelle
>>>>
>>>>
>>>> Best regards.
>>>>
>>>> Chengjun Wang
>>>>
>>>> Web Mining Lab
>>>> Department of Media and Communication
>>>> City University of Hong Kong.
>>>> Room 5008, 18 Tat Hong Avenue, Run Run Shaw Creative Media Centre
>>>> Kowloon. Hong Kong
>>>> Email: wang...@gmail.com; cheng...@student.cityu.edu.hk
>>>> Mobile: +852-96442905
>>>>
>>>>
>>>>
>>>>
>>>>

>>>> On Sun, Jul 22, 2012 at 4:12 PM, 王雄 <wangxi...@gmail.com> wrote:
>>>>>
>>>>> 音乐之所以和谐美妙，很大程度上得益于两个数学上的约等式同时成立：
>>>>>
>>>>> 1) 2 ^ (7/12) = 1.4983 ≈ 3/2，误差 0.1%
>>>>> 2) 2 ^ (4/12) = 1.2599 ≈ 5/4，误差 0.8%
>>>>>
>>>>> 这个到底啥意思?
>>>>>
>>>>> 2012/7/22 lingfei wu <wlf8...@gmail.com>
>>>>>>
>>>>>> 我以前用mathematica 写过一个钢琴曲，叫e。附件可以播放。
>>>>>>
>>>>>> 其实就是把e表达成钢琴曲。网上有人做过pi的，我觉得不好听，做了一个e的，感觉好一点。
>>>>>>
>>>>>> mathematica代码很简单，如下
>>>>>>
>>>>>> f = Sound@Flatten[Table[(SoundNote[#, 0.2, "Piano"] & /@ ((Mod[#, 10] & /@First[RealDigits[E, 10, 108]]) /. {0 -> None})), {y, 1}], 1]
>>>>>>
>>>>>>
>>>>>> 2012/7/22 chengjun wang <wang...@gmail.com>
>>>>>>>
>>>>>>> 用Mathematica演奏卡农 Pachelbel's Canon in D http://t.cn/zWX1YcU，之前，有介绍用matlab演奏卡农的：http://t.cn/zWX1Yc4
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Best regards.
>>>>>>>
>>>>>>> Chengjun Wang
>>>>>>>
>>>>>>> Web Mining Lab
>>>>>>> Department of Media and Communication
>>>>>>> City University of Hong Kong.
>>>>>>> Room 5008, 18 Tat Hong Avenue, Run Run Shaw Creative Media Centre
>>>>>>> Kowloon. Hong Kong
>>>>>>> Email: wang...@gmail.com; cheng...@student.cityu.edu.hk
>>>>>>> Mobile: +852-96442905
>>>>>>>
>>>>>>>
>>>>>>>

[lingfei wu]

《科学美国人》上的原文pdf链接在这里

虽然这个研究并不是作者所做，但即便是译介此类paper，也是善莫大焉。

2012/7/25 chengjun wang <wang...@gmail.com>

[Cui Anyong]

现在很多音乐人都在用编程工具来做音乐~ 比如max/msp

发自我的 iPhone

[Cui Anyong]

To PianPian

李爽也有在搞音乐计算这块~

发自我的 iPhone