打开 Do Not Disturb

过去半年多以来,手机上收到的诈骗电话多到了无以复加的地步。让我只能感慨世风日下,人心不古。无奈之下,我只有抓起电话研究一下如何过滤这些电话。最后的结论是Android 有一个选项是 “Do Not Disturb”,打开以后就只有你的通讯录上的人给你打电话才能响铃,其他的电话就全部过滤掉了。看来这是目前最为有效的方法了。

The Art of Piano Fingering: Traditional, Advanced, and Innovative is very useful book

During the Covid 19, I have to give up my ping pong play since it is impossible to find partners any more.  It did not take me long to decide to pick up piano as the next activity, since I have a piano right at home. After some basic scales practice and childish songs, I decided to start to try some more adult-style songs since it is really hard to keep motivated if I keep playing those naive songs. Anyway, first I picked a well-known song The Moon Represents My Heart, and it took me a few weeks to be able to play it by heart without making any mistakes (but not always be able to do so), then I picked a new song The main theme from XuanYuan Sword:The Scar of the Sky, although this one looks only a little bit harder than the previous one, but it proves beyond me: I practiced for a few weeks, but only finished the  one third, and never be able to play even this one third part without any mistakes: some part are just too hard to play, let along the fact many part are played in a quite hasty way, and music produced by me also sounds poor.

Only at this occasion, it occurred to me that I need some help instead of just keep trying by myself, not just some music theory, but some more practical guide about playing piano. Very fortunately, I found the book The Art of Piano Fingering: Traditional, Advanced, and Innovative, which focuses on fingers arrangement in piano play. It has a lot of simple but very effective advice for how to arrange fingers for various music pieces, from simple scales, triads, to arpeggios which spans more than 1 octave. By applying these advice to my piano, I can play the  The Moon Represents My Heart with more confidence and easier hand moves, and got some new ideas about how to play The main theme from XuanYuan Sword:The Scar of the Sky. Hopefully in the next a few weeks, I can really master this song and I am looking forward to that day. 🙂

Text from Yeti:

BTW I am thinking about getting a digital piano cuz I seem to be driving Yeti crazy soooooo yea abut dat anyways i should rlly start to apply the pedal more cus life would just be so much easier ok thats it yeti out baiiiii :))) :PP




频率是一个连续的数值,这对应着无穷多个音,但是人们在创作音乐作品的时候并不会全部使用,那样的话只会产生噪音。人类的听觉有一个奇妙的特性:当同时听到两个频率的单音的时候,人们会根据这两个频率之间的比例来决定听到的声音是否和谐。如果两个音的频率完全一样,或者是简单的倍数关系,那么人们就会认为这两个声音完全和谐。除开1:1或者 2:1这样最简单的关系,还有一些频率比例也会让人们认为是非常和谐的,其中最著名的就是 2:3 (音乐上把这样两个音的关系称为纯五度,不过这里就不展开讲了)。下面是引自 Plomp & Levelt (1965) 的一张关于和谐程度与频率关系的图。

图中可以看到,几个最为和谐的比例是 1:2,2:3,3:4。如果我们要找到一组频率作为单音,然后穷举它们中所有可能的一对单音,大部分都能够形成一个比较和谐的音响效果,而这一组单音又不要太多的话,那么12是一个非常合适的选择:太少的话形成的音乐太单调,太多的话人的记忆力有限,很不方便使用。这也是十二平均律中的12这个关键数字的来源。

有了12这个数字以后,下面的问题就是一个简单的等比数列求解了。假定我们选定一个基准频率 f,和它完全和谐的倍频2f,然后我们把这个频率段分为12等分,一共有13个数,分别是:

(1)   \begin{equation*} f, x_1, x_2, x_3, ..., x_{11}, 2f \end{equation*}


(2)   \begin{equation*} \begin{split} &\dfrac{x_1}{f} = r \\ &\dfrac{x_2}{x_1} = r \\ &\dfrac{x_3}{x_2} = r \\ & ... \\ & ... \\ &\dfrac{x_{11}}{x_{10}} = r \\ &\dfrac{2f}{x_{11}} = r \end{split} \end{equation*}

这里一共有 r, x_1, x_2, ..., x_{11} 12个变量和12个方程,把上面的各项方程乘在一起就可以得到:

(3)   \begin{equation*} \begin{split} & r^{12} = 2 \\ & r = 2 ^ \dfrac{1}{12} \end{split} \end{equation*}


(4)   \begin{equation*} \begin{split} &x_1 = f \times 2 ^ {\dfrac{1}{12}} \\ &x_2 = f \times 2 ^ {\dfrac{2}{12}} \\ &x_3= f \times 2 ^ {\dfrac{3}{12}} \\ & ... \\ & ... \\ &x_{11} = f \times 2 ^ {\dfrac{11}{12}} \end{split} \end{equation*}

通常人们选定 A 的频率为 440Hz,这样就可以推算出所有其他音的频率了。


(5)   \begin{equation*} 2^{\dfrac{7}{12}} = 1.49830707688... \end{equation*}


英文音乐术语中英对照(Music Terms in English and Chinese)

  • harmonic intervals (音程): two notes played together.
  • chords(和弦): three or more notes played together.
  • scale(音阶): a set of musical notes ordered by fundamental frequency or pitch.  Due to the principle of octave equivalence, scales are generally considered to span a single octave,
  • pentascale(五声音阶): five notes scale.
  • triad(三和弦): three-note chords.
  • broken chords(分解和弦): A chord broken into a sequence of notes.
  • arpeggios(琶音和弦): A special type of broken chords in which the notes that compose a chord are played in a rising or descending order.
  • Suspension triads(不和谐三和弦):比如 C-D-G or C-F-G.
  • Harmonic triads(和谐三和弦):比如 C-E-G.
  • Major Scale(大调音阶): A Major scale is made of 7 notes, and the eights duplicates the first at double its frequency so that it is called a higher octave of the same note. The sequence of intervals between the notes of a major scale is: whole, whole, half, whole, whole, whole, half
  • Minor Scale(小调音阶): This usually means natural minor scale. The intervals between the notes of a natural minor scale follow the sequence below: whole, half, whole, whole, half, whole, whole.
  • Related Scales( 关系音阶):The two scales use the same notes but with different root, like C major and A Minor, they both use (A, B, C, D, E, F, G), but the root of C Major is C, and root of A minor is A.  From the sharps and flats on scores we can NOT tell which scale it is, but observing the root is usually easily tell.
  • The perfect fifth (纯五度): In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. A perfect fifth interval contains 7 half steps. For example, C-G
  • The perfect fourth(纯四度):In music theory, a perfect fourth is the musical interval corresponding to a pair of pitches with a frequency ratio of 4:3, or very nearly so. A perfect fourth interval contains 5 half steps. For example, C-F。
  • Tonic(主音), also called keynote, in music, the first note (degree) of any diatonic (e.g., major or minor) scale. It is the most important degree of the scale, serving as the focus for both melody and harmony.




作者的观察很准确呀,现在YouTube上纵论国际政治的中文自媒体越来越多,不就是一个活生生的证据吗。无论是“文昭谈古论今”、“王剑每日观察”,还是“stone 记”,话题都是围绕着国际政治展开。按照文章作者的说法,这些才是真正的聪明人:

复旦名嘴张维为、人大教授金灿荣、局座张召忠、” 至道学宫 ” 创办人 …… 才是这个时代最具 ” 顶级智慧 ” 的人。面对如此庞大的粉红群体,你既然改变不了他们,何不利用他们赚钱呢?


轮指不如移手 (Moving Hands is much better than using thumb and index fingers alternatively)

《天之痕》里面有一部分的左手和弦是连着两个小节的上行四分音符,这两个小节下来以后,左手就向高音部分移动很远,接着弹下面小节的和弦又要向低音部分移动回来很多,自己常常弹得手忙脚乱,错误连连。苦练了很久,进展不大。直到今天下午,自己才突然认识到:原来自己处理上行音阶,全部是用拇指和食指交替进行,虽然一时方便,但是整个左手手掌的姿态是很不协调的,这样给快速切换到下一个小节的低音带来了很大的困难;如果我采用移动手掌的办法来处理上行音阶,虽然弹起来稍微难一点,但是整个左手的姿态是舒展的,大拇指按完最后一个高音四分音符,左手很容易快速向左移动用小拇指去够下一个小节的低音。其实这件事情我女儿 Yetao 很早就向我指出过,只是当时没有明白这个道理。想通了这个道理以后,我按照新的方法练习了一会,结果原来老也弹不好的几个小节,竟然奇迹般的变得轻松起来。听着音乐从自己的手指下流淌出来,这种感觉真是让人陶醉。特别是当整个乐曲中从来没有顺利弹出的那一小段在自己的双手中完美呈现出来的那一刻,我感到极大的感动:所有的辛劳都得到了最大的回报,真是太美好了。



自己为此灰心了好一阵子,期间也上网研究过一些解决办法,但是都没有什么结论。Amazon 上很流行的单手键盘,是给打即时战略游戏的人用的,并不符合我的要求。无奈之下,只有先用右手不疼的几个手指勉强应付,但是键盘指法就都谈不上了,遇到有大块文字的输入,真是很让人恼火。


既然只能用一只手按键盘,那么我那个高级的 Kinesis机械键盘就反而变成一个累赘了,因为它的键面是弯曲的,一只手找键很不方便。等换上普通键盘以后,我又随手抓起一只铅笔,反过来用用带橡皮的的那一头代替右手按键盘,发现其实比两只手慢不了多少,自己心里很是高兴。看来天无绝人之路啊。上帝给你关上一扇门,总是会打开另外一扇窗。我的心里充满了感激。

Ben 帮助我练习钢琴


只练习和声部分总是有些枯燥,但是自己也没有什么好办法。有趣的是这天晚上 Yetao 跑过来要帮助我弹右手部分,真是一个很棒的主意。后来Ben也跑过来帮忙,Ben右手的旋律弹的像模像样,和我配合在一起听上去很不错,特别是弹到自己从来没有合起来过的部分,旋律与和声第一次响起来的时候我真是有些感动。孩子们帮了我一个大忙,真好。

Citrus Leafminer


看着越来越多的新叶受到侵害,我终于下定决心研究一下这到底是怎么回事。我把 “Orange Tree Disease” 放到Google图片里面搜索一下,结果很快就找到了很多讲述这个问题的网站,原来这是一种叫做 Citrus Leafminer 的小虫子,专门在橘子树的新叶子里面打洞,最后变成成虫飞走了。 令人感到欣慰的是,文章说这种小虫子造成的损害很小,绝大部分时候都不需要任何处理:因为它只能侵害新叶,老叶子比较坚固,不受影响,所以只有你的树是新栽种的情况下才需要操心,否则没有什么大不了的。文章建议不要使用杀虫剂,也不要剪去受损的树叶(因为这不是由细菌或者病毒引起,不会传染)。文章甚至建议为了避免这种害虫过度繁殖,应该避免夏天给橘子树上太多肥料,这样树就不会发出太多新叶而招致害虫。

文章的作者很达观,对于这种虫害基本上采用放任自流的观点。我看完文章以后也放心多了。 🙂


说来惭愧,虽然修炼了这么多年,但是听到别人对于自己的负面评价,还是难以淡定,特别是如果这些评价还是基于事实的话,那更是会让我长久挂怀,比如有人说我是一个“Self Worker”,暗示我没有领导力;还有人说我“就是太喜欢写程序”,暗示不能抓住项目重点,都是我常常想起来的例子。

最近渐渐意识到,对于别人的评价,还是要分清楚事实和观点。如果评价不是基于事实,那就根本没有必要理会。即使说的是事实,对方的观点你是否需要接受也是大可商榷的事情。我自己确实很喜欢写程序,写出来漂亮的程序自己也很高兴,这一点其实没有什么不好,没有人能够把所有的事情做到面面俱到,在自己喜欢而且擅长的事情上深钻是理所应当的,所以上面这个“就是太喜欢写程序”的评价事实正确,但是观点不一定就是正确的呀。 就像我最近有时候跟太太抱怨,太太就会笑眯眯的说,哎呀我就是这个样子,请你多多包涵啦,这种懂得自嘲的态度不是更健康吗?