写给理科生看的基础乐理

其实就是一些很基础的东西,只不过我想用美妙的*人话*改写一下。(谁知道小水站站主为什么又不务正业写起这个了呢?)

直接上图。

十二平均律

C大调音阶

但是平均下来的12个音听起来并不都和谐。因为音乐重要的是两个音的频率之间的比值,指数关系没有意义。其中G很和谐,因为它的频率1.4983f非常接近1.5f。其它如F、A也不错,因为1.3348和1.6818接近4/3和5/3。E也还行,离5/4不远。D和B也还可以,接近9/8和15/8。但是其它几个音像C#之类,就太不和谐了。于是有了调式和音阶。在12个音里只取其中7个,就是七声音阶。

只取C, D, E, F, G, A, B七个,就是C大调音阶。

转调

转D大调后

因为任何一个音都可以作为主音嘛,然后从这个音到它的2倍频的音之间等比12均分。

转调就是把12平均律的主音改变了而已。转任何一个大调音阶,以主音频率为f0,7个大调音阶的频率都会是
f0* (1, 1.1225, 1.2599, 1.3348, 1.4983, 1.6818, 1.8877)
也就是
f0*(1, 2^(2/12), 2^(4/12), 2^(5/12), 2^(7/12), 2^(9/12), 2^(11/12))

只不过do re mi fa so la xi do在黑白琴键上的位置改变了而已。

其他转调以此类推。

C大调和弦

频率

波形

观察观察这些图,你有什么直观感受?

像F和弦和G和弦这种波形,那些尖峰好突出,一看就很高昂,有种号角一样的感觉。

像E和A这种,看起来杂杂的,应该会比较柔和,没有F和G那种很亮很突出的感觉。

像D也是。而且D和E长得还好像。E也是有点杂,但波包比起前几个还是更清晰一点。

C就很和谐,同时也没有F和G那样的尖锐。

以上看起来像胡扯。但是有些我是能实践证明的。比如F和G和弦,就是很突出,就是一出现就有种耳前一亮的感觉。这是纯粹的听觉反应,就像红色是红色而绿色是绿色一样。而感性认识还在感官的反应之后,这里没有,这里是纯粹的感官反应。我也不知道为什么。我一直觉得人的听觉和嗅觉机制很神奇。我觉得生物的感官系统都好神奇。脑子也神奇。生态系统也神奇。人类社会也神奇。历史的进程也神奇……

离题太多了。

时间再长一点呢?

再再长一点呢?

噢怪不得C和弦最中正,F和弦和G和弦除C外最和谐。B很特别。

美妙!

五度循环圈

下次再更。啥名称记号都不需要,一张图足矣。

方馆(小水站)的站主。可能是一只猫,也可能是一只鸽子。也可能是一只会用膜法变成鸽子的猫。不过谁知道它是一只会梦见自己变成了鸽子的猫,还是一只会梦见自己变成了猫的鸽子呢?
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