中学以来，我粗浅的音乐知识一直告诉我，不同的音高其实就是不同的频率。具体地说，乐音的基频决定了它的音高，泛音的组合关系决定了它的音色。
但是，实际情况可能要复杂的多。在尝试用Matlab作曲时我发现，用频率组合的思路，很难产生真实的乐器发出的声音。这也是为什么第二部分一直难产，我没拿准频率组合的思路最终可以做到什么程度。
这几天在看维基的时候才发现，根本的问题在于，音高并不等同于频率。频率是一个可测量的物理指标，而音高是人类大脑对于频率组合的总体解读。这个解读跟乐音的基频有很大关系，但是不绝对。
这么说可能很抽象，还是简单看一个例子（来自维基百科）：
这一段音乐的独特之处在于，听上去，音高在1分钟时间内一直在降低，而实际上音乐是重复的（都不用分析频率）。
频谱图在这里，这里的频率是线性坐标：
更多的信息请查看：
The documentary Test you Brain from National Geographic is awesome!
Illusions are well known to human, but not all of them have been well illustrated in action. The problem is, some of the illusions are very best described in experiment to shows all the intricacies. For that we need carefully designed experiments and video making. This is the first time I saw something like this is made.
As an example, here’s how this documentary illustrated an attention saturation situation devised in David Copperfield’s studio:
First you see a magician told you that he wanted to do something not at all legal with money. After showing you the cash, then messing around it, the silently putting it back to his pocket, you’re asked, “did you notice anything?”.
Of course you didn’t. Then the video rewind and show you what had happened before and after.
Then another video shot by a camera from another angel showed you these changes were made actually well you were watching. You didn’t notice only because you didn’t pay attention to them.
So after you see this, you cannot help to say to yourself, aha, that’s how they’ve deceived me. But then you have to rethink about perception and illusion.
While it’s not available in Youtube, we Chinese can already watch it here: