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This is not so much about mathematics, but I wanted to put this somewhere.

I once made a computer program that takes recorded singing or whistling and analyses the tones to find the melody. When i did that I realized that it is not as simple as one might think. The frequency of the tones is not as unambiguous as we think, and the beginning and end of a tone is also not as clear as we might think. It is very much like spoken language, to make a software that finds and isolates the words (not even talking about the meaning here) encounters similar problems.

It seems that the musically experienced brain fills in the "assumptions" or the missing or unclear parts.

I did succeed to make that program though.

After that experience of writing that software I sometimes think of the problems I encountered, even when I hear a professional opera singer, and it seems, when I listen carefully, that even they do not hit the notes exactly. And I don't think they should, it is not that they are bad singers, they are maybe very good at it, but they do it consciously, or rather it is an expression of them. If the notes would be perfect, the personality, the dramatic feeling, etc. would be lost, or at least reduced.

If you hear a voice singing, it sounds so clear, here is this note, and here comes the next. And this tone is that note, and that tone is this note. But when you look at the waveform on the screen it is difficult to find the frequency and the border between the tones.

A note might begin way off in frequency and stabilize after half a second, and it is difficult to know if it is supposed to be two notes of different frequencies or just one note that took a while to stabilize.

But when your musically experienced brain hears it, it is as clear as the sun in the sky.