Making music sound nasty or nice
The tree is up, the presents have been bought and it’s almost time for the big day itself. But whether you sing like a cherub or you screech like a cat, what’s Christmas without a few carols? With help from the Cambridge University Music Society singers, Chris Smith hears about the physics of sounds, songs and singing from engineer, Hugh Hunt...
Hugh - Sound is all about vibrations in the air. If you think of waves in water or… well, I’ve got a slinky spring here...
Chris - I’ve got a giant one here to play with!
Hugh - One end of the slinky spring is attached to a brick, as it happens, and I’m holding the other end on the table and I’m wobbling the end backwards and forwards, and I’m getting a wave. It’s going at a sort of a speed like one…
Chris - And just to explain for people at home what we’re seeing. At one end of this long table we’re all sitting around, Hugh has a house brick, which he has tied to his slinky spring. He has stretched the slinky spring 2 or 3 metres to the other end, and is now shaking the other end which he’s holding and it is making this wafting motion backwards and forwards in time with the metronome you’ve got beating on the desk.
Hugh - And it’s just one curve. But if I double the speed that I’m shaking the end of the slinky so instead of one, one, one - one two, one two, one two.
Chris - Ah, that's interesting. What we’re now seeing is that there’s a point roughly in the middle of the slinky which is now not moving but you’ve got two little waves either side of it going up and down.
Hugh - That’s right.
Chris - We’ve got two waves where previously we had one. So you’ve doubled the frequency, the rate at which you're doing it and you’ve now got twice as many waves.
Hugh - It’s called a “standing wave”. Now if I do three times: one two three, one two three, one two three...
Chris - Yes. We’ve got three points along the slinky which are not moving, and three little wavelets either side of those.
Hugh - And I can do four - one two three four, one two three four, one two three four…
Chris - And it’s called a “standing wave” because when I look at this it looks like there is a wave standing still in space almost?
Hugh - Exactly. If you think of waves in water, you would see the wave moving along in the the distance, but a standing wave doesn’t appear to be moving at all. These are called “harmonics.” The first one was the fundamental, and the second harmonic, the third harmonic.
Chris - So the fundamental is the one, two, three and that’s just shaking backwards and forwards. The second harmonic is twice as fast.
Hugh - The third harmonics three times, the fourth harmonic is four times. If you think of the note on the piano - the note C, then an octave above it is another C, and that’s the first harmonic, double the frequency.
Chris - Right. So that second C is twice as many waves as the first C?
Hugh - That’s right. Then the third harmonic is then the G above that. And then the fourth harmonic is then the C above that, and then the fifth is E, then the sixth is G, then the seventh is B flat.
What we can do with the choir is we can sing them for you if you like?
Chris - Oh, lets do it.
Choir sings harmonics
Chris - That was lovely.
Hugh - There we go. We went up to the tenth harmonic there, and each one of those was progressively increasing the number of cycles of that slinky spring, if you like.
Chris - Why does it sound nice? Because it’s perfectly possible to get them, I presume, to sing something that doesn’t sound nice. so what’s the difference between ‘nice’ and ‘nasty’?
Hugh - When you have a general sound, you can decompose it into these harmonics. That’s why different voices might sound different or a french horn might sound different from a clarinet, might sound different from a violin, but they all basically have this same harmonic structure. But one thing that is really weird is that Bach figured out that you didn’t have to get these harmonics exactly right; that our ears are quite forgiving.
It turns out, rather curiously that if you start off with a certain note, and you double it, and you double it, and you double it, double it, double it. You could start off with the same note and do 1½ times it and 1½ times, 1½, 1½, 1½ and you ought to get to exactly the same note again after a while, but it doesn’t work, the maths of it doesn’t work. And it turns out that no matter how we might try it is impossible to get perfect tuning, and yet beautiful music can be made by instruments that we can’t get perfect tuning on.
Chris - So this is an artifact of the human auditory system that we like that particular combination of sounds and we don’t like it when the multiples don’t add up correctly?
Hugh - It’s something that we have got used to certain sounds, and then other cultures have got used to sounds. We can sometimes find music from other cultures just not particularly musical.