#### Mathematics AND Music

David: The laws of harmony. This link between music and mathematics. It’s a completely different subject, but…

DN: Yes.

David: If you would do that basic job of explaining that there is this sort of Pythagorean deep link between mathematics and music.

DN: Yes, very much so, because I play the guitar, so I sort of experience this almost every day when I practise or perform. And I know, as a matter of fact, that if I stop the string at this point, and I do something like that, to get what we call a harmonic, I get a totally different sound from what I would get if I tapped the string just at that point normally.

And I get a different sound because I’ve divided the string exactly into two. I jump an octave – it’s beautiful. You get lovely bell-shaped sounds out of that. I mean, if you don’t think that’s beautiful, I don't know what is! And, as you say, it comes out of the equations of the vibrations of that string.

DN: Those are both E’s. That one is a high E because I’m dividing the string by exactly 50 percent of its length. I can play it in a different way to get what are called octave harmonics which are using that halving principle in a way that produces a very different kind of note.

David: And that’s Pythagoras: that’s the mathematics.

DN: Absolutely so, yes. And you can do the same of course by dividing up into thirds, fifths and so on which is how you get chords that are harmonic and pleasing to the ear.

David: Can you show us a third or a fifth.

DN: For example, if I do here, those two notes sound nice together. So do those. Those all sound nice, because they are related by the mathematics of the way in which the string is working.

DN: Exactly so, and you can put a whole chord together with those, you see. It’s the relationships that enable all of that to happen: it’s not the individual notes. I can play individual notes, nothing’s there. Together you get a totally different flavour and you can only say that that is beautiful, but the individual notes on their own are not.

David: Is it stretching it then to say that the music emerges out of the individual notes when you put them together.

DN: Not only that, but it emerges when you put them together in relation to each other, just as you put hydrogen and oxygen together to form water. It’s also the case that the way I play this in every concert is different, so it depends on your mood and so many other things. The way in which I will play that will be different each time: it will never be the same.

David: And yet the music is the same, the score.

DN: The notes, the chords are the same. What’s written in the score is the same, but a performer never performs it exactly the same way.

David: Does this metaphor then of music… it seems like it’s helped you to formulate your ideas. It’s a powerful metaphor for you?

DN: For me it’s an extraordinary powerful metaphor, because after all we are dealing here with some things you can give a nice, reductionist, scientific account, which is if I do that [plays two notes], I get an octave, and if I do the thirds and the fifths, I get what I get. So all of that looks nice and reductionist: the individual notes. But it is really only when I put it together that I get something beautiful.

Ard: And the beauty is in those variations.

DN: Exactly so. In fact that beauty comes out of what is not in the score. Precisely. It’s a creative process, and I think the evolutionary process has been a creative process that is built on each novelty as it’s arisen to build meaning into the process of how it has all changed and evolved. So you don’t have to ask the question, where does the meaning all come from? You can ask that question if you want, and if you are of a particular disposition of a particular metaphysical kind you will do that, but you don’t have to ask that question in order to see the meaning. The meaning is there, obvious, just as in the heartbeat – I’m pretty clear about the purpose of the heartbeat. As a physiologist I couldn’t be anything other than clear.