Episode 213: Music is what maths sounds like. Art is what maths looks like

I've been thinking about how art and maths and music and all types of different art can come together. Dance, Andy, you dancer, you. Yeah. How can we bring them all together? How do they come together?

Okay, well, I think there's two parts to this, right? So the links between music and maths are hugely wide ranging. And I think that's the same with dancing and sort of rhythmic, but creative, all of those aspects of it. But there was another thing that prompted me the other day that was thinking, was reading something about a teacher and educator talking about the shift in attitude towards mathematics, about when they started doing maths when they were kids. And it was certainly true of me and perhaps you.

It was about how much you could get through, but there was a finality to it. And when you look at those disciplines of art and music, dance, those areas, it's not about how much you get through, right?

It's about that creative process about whatever it is, whatever it is you're working on, can I do this a little bit better? Now that I've learned this, can I bring this into this? And I think that that approach to a lot of those broadly under the banner of artistic subjects, is just so healthy, like so, so healthy because there's that, those inherent parts of it about making mistakes, you can't pick up, listeners may not be able to see this, but Andy's got some guitars behind him.

There's no way in the world Andy could pick up those guitars and just play for ages without making a mistake. But I guarantee you, if there's one mistake, it doesn't go back on the rack, right? Like it's not. So I think, I think there's already those crossovers that we know in terms of like the links between maths and music.

But I also think that the attitude towards creativity, which is mathematics, exists within those disciplines. And that is so healthy. We hear it all the time about resilience and this and that. You look at anyone that sits down and doodles and draws and stuff, you know, like it just continues. It's not, it's, I want to develop this and I've drawn this and I really like it. I want to draw it again, but make it a wee bit better.

I've just played this bit. What if I added a wee bit of this in? I've just painted this. I've just danced. This is what I've just done. You know, I've just done this and I'm going to build on this. That attitude's so healthy, eh? So healthy.

Yeah, for sure. And I know Andy wants to turn around right now and grab his guitar or one of them and start playing for us because I do think music and maths do share a deep connection.

You've got the rhythms and the harmonies and the scales and all rely on mathematical ratios and patterns and that's just one aspect of art and you've touched on others with drawing.

You know, I think the beauty of maths in art can show how logic and creativity can, you know, they're not opposites. They actually can come and work together.

So I would, know, I'm listening to you guys here and I'm like, the head's kind of turning and some of the great points that you guys have made.

You know, the thing is that what any of these disciplines are, any like the creative disciplines are an example of the beauty of mathematics. That's what they are.

And...all-encompassing sort of nature of mathematics. So, you know, if you think of like visual arts, you know, the things that we do, the colors, it's all based on mathematics. I mean, this...

you know, wavelengths of, of light and, and, visual patterns and repetition and symmetry and all these things, were all mathematical concepts, right? the mixing of colors works, you know, the, the wave forms, the reflective wave forms versus the light versus that, know, like I, I mean, I studied color theory. I worked in color theory. I wrote about color theory for a long time in a professional capacity before I got into this mathematics stuff. And of course, you guys know as well, music's always been a huge part of my life and did that professionally for a while as well.

You know, the reality is it's nothing but manifestations of mathematics, either visual or audible, right? This music is what math sounds like and art is what math looks like, visual arts, right? It's what it looks like. It's what it sounds like. It is mathematics. It's nothing but mathematics, right? And that we need to...

teach it that way sometimes as well. To remember a musical pattern. It could be as simple as… [rhythmic clapping]

You know, that's mathematical, that's, you know, we talk about patterns in mathematics. That's a pattern, right? It's audible. It's not visual, but it's also a pattern. Well, that can translate into a dance step. That's a physical enactment of mathematics, right? You know, do this, then do that, then do this, then do that, then do this, then do that, then do this, then do that. You know, that's.It's a manifestation of mathematics, right?

So it's all mathematics. mean, so you could be a cynic and say, Andy, you're just, you know, looking at everything through a mathematical lens, but I'm not, it's, it's not, it's not something that we're forcing. It's just what it is. It's just mathematics. They're just different.

Yeah, we don't have to realize that it's mathematics. I'm not drawing a picture and thinking, this is very mathematical. But the reality is, as you said, it is.

It's yeah, it's like if you just think of transposing a piece of music, right? So transposing a piece of music is taking music and playing exactly as it is and playing it in a different key. Okay. So let's say that you compose a piece of music and it's in the key of G and now you transpose it to the key of A. Okay. So it's the exact same piece of music, but you're moving it from one key to another. That's algebra. That's algebra.

Right? That's what it is. You're changing the variable, right? In algebra, right? It's an algebraic equation, right? So you're taking a pattern, you know, that's expressed in a particular way and you're changing one of the, so you can totally express that as algebra, right?

Now you could, I'm not saying we should teach algebra using music, but you can certainly, you know, try to make that connection or get people to think about, you know,

Okay, well, if I do this in this context, it's actually not, you know, get them thinking in that way. You know, so can you paint the same thing in a different color? For example, it's again, algebraic problem in a way, right? You're changing a variable, changing the frequency of light. So, you know, these are things that like, if you can explain to people that these are concepts.

All these concepts exist. And by the way, in mathematics, this is how we write these things down. You know, it can be part of the learning. I suppose teaching a child a dance is a valid way of teaching patterns. Right? Yeah.

100%. But I think it's things, without being too overwhelming, the world is maths. It's that simple. Like, there's nothing. I'm looking around, I'm looking at your guitar, the guitar over your left shoulder, Andy, I'm just thinking, right, there are six strings that have been chosen, they've been chosen because of the frequency, I'm assuming.

The way that it's been constructed is the engineering that required the mathematics, the circuits that provide the sound through the amplification are done through, you know, you can scale up and down. It's all of those things. So without getting too heavy, it is, it's maths.

If you take a guitar string, right, and go to the half point, right, there are 12 tones in there, okay, that have been split, but they're not equal in length, okay? They're gradually, so it's logarithmic in nature, right? Okay, so half the length of the guitar string is 12 notes.

Now take the remaining half and cut that in half and those 12 notes are in that half. Right?

So then take the next half and there's another. So now you've spanned three octaves of stuff, but you're still got a section left which can be split into an infinite number of octaves, right?

It's logarithmic. It goes, it goes up. It's not a straight line. It's not linear. That's a mathematical concept, right? The whole idea of music, like that you cut something in half every time you take a half and cut it in half again, there's a whole 12 notes in there, right? So how many octaves are there on one string? It's infinite, right?

Because, so you're saying musical scales follow mathematical ratios.

Well, it's not only ratios, but it's logarithms, right? So it's kind of like, it's exponential. It keeps, you know, so at every point, right? So if you wanted to add another octave to a guitar, you'd have just one octave, you'd have to make it twice as long. Right?

Your guitar would be this big, you know, to add an octave. So that's kind of interesting, right? To me, that's interesting. But then there's this other variable. You can change the, you can change the, the tuning. You can change the gauge of the string, how thick the string is. All these things have an effect, right?

All of it is mathematics. It's all derived from mathematics. The same with the piano. The piano is just a different layout, but it's the same notes, right? And all that hidden length of strings is hidden behind inside the bit that you never open in the piano. The bit that only the tuner goes in and plays with, right? It's all in there.

All that math. It's all kind of really cool. And just the idea that we discovered this and then we worked it out and we figured out of those 12 notes, that are seven that work really well together. Out of all the infinite tones from in an octave, seven of them work together and five of them work particularly well. And four of them make a chord that's somewhat interesting, but three makes the most resonant, most beautiful out of those seven tones.

And that makes a chord and it makes a major chord or a minor chord. That's all, it's all math. It's all can be explained through math, right? Intervals and...

Isn't it wonderful that it's able, that you were able to make sense of something through mathematics with accuracy? You know, I just, find it fascinating.

But, here's the thing. Nobody, I don't think anybody sat down and worked out the mathematics in the early days when they figured out the harmonics, the heart, you know, and, and stuff, they heard it. They heard the math. Right. And that is really cool.