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[MUSIC PLAYING]
BRADY HARAN: Do you like it still?
ALAN STEWART: It's all right.
It's got a nice bounce to it.
BRADY HARAN: Hi there, everyone.
I'm Brady from Numberphile.
And this is going to be bit of a video with a difference
because I've come all the way to Southampton to visit
someone I've never met in the flesh until now.
He's real.
This is Alan Stewart.
And for those of you who watched a few of my videos,
you'll be familiar with Alan's work because he makes music,
as you probably guessed.
And he's put music on loads of my videos.
And what we're going to do now, before we get going, is
play you a bit of a montage of some of the videos for which
Alan has composed his masterpieces.
[MUSIC PLAYING]
MATT PARKER: To get any kind of accuracy on our final
answer, we have to be as precise as we can be.
[MUSIC PLAYING]
BRADY HARAN: So that's some examples of Alan's work.
Now very quickly, before we get going, I must say early on
Alan has a YouTube channel, ALANKEY86.
Subscribe to ALANKEY86.
Because if you do that, you might make more music for me.
But also, Alan does loads of other things.
He's always putting all sorts of cool stuff on there.
Sometimes he just puts raw tracks of the stuff he makes
for Numberphile.
But he also does all of his own work.
And it's always full of really interesting stuff.
So go and check it out.
ALANKEY86.
They'll be a link underneath and on the screen and
everywhere.
And I'll sure we'll talk about it more later.
So first thing's first, we're going to get to
know the man himself.
And after we've spoken about that, we're going to talk
about some of the music and some of the maths and science
embedded in the music, which will be really interesting.
First of all, I've been doing a lot of talking here.
You want to say something?
ALAN STEWART: Yes.
I don't know what to say.
BRADY HARAN: Let me ask you some questions.
ALAN STEWART: Thanks.
BRADY HARAN: The first thing we should ask, because we'll
probably get asked about it in the comments,
is about your eye.
Your two eyes are slightly different.
And I know YouTube is--
they're not shy about writing about what they see.
Should we talk about that?
What's going on there?
ALAN STEWART: Let's do that.
In my right eye, I have a condition called band
keratopathy, which is a buildup of mineral.
So it's just cloudy.
And I can't see out of that eye at all.
My left eye is going the same way.
So my vision in my left eye is not perfect either.
BRADY HARAN: OK.
There you go.
Now you know.
So you probably don't need to write thousands comments.
What's it's called again?
ALAN STEWART: Band keratopathy.
BRADY HARAN: Band keratopathy.
There we go.
So now, let's find out a bit about you.
You have a sort of a sciency background or a mathematicky
background?
Talk to us.
ALAN STEWART: Yes.
I did a degree in physics at the University of Southampton.
And I got my master's there in 2008.
My musical background is kind of nonexistent.
I had a piano lessons for two years when I was a teenager.
Well, because of my eyesight, I never learned to read music.
I can't physically see the music to read it.
So that kind of limited what I could do.
So I stopped having lessons.
But I continued to play and just kind of taught myself.
BRADY HARAN: So you've taught yourself.
You don't read or write music.
ALAN STEWART: No.
BRADY HARAN: If you don't read or write
music, what do you do?
Do you just learn what key sounds like what?
And when you press these in this order, it sounds good?
ALAN STEWART: Yeah.
I play by ear.
So if I hear something, as long as it's not like Bach or
something, I can usually emulate it, try
and copy what I hear.
And I've been told I have perfect pitch, which is like
the ability to hear a note and just say, oh, that's an A. So
I guess that helps.
BRADY HARAN: OK.
Don't look.
What's this?
[NOTE PLAYING]
ALAN STEWART: Oh.
Do you know?
BRADY HARAN: No.
You're all very quickly going to learn that I have no idea
what any notes are.
Do you know?
ALAN STEWART: Sometimes I have to think about it.
BRADY HARAN: I'll play a different one.
It won't be the same one.
ALAN STEWART: Was it G?
BRADY HARAN: I don't know.
It was one of these ones.
ALAN STEWART: Go on, go on, play it again.
BRADY HARAN: It was one of these ones.
ALAN STEWART: One of these ones.
BRADY HARAN: I don't even know what one it was.
ALAN STEWART: And I can play it again.
[NOTE PLAYING]
ALAN STEWART: It was B.
BRADY HARAN: It was B.
ALAN STEWART: I was way off.
But I was able to play it again.
BRADY HARAN: You were.
So what's that, semi-perfect pitch, maybe?
ALAN STEWART: I think, yeah.
Perfect is a stretch.
Let's just say able to hear a note and play it back again.
BRADY HARAN: Now you're not a professional musician.
That's not how you make your living.
ALAN STEWART: No.
BRADY HARAN: What's your job?
ALAN STEWART: I am a teacher.
I teach A-level physics at Queen Mary's College.
I've been a teacher for four years.
And I love it.
BRADY HARAN: People are going to ask how we
ended up working together.
So tell us that story for as long as it takes.
How did we end up working together?
And go back as far as you need.
ALAN STEWART: OK.
I think the first thing I did--
I'm embarrassed about it, though.
So I don't want to talk about it.
BRADY HARAN: Really?
ALAN STEWART: Yeah.
BRADY HARAN: Is it criminal or something?
ALAN STEWART: No, no.
It's that "Sixty Symbols" song.
BRADY HARAN: Ahh, you made a "Sixty Symbols" song.
ALAN STEWART: Yeah.
It wasn't very good.
It wasn't very cool.
BRADY HARAN: No, it wasn't very cool.
ALAN STEWART: So I've actually unlisted it now.
BRADY HARAN: Really?
ALAN STEWART: Yeah.
Because it wasn't as good as--
BRADY HARAN: Oh, well, I'm going to tell everyone.
ALAN STEWART: No, you don't.
Don't.
BRADY HARAN: No, I'm going to tell you.
I'm going to tell you.
Alan made little song about the "Sixty Symbols." And he
sent it to me just to see if I thought it was all right,
because you had used some of our video footage, too.
ALAN STEWART: I had.
BRADY HARAN: You asked permission.
And he was just saying that he doesn't like it any more.
And he's unlisted the song.
He's embarrassed by it.
But I think it had some pretty cool bits to it as well.
I thought it was very Vangelis.
How do you say his name?
ALAN STEWART: Oh, Vangelis?
BRADY HARAN: Yeah.
Vangelis.
ALAN STEWART: Yeah.
BRADY HARAN: I thought bits of it sounded quite like him.
I quite liked bits of the song.
[MUSIC PLAYING]
BRADY HARAN: And as a result of that--
ALAN STEWART: Yes, that's the way it was.
BRADY HARAN: As a result of the bits I liked, I asked you
if you'd compose some more music.
[MUSIC PLAYING]
ALAN STEWART: I think the first bit of music I did was
for the Rubik's cube video, where you had all the
different people solving Rubik's cubes.
And I wrote some '80s backing music.
[MUSIC PLAYING]
-OK.
I actually git a pretty easy case.
-Hello, YouTube.
And hello, Brady.
This is my Rubik's cube attempt.
BRADY HARAN: I asked for it to be kind of retro and
'80s, didn't I?
ALAN STEWART: Yeah.
But I also did some other bits of music.
I think I sent you maybe four or five different ideas.
And actually, you ended up using all of them.
BRADY HARAN: On different videos.
ALAN STEWART: On different videos, yeah.
It wasn't my intention.
But you decided to use one for Periodic Videos, and another
one later on in Numberphile.
BRADY HARAN: Well, there you go.
It shows how good they were.
ALAN STEWART: Yeah.
BRADY HARAN: Let's talk a bit about some of
these track, then.
We talked about the Rubik's cube, where you
sent a whole bunch.
And I used them in different videos.
ALAN STEWART: Yeah.
BRADY HARAN: None of them were particularly
mathematical or science.
ALAN STEWART: None of them had any particular
math element to them.
BRADY HARAN: OK.
Well, let's skip to some that do.
Let's not go chronologically.
But let's go to one that I think we should do with CERN.
And this is the Fibonacci bagpipes.
ALAN STEWART: Fibonacci bagpipes.
BRADY HARAN: By way of background, I should probably
give some background, because I had a tartan made which was
based on the Fibonacci sequence.
And as a result, I wanted some sort of Scottish music that
was sort of imbued with Fibonacciness.
And I sent an email to Alan.
Did I mention his YouTube channel?
ALANKEY86.
I sent an email to Alan.
And one of the best things about working with Alan is he
works so quickly.
I'm so lucky that people help out with the YouTube channels.
And sometimes I'll ask someone for
some music or an animation.
And because everyone's busy-- you're a busy man--
maybe a week or two later, I might get a
response and some help.
But whenever I ask Alan for a piece of music, sometimes
within half an hour or an hour, I get an email of
something he's just composed and played and recorded.
And the Fibonacci bagpipes, even that was a really quick
turnaround.
ALAN STEWART: Thank you.
I just have nothing better to do.
BRADY HARAN: You have nothing better to do.
ALAN STEWART: Being a school teacher.
BRADY HARAN: There is nothing better than helping out
Numberphile.
But anyway, so I wanted some Scottish music imbued with
Fibonacci sequence.
And now I'll just play you a little bit of the music as
that appeared in the video.
So let's play that now.
[BAGPIPE MUSIC PLAYING]
BRADY HARAN: Now I don't see a set of bagpipes in here.
I'm guessing you don't own a set.
ALAN STEWART: Certainly not.
BRADY HARAN: First of all, how were you able to make a
bagpipe noise at all?
ALAN STEWART: Well, I feel like I should acknowledge the
fact that it is just completely synthesized in a
very unprofessional way.
BRADY HARAN: OK.
ALAN STEWART: I mixed together trumpets and piccolos and
various presets on the keyboard until I had something
that sounded squeaky and slightly annoying.
BRADY HARAN: So it's just a composite of other instruments
that sounds squeaky and annoying.
ALAN STEWART: Layered on top of each other.
BRADY HARAN: Yeah?
ALAN STEWART: Yeah.
BRADY HARAN: Can we load that on?
Can we have a listen to what they sound like?
ALAN STEWART: Here it is.
[NOTES PLAYING]
BRADY HARAN: So if you hit different keys, like--
[MUSIC PLAYING]
ALAN STEWART: Like that.
BRADY HARAN: OK.
So that's how we got our bagpipes.
I tell you what, I'm going to grab the camera, and you can
talk through the Fibonacciness of it all.
ALAN STEWART: OK.
BRADY HARAN: Alan, you've made bagpipe noise.
Talk to me about the Fibonacciness of
this piece of music.
ALAN STEWART: OK.
The original piece is in B flat, because that's what I
thought bagpipes were tuned to.
[MUSIC PLAYING]
ALAN STEWART: That's the scale of B flat.
But I think to make it simpler to explain, I'll actually play
it in C. So you can number the notes.
Here's the very first note-- number 1, 2, 3, 4, 5, 6, 7.
And then, of course, the eighth note is the octave.
What I did was I took the terms in
the Fibonacci sequence.
And I mapped them onto the musical scale.
So the Fibonacci sequence starts 1, 1, 2, 3, 5.
So that just comes out as 1, 1, 2, 3, 5.
The next term is 8.
So I could jump up to the eighth note.
But instead, I decided to take it full circle and just go
back to the first note.
I mean, it's the same note.
It's still a C.
[NOTE PLAYING]
ALAN STEWART: So that's the eighth note.
So it goes 1, 1, 2, 3, 5, 8.
The next term in the Fibonacci sequence is 13.
So I suppose I could have continued to
climb up the keyboard.
The 13th note is--
[NOTE PLAYING]
ALAN STEWART: --that.
The next term is 21.
The 21st note is--
[NOTE PLAYING]
ALAN STEWART: --that.
But that will not sound nice.
[MUSIC PLAYING]
ALAN STEWART: It doesn't sound right.
So can I use maths?
Thanks.
What I did was I took all the terms of
the Fibonacci sequence.
And I did mod 7 of the term, which basically means if you
take the number-- there's the Fibonacci number--
and divide it by 7, what remainder are you left with?
So if you take, say, the number 8 and divide that by 7,
obviously you're going to get 1 left over.
If you take 13 and divide that by 7, you're going to have a
remainder of 6.
So in this column here, these are the result of doing mod 7
on all the Fibonacci terms.
And this then allows you to map the notes into one sort of
zone on the keyboard.
Well, it gives you 1, 1, 2, 3, 5, 1, 6, 0, 6,
6, 5, and so on.
Then I just took those numbers and mapped them onto the C
Major scale.
BRADY HARAN: What do you get?
ALAN STEWART: You get this.
[MUSIC PLAYING]
ALAN STEWART: Which I've clearly just played in an
awful way, because every note had the same length.
So to give it a bit more rhythm--
because the Scots like their rhythm--
I just arbitrarily made the notes whatever length I
thought sounded best.
So what you end up with is--
[MUSIC PLAYING]
ALAN STEWART: Which has a bit more of a lilt to it.
It just sounds more musical.
BRADY HARAN: I'm incredibly impressed by this, because I
couldn't do this.
I'm impressed by anything I can't do.
Cool.
ALAN STEWART: Can I just point something out about the
Fibonacci sequence, though?
Is that there I just played 16 notes.
So you may say, OK, well, what's the 17th note?
It turns out that the 17th note is note number 1.
[NOTE PLAYING]
ALAN STEWART: The 18th notes is note number 1.
[NOTE PLAYING]
ALAN STEWART: The next note is note number 2, and
then 3, and then 5.
And it turns out that it's actually exactly the same
sequence again.
The same 16 notes just keep on cycling.
I know we don't need to show you this.
But on the spreadsheet, you can just keep on going up the
Fibonacci sequence.
The remainder, the mod 7 number just keeps cycling.
I don't know if I'm explaining that well.
So there is no more to the Fibonacci music.
I couldn't possibly have done any more mapping, because it
just keeps repeating.
BRADY HARAN: Man, that's awesome.
ALAN STEWART: Maybe.
BRADY HARAN: I'm sure there's a perfectly logical reason.
ALAN STEWART: I'm sure there is.
And being a physicist, I'm not quite good enough at the maths
to be able to explain why that is.
Maybe a numberphile will be able to explain what is it.
BRADY HARAN: Excellent.
ALAN STEWART: Anyway.
That's one Fibonacci element.
The other thing is the tempo is 89 beats per minute.
There's a pulse, click to the music that just taps a regular
89 beats in a minute.
Now the drumming in the song isn't just a simple pulse of
89 beats per minute.
BRADY HARAN: But where's that pulse?
I can't hear a pulse.
ALAN STEWART: I had a click track in Audacity that was
just constantly ticking at 89 beats per minutes.
BRADY HARAN: And then you took that out?
ALAN STEWART: I took that out just to keep me in time.
BRADY HARAN: So what is in time with that, then?
What's happening 89 times in a minute?
Can you play the track for me?
Play the click track.
ALAN STEWART: Yeah, sure.
[CLICK TRACK PLAYING]
ALAN STEWART: There you go.
That's what 89 beats per minute sounds like.
And I just make sure that I kept in time with that as I
was playing.
So I was going--
[MUSIC AND CLICK TRACK PLAYING]
ALAN STEWART: Of course, I took the click track out after
I'd finished recording, because no one wants to heat a
click track.
[CLICK TRACK PLAYING]
BRADY HARAN: But Alan, I don't really know what--
because some notes you do are short, and some are long.
They don't all hit.
What is the thing that's keeping in time with that
click track?
Does every fourth note have to hit the boot pedal?
I don't know what you mean by keeping in time with that.
ALAN STEWART: Oh, dear.
That's such a difficult question.
OK.
BRADY HARAN: Play it.
And talk to me of what you're thinking
and what you're doing.
ALAN STEWART: You ask a lot, Brady.
BRADY HARAN: This is how these videos get made, right?
ALAN STEWART: Right.
So I suppose I could play it so that every note lands on
one of the clicks.
So I could play.
[NOTES PLAYING]
ALAN STEWART: Except the click track just stopped, because it
was only 32 bars.
BRADY HARAN: Start again.
ALAN STEWART: I'll start again.
I'll just loop it.
BRADY HARAN: Yeah.
ALAN STEWART: There we go.
It's on loop.
[CLICK TRACK PLAYING]
BRADY HARAN: But you don't do that, because that sound
boring, is that right?
ALAN STEWART: Yeah.
BRADY HARAN: Then what do you do instead?
If you're going to break the rules and not follow the click
track, what's the point of the click track?
ALAN STEWART: Well, maybe if I talk about breaking the rules,
when I break the rules, I'm taking the time interval
between one click and the next click.
And I'm cutting it in half, for example.
So when one click happens, I might play two notes of the
same length.
So I'll just try and demonstrate that.
[MUSIC AND CLICK TRACK PLAYING]
ALAN STEWART: No.
That was notes on the click.
Let me try and demonstrate.
This is quite difficult.
[NOTES PLAYING]
ALAN STEWART: There.
That's what it would sound like to have half the click
separation as a note.
And I think that's how all music and all
rhythm is made up.
You take the click track.
And then the space in between the clicks, you cut
it perhaps in half.
Or you cut it into three pieces or cut
it into four pieces.
And usually you stick to notes of those durations, so half a
click or a third of a click.
BRADY HARAN: But, Alan, if you put two notes between clicks,
aren't you playing at 178 beats per minute?
ALAN STEWART: I suppose you could say that I was, except
that not every note is two notes between the clicks.
Some of the notes are just the duration between one
click and the next.
BRADY HARAN: Do you ever skip a beat?
ALAN STEWART: Oh, yeah, sometimes.
Everything I do in this song is some multiple of that or
some division of that.
I guess that's what rhythm is.
BRADY HARAN: All right.
Let's turn that off then, that little click.
So now we know that 89, a Fibonacci
number, plays a big role.
What else you got in there?
ALAN STEWART: Drums.
I really just need to change the drum kit on the keyboard,
which I know to be number 86, I think.
No, that's the Cuban percussion kit.
[NOTES PLAYING]
ALAN STEWART: Sounds nice, though, doesn't it?
I particularly like this one.
[NOTES PLAYING]
ALAN STEWART: This is the orchestral percussion kit on
the keyboard.
And it's got some nice, low drums, tympani possibly, or
I'm not sure.
And it's also got some snare drums.
[SNARE DRUMS PLAYING]
ALAN STEWART: And it's got snare roll.
[SNARE ROLL PLAYING]
ALAN STEWART: So you can generate a sort of drum track,
I suppose, for the song.
So in the Fibonacci bagpipes, I used the drums to mark out,
first of all, one accent, one loud note.
[NOTE PLAYING]
ALAN STEWART: One.
And then the next term in the Fibonacci sequence is 1 as
well, so another one of those.
[NOTE PLAYING]
ALAN STEWART: And then 2.
[NOTES PLAYING]
ALAN STEWART: And then 3.
[NOTES PLAYING]
ALAN STEWART: And then 5.
[NOTES PLAYING]
ALAN STEWART: And those can be heard underneath the bagpipes
about halfway through the track.
[MUSIC PLAYING]
BRADY HARAN: That's my favorite bit, by the way.
ALAN STEWART: When everything comes in?
BRADY HARAN: I like how they're going
at Fibonacci numbers.
Maybe that's because it's the only bit I recognized.
ALAN STEWART: Yeah.
I think it's punctuated.
It stands out.
And of course, there's also the snare drumming.
I could have done some clever Fibonaccis with the snares.
But instead, I wanted it to remain musical sounding.
Because I think if I'd based all of the drum rhythms on the
Fibonacci sequence, it would stop sounding musical.
So for that snare drums, I just did some
typical snare drumming.
BRADY HARAN: Do it again.
Do it again.
[NOTES PLAYING]
BRADY HARAN: So there's no Fibonacci there?
ALAN STEWART: No.
[MUSIC PLAYING]
ALAN STEWART: There's one more thing, one more element.
In the chorus, if you will, we hear this melody.
[MUSIC PLAYING]
ALAN STEWART: Very short.
That is the same melody as Philip Moriarty and Dave Brown
used in the phi song.
[MUSIC - "GOLDEN RATIO SONG"]
[MUSIC PLAYING]
ALAN STEWART: Now what does phi have to do with Fibonacci
numbers, Brady may ask.
BRADY HARAN: What does phi have to do with
the Fibonacci numbers?
ALAN STEWART: If you take two consecutive Fibonacci numbers
and you do the bigger one divided by the little one,
then the result is close to the golden
ratio, close to phi.
Now obviously, if you choose little Fibonacci numbers, like
8 and 5, that comes out to be--
panic--
8/5.
What's that?
1.4, which is not very close.
But if you use larger Fibonacci numbers, it tends
towards the golden ratio.
It gets closer and closer and closer to the golden ratio.
Proportion is divine.
[MUSIC PLAYING]
[MUSIC - "GOLDEN RATIO SONG"]
ALAN STEWART: Very nice.
The proportion is divine.
BRADY HARAN: You have this mathematical, sciency
background--
and not even a background.
You're a physics teacher.
And you have this interest in music.
To what extent is music this arty experience for you?
And to what extent are you thinking very much about
numbers and octaves and science and dividing beats
into factors and things?
ALAN STEWART: I think that's a really good question.
And I would say none at all.
I don't think in terms of mathematics.
I don't think in terms of the science of it.
I just literally play what I think sounds good.
However, if I want to compose a piece which is based on,
say, the Fibonacci sequence or pi, then I can use maths to
map it onto music and art.
And so I feel like there is a crossover.
But I'm not conscious of it when I'm playing.
BRADY HARAN: So when I drop you an email and say,
can you help me?
Can you come up with some music based on this
mathematical principle, how much is that putting a
straitjacket on you?
And how much is that making it more fun and enjoyable?
ALAN STEWART: I think sometimes having a
straitjacket, having a very specific brief can actually
really help.
Because if you're just told to compose some background music
for, I don't know, an elephant--
actually, no.
That's probably quite easy to do, actually.
But if you were just asked to compose a nice piece of music,
where do you start?
Whereas if you're asked to compose a piece of music
that's based on Fibonacci, then that does actually help
to have the restriction.
BRADY HARAN: Well, speaking of restrictions, another request
that I put in to you was to help with some music for our
video about calculating pi with pies, which was an
interesting video, and certainly attracted some
interesting comments, not because of your music, but
because of our use of pies.
But let's not go into that.
Let's talk about the music.
Do you remember what I asked you for?
I can't even remember what I asked.
I told you what we were doing.
ALAN STEWART: You told me that you were going to measure pi
using laser pi's and you wanted something
quirky, you asked for.
No.
What did you ask for?
BRADY HARAN: There was some kind of toing and froing on
this one, wasn't there?
Did you send me something, and I--
ALAN STEWART: Yes.
No.
I think what it was was I think you said you were going
to do a video--
yes.
You said you were going to do a video where you were going
to measure pi using pies.
And could I come up with some music?
It could be based on pi, you said.
And I thought, it's got to be based on pi.
Because if it's not based on pi, then
what's the point, really?
So I sent you some just very light piano music with a
classical feel.
It was very backgroundy, very similar to the "Spaghetti
Numbers" music.
BRADY HARAN: Well, let's play that now, because
I still have that.
Let's play what Alan first sent.
[MUSIC PLAYING]
ALAN STEWART: You weren't unhappy.
You said it was nice.
But then I asked you, because you described
the activity to me.
I asked you, was there any sense of it being a bit
sneaky, like you were doing something you weren't supposed
to be doing?
Because what I'd done was I played around a
but more with pi.
And I discovered that on a minor scale, as opposed to a
major scale, it had a very different feel to it.
And I'd come up with something that I thought sounded quite--
James Bondy was how I worded it in my email to you.
BRADY HARAN: I believe so.
ALAN STEWART: So yeah.
BRADY HARAN: We ended up with something different.
ALAN STEWART: We did, yeah.
Something with a little bit more tension to it.
BRADY HARAN: A lot of people who I showed the video said it
wasn't what--
because I told a lot of people like my friends and things
what I was doing, and that you were making some music.
And then when I showed them the cut piece, a lot of them
said that's completely not what I expected
the music to be like.
ALAN STEWART: Oh, really?
BRADY HARAN: And it works really well.
ALAN STEWART: Oh, that's cool.
BRADY HARAN: It was kind of like I think everyone who had
an expectation of what that video was going to be like was
thrown a bit of a curve ball.
But I still really like it.
[MUSIC PLAYING]
MATT PARKER: My goal is to not actually do any measurement
other than using pies.
So the entire thing is going to be pie based.
[MUSIC PLAYING]
MATT PARKER: We get the circumference in the exact
number of pies, give or take.
BRADY HARAN: Shall we talk to people about the music and
tell them about how you embedded pi in it?
ALAN STEWART: Yes.
BRADY HARAN: Let me go and get the camera.
Let's do it.
[MUSIC PLAYING]
ALAN STEWART: I come up with very boring names, which are
just for my benefit to remind me what the feel of it is.
I think this one was probably just called--
oh, no, wait.
No, this had an important name.
This was called "Pi March," because musically it's similar
to a march, like a marching band.
And Pi Day is in March.
BRADY HARAN: Very good.
By the way, if anyone's hearing the construction work
outside, there's nothing we can do about that.
It's because Alan's having another house built, because
he's a millionaire.
ALAN STEWART: OK.
So again, I don't know how to describe it.
It's very conventional to map, I think, the digits of a
number onto a scale.
And with Fibonacci, we were putting the numbers of the
Fibonacci sequence on to the notes of the C major scale,
these ones.
[NOTES PLAYING]
BRADY HARAN: OK.
Yeah.
ALAN STEWART: So just to be different, just to be
outrageous, I thought, let's put pi on a minor scale.
So here's the scale.
BRADY HARAN: And why is that outrageous?
ALAN STEWART: Because I'm using hyperbole.
BRADY HARAN: Obviously you're exaggerating.
ALAN STEWART: Sorry.
BRADY HARAN: It's not outrageous.
ALAN STEWART: No, sorry.
BRADY HARAN: Why is that outside the box?
Or why is that a twist?
ALAN STEWART: Sure.
Well, there have been quite a few people who
have put pi to music--
Vi Hart, for one, and some other people.
And there's a very well-known video called "The Sounds of
Pi," I think.
In all of the videos I've ever seen, they've always put pi on
a major scale.
Professor Moriarty put pi on a major scale on the guitar.
[ROCK MUSIC PLAYING]
PHILIP MORIARTY: 3, 1, 4, 1, 5, 9, bend up to 9, back to 2.
And then we've got 6, 5, 3, 5, 8, 9.
ALAN STEWART: So I thought I'd like to hear what it sounds
like on a minor scale, just to see.
And it sounds quite different.
BRADY HARAN: Go on.
ALAN STEWART: I need to play it.
OK.
So first of all, the notes of the minor scale go like this.
[NOTES PLAYING]
ALAN STEWART: So a very different feel.
It's a sad scale, as my piano teacher would have said.
The third note.
[NOTE PLAYING]
ALAN STEWART: The first note.
[NOTE PLAYING]
ALAN STEWART: The fourth note.
[NOTE PLAYING]
ALAN STEWART: The first note.
[NOTE PLAYING]
ALAN STEWART: The fifth note.
[NOTE PLAYING]
ALAN STEWART: The ninth.
[NOTE PLAYING]
ALAN STEWART: The second.
[NOTE PLAYING]
ALAN STEWART: And then the sixth.
[NOTE PLAYING]
ALAN STEWART: And the fifth.
[NOTE PLAYING]
ALAN STEWART: So just then, I played it pretty much on a
pulse, just boring.
[NOTES PLAYING]
ALAN STEWART: Which to me, it didn't really have much of a
rhythm to it.
So again, I just arbitrarily made the notes as long as I
wanted them to be until it sounded good.
There's actually a rest at the start which I have to play
with the left hand.
Sorry.
It goes--
[MUSIC PLAYING]
ALAN STEWART: And that rhythm I thought sounded good.
And that's what I ended up with.
BRADY HARAN: What were you doing there?
Was that breaking the rules?
Or was that part of pi as well, that little thing you do
with your left hand?
Or is that just a little bit of a flourish you put in for
musical reasons?
ALAN STEWART: That was the arty, musical side of me, and
has nothing to do with math.
It's just me making it sound good.
[MUSIC PLAYING]
BRADY HARAN: OK.
So the notes were based on pi.
You went a bit further, didn't you, as usual?
ALAN STEWART: Yeah.
Yeah.
The tempo, the number of beats per minute, was
some multiple of pi.
It was 104 beats per minute.
BRADY HARAN: Why is that?
What's that?
ALAN STEWART: That's pi multiplied by 33.3 recurring.
What I did was pi times 100 divided by 3.
BRADY HARAN: What else was marching?
There were drums and things, weren't there?
ALAN STEWART: In the "Pi March," yes, yes, the same
drum beats that were in the Fibonacci, the same
principles.
So the first digit of pi is 3.
So there were 3 blasts on drum, and then one blast on
the drum, and then 4.
And I think that stands out.
That's quite obvious.
[MUSIC PLAYING]
MATT PARKER: This is a mild problem, because I want to go
from the very edge of the circle.
But as you can see, I've positioned all the pies.
BRADY HARAN: What's it like for you when you make a bit of
music like you do for people like me, and then you see the
video on YouTube with your music on it?
What's that like?
ALAN STEWART: I love it.
I'm always really excited if it's going to be a video with
some music.
And I guess--
I don't know.
It makes it come alive.
BRADY HARAN: Is it different for you
when you see the video?
I say, this is what the video is about.
Do you feel like, no, that's not what I expected the video
to be like, or how I expected my music to used?
ALAN STEWART: I think usually your editing fits really well
with the music.
So in the pi video, you cut on the beat, for example.
Or you would cut at the end of a phrase.
And so I was really delighted with how it looked in the end.
It matched the music.
[MUSIC PLAYING]
BRADY HARAN: Do you like it still?
ALAN STEWART: It's all right.
It's got a nice bounce to it.
I don't know what else to say.
BRADY HARAN: You don't like listening to you own music?
ALAN STEWART: I guess I play it.
I play it.
I play it.
I play it.
I practice it.
I record it.
I listen to it.
And so after you've heard it like 50 times, it loses its
initial excitement and the feeling that
you get from there.
And it just becomes a song you've heard
too much on the radio.
But to begin with, when I first came up with that, I
just, I don't know, smiling to myself, it
just sounded so good.
I like making something up.
And I enjoy it for the first hour or so.
BRADY HARAN: I've made a little list here of some of
the other bits of music that I particularly enjoy, because I
just wanted to ask you a bit about the making of them.
ALAN STEWART: Yeah.
BRADY HARAN: Our "Good Will Hunting" video.
Because we made a video about mathematics in "Good Will
Hunting." I emailed and said basically, can you make
something that sounds like the theme music from "Good Will
Hunting?" Because I can't use the actual music.
And you came up with this.
[MUSIC PLAYING]
BRADY HARAN: Which I really liked.
It really sounds like the theme of "Good Will Hunting,"
without being it.
Tell us about how you came up with that,
because I'm really curious.
ALAN STEWART: Yeah.
So I mean I've seen "Good Will Hunting." But I can't say I
remembered the music.
So I went on YouTube.
And I just searched for the theme tune.
And I listened to it probably for about an hour just in the
background, just having it there.
I felt like I was trying to soak it up.
And there were certain parts of it-- because it's quite a
complicated piece of music.
There's loads going on.
And it's a bit crazy.
But there were parts of it that I thought I can emulate
what Danny Elfman, the composer, has done here.
So there's the high-pitched, piccolo-like
sound at the beginning.
And then there's also something quite beautiful
about it, but also something slightly discordant.
Like in the introduction, those piano chords are not
what I would think of as normal chords.
They're a bit dissonant.
They're a bit odd.
So taking all those different bits that I soaked up from it,
I just tried to write something
that sounded similar.
[MUSIC PLAYING]
BRADY HARAN: When you listen to something for a hour,
though, like when a song gets stuck in your head, how do you
stop that being so stuck in your head that you can be
original with it?
ALAN STEWART: I think the "Good Will Hunting" theme tune
is quite unique in that, even after listening to it for an
hour, I still find it quite unpredictable, because it is
such an interesting, rich piece of music.
There's so much going on in it.
Actually, that's why I had to listen to it for so long.
Because normally if I hear a song four or five times, I can
usually just play it after that.
But yeah, that theme tune is complicated.
So I didn't get tired of it.
BRADY HARAN: Is your mimic, is your homage to it equally
unpredictable?
ALAN STEWART: No.
My homage to it is simple by comparison.
I feel like mine is a little bit more tuneful.
There's an actual tune that you could sing along to.
Whereas in Danny Elfman's score, it's quite a random
piece of music.
And I challenge anyone to sing the theme tune to "Good Will
Hunting." Whereas, I think mine, you could
actually sing it back.
BRADY HARAN: All right.
Well, if anyone sings the theme tune to "Good Will
Hunting," or if they sings Alan's version of it and post
it as a video response, I will allow the video response.
ALAN STEWART: That'll be great.
BRADY HARAN: Because that would be quite a sight.
ALAN STEWART: It would.
It's such a weird piece.
[MUSIC PLAYING]
BRADY HARAN: Well, another piece of music, this is
actually more of a project that you did quite
independently of what I was doing.
And that's the "Dragon Curve" music.
ALAN STEWART: Oh, yeah.
BRADY HARAN: Obviously, we did a video about the "Dragon
Curve." And there are other animations
that have been done.
And you contacted the animator and you made your own piece of
music to that animation.
ALAN STEWART: Hmm.
BRADY HARAN: And then we sort of brought it all together
into a Numberphile video.
ALAN STEWART: Yeah.
BRADY HARAN: That's obviously a really nice piece of music.
Is that mathematical or inspired?
Or was that just you making a nice piece of music?
ALAN STEWART: I'd say that the mathematical link is even
weaker than the pi song, Fibonacci song.
But to me, it does reflect things about the curve, about
the shape, the way it unfolds.
There are parts of it that, to me, do connect with the shape.
[MUSIC PLAYING]
ALAN STEWART: It's quite difficult to explain.
But one thing, actually, about the
animation is that it rotates.
And so in my head, I had the idea of circles.
And in music, there's this thing called
the Circle of Fifths.
And I wanted to use the Circle of Fifths somewhere in the
song to reflect that rotation of the animation.
There was something about the animation that just looked
like the original one that looked quite lonely.
And it was just a fractal forming slowly in
a vast black space.
So I wanted something that sounded lonely.
[MUSIC PLAYING]
ALAN STEWART: Shall I carry on talking?
BRADY HARAN: Nah, you can stop now.
ALAN STEWART: Yeah.
BRADY HARAN: One more thing, and this is not Numberphile.
It wasn't for a Numberphile video.
It was for a Deep Sky Video.
ALAN STEWART: Yeah.
BRADY HARAN: And as far as I, know there's no math or
science involved.
But it's actually my favorite piece of music that you've
made for me.
So I wanted to ask you about it and hear a bit about the
story from your end.
And that's a piece of music that you called "Time Passes."
ALAN STEWART: Oh, yes.
BRADY HARAN: I'll tell it from my end first.
Basically, I was in Paris.
And I went to Charles Messier's grave.
And I'm going to stop now, because the battery is about
to run out.
I'm going to change the battery in the camera.
As I was saying, I was in Paris.
And I went to Charles Messier's grave.
And I wanted a piece of music to reflect us walking through
the cemetery.
And I emailed to you.
ALAN STEWART: Uh-huh.
BRADY HARAN: Basically I just said, I've just been walking
through a cemetery.
And I want a piece of music that shows me walking through
a cemetery.
And really quickly, while I was still in the hotel, you
sent me a few options from memory.
And I really liked all of them.
They were all really lovely.
I could have used any of them.
But in the end, I used this one.
[MUSIC PLAYING]
BRADY HARAN: I thought I read about it.
Straight ahead to the right of the monument, and then right.
[MUSIC - ALAN STEWART, "TIMES PASSES"]
BRADY HARAN: What happened when I sent you this email to
result in these pieces of music?
ALAN STEWART: I think I find it easier to write
sad-sounding music.
So you said you were in a cemetery.
So I thought, it's got to sound sad.
You also said that the video was going to feature you
traveling to the place.
So I wanted something that had a bit of movement to it, a bit
of motion, which is why it's got a fairly fast pulse.
It's like a ticking of a clock.
And that's why I called it "Time Passes" as well.
BRADY HARAN: Well, I liked it.
ALAN STEWART: Thank you.
BRADY HARAN: Well done.
ALAN STEWART: Thanks.
BRADY HARAN: Well done.
[MUSIC - ALAN STEWART, "TIMES PASSES"]
BRADY HARAN: Thank you for all the bits of music you have
made for the Numberphile videos.
I know from the comments under the videos that people
watching also enjoy them.
And a final reminder, ALANKEY86
is the YouTube channel.
Go and subscribe.
Let me tell you the main reason I want you subscribe.
It's because every time I link to Alan's channel, I get an
email from him where he says, oh, five new people have
subscribed.
And he gets really excited and says he knows when I put a
video up, because he'll have 10 new subscribers or 30 new
subscribers.
And I feel a bit disappointed that so few people subscribe
after all the hard work you put in.
So if a whole bunch of you go and subscribe, well, that
would be good, wouldn't it?
ALAN STEWART: Thank you.
BRADY HARAN: Yeah.
Why should they subscribe, though?
They shouldn't just do it to be nice to me or you.
What are they going to get if they do?
ALAN STEWART: They will get piano music.
I try and upload maybe once a week or once a fortnight,
something I've written, some composition.
Occasionally, I'll do something a bit different,
like a song.
BRADY HARAN: All right.
ALAN STEWART: Yeah.
BRADY HARAN: And just as a little teaser, I know, because
we were talking off camera, that Alan is working on a
couple of new compositions which hopefully might appear
on Numberphile, if I can secure the rights.
And you're doing them with Professor Phil Moriarty, who
also appears in Numberphile in Sixty Symbols.
And I have had bit of a preview.
And they're pretty exciting.
They're pretty quirky.
ALAN STEWART: They're a bit different.
BRADY HARAN: They are different.
One of them I really like.
One of them I like for its craziness.
So that will be coming soon.
So stay tuned to Numberphile and Sixty Symbols, but also to
ALANKEY86, because Alan puts a lot of his raw material.
And videos of him playing the pieces appear on that channel.
So it's always a good little supplementary to some of the
stuff you see on Numberphile.
Those long, slender piano fingers--
there we go--
which are so famous on your channel.
ALAN STEWART: Thank you.
BRADY HARAN: Thank you for watching.
I don't know how long this video is going to be.
We've recorded 54 or 55 minutes.
ALAN STEWART: Wow.
BRADY HARAN: That's a load.
Do you think we can put 55 minutes on Numberphile?
ALAN STEWART: No.
BRADY HARAN: People won't watch that.
ALAN STEWART: I don't think so.
BRADY HARAN: I'll cut the bits out.
I'll cut the bit out where you got really
abusive and started swearing.
ALAN STEWART: Yeah.
BRADY HARAN: All right.
[MUSIC PLAYING]