PHIL MORIARTY: Right I've got my trusty guitar on my back.
Last few months I've been working on a special musical
collaboration related to a very
important number in nature.
We're about to head off down the road to meet this
collaborator for the very first time, and I'm very
excited about it.
We're at the studio of Mr. Dave Brown, here--
DAVE BROWN: Hi!
PHIL MORIARTY: Yes, with his trademark "hi," who's a very
talented musician, producer.
So we're writing a song, a math metal song about phi.
Math metal's a genre which is very sort of
mathematically-based riffs, I guess.
Very, very syncopated, very technical.
And after we filmed a video on pi for Numberphile, a few
months, Dave got in touch and was keen to collaborate and to
really take that idea and push it further.
And so what we've done is we've based a song around to
the number phi, based the rhythms, based the melody-- if
you can call it that--
based the lyrics, all around phi, the number phi.
DAVE BROWN: First riff I've got in the song--
it's a nice clean one.
[MUSIC PLAYS]
DAVE BROWN: Before we punch you in the face.
And that's derived from a riff Phil came up with--
as you can see here, quite conveniently--
from the different digits of phi.
PHIL MORIARTY: What we also want to do as well as mapping
the digits of phi on to the melodies, on to the riffs, and
on to the rhythms, is also somehow embed the geometry of
phi in the song.
And the way we're gonna do that is we're going to take
the guitar string, length of the guitar string, and we're
going to pick out the note which defines, or the position
on the string which defines the golden ratio, the note of
the golden ratio, as it were.
And so what we're doing is--
this is a guitar string, from here to here.
The fundamental definition of the golden ratio
is you've got AB.
So you've got a length A and you've got a length B here.
So A plus B over A is equal to A over B, and
that's equal to phi.
What we're going to do now is use your wonderful golden
ratio calipers--
where have they gone--
to define where that note is.
It's going to be a note that's not going to match up exactly
with to where-- though it's not too far--
where we have a fret on the guitar.
It's just slightly below the 17th fret.
And then what we're going to do is we're going to overdub
on top of that, or maybe build it up-- we'll see.
As Dave suggested, what we're going to do is
then build this up.
So we'll go from that, just below the 17th fret.
Then we're going to choose another note, which as you can
see is just around about where the screws in the pickup are.
And then we're going to subdivide that down again,
each time building up and each time defining the note of the
golden ratio geometrically.
DAVE BROWN: OK.
So this next riff, I thought it'd be quite cool if we took
the number of chugs that a guitar plays-- technical term,
a chug is when the guitar goes chnnh.
Sounds like-- it's onomatopoeic.
And we took a number of them and put a gap in
between each one.
And if you count the number of chugs between each gap, you
actually get the number phi, which is quite cool.
So take a listen.
[RIFF PLAYS]
So there was one chug, six chugs, one chug, eight--
yeah, you get the idea.
PHIL MORIARTY: So these are gold nanoparticles, two
nanometers across, in water.
We're not going to really use the nanoparticles.
What we are going to use is the vial that the
nanoparticles are in.
But of course, it's gold.
It's the golden ratio, so we thought it was apt.
Well, I thought it was apt.
[MUSIC PLAYING]
DAVE BROWN: Next up, we get to a riff that's kind of like the
pi video that you guys did, where Phil mapped the digits
of pi onto a scale.
We did that with phi onto the B-flat harmonic minor scale.
I'm not really good at musical tech.
I do it by ear.
Could I get him shouting into the mic?
I need to get a level, unfortunately.
I'll give you some volume so you can do it, but.
PHIL MORIARTY: [SHOUTS]
DAVE BROWN: (SHOUTING) Real but uncountable!
PHIL MORIARTY: I've done this for a long, long
time, over 20 years.
So I was in a band while I was a student.
While I was a post-graduate as well.
(SHOUTING) Irrational.
DAVE BROWN: I did A-level maths.
I got a C. I blame my teacher.
I'm more of a musician now.
I have a YouTube channel called Boy in a Band.
You can search for that.
It'll probably be in the description.
I'll make sure Brady puts it there.
BRADY: I will even put it-- it'll be just on this--
just there.
DAVE BROWN: Oh, there we go.
How about that?
BRADY: Cool.
DAVE BROWN: But, yes.
I make music of varying styles.
Lots of electronic music, but I'm horrendously
into metal as well.
I just used horrendously twice.
I hope that's OK.
(SHOUTING) Emerge from the equation!
Spirals out of control!
PHIL MORIARTY: One, six, one eight, oh, three, three, nine,
eight, eight, seven, four--
It's been a hell of a lot of fun.
And I'm really happy with the song.
I think we've done some very interesting things.
We've gone beyond--
people talk about math metal, but math metal, those riffs
sound complicated, but they're not really mapped onto maths.
In this case, we've actually gone beyond that.
And there's only one other band, to the best of my
knowledge, that has attempted anything like this before, and
that's a band called After the Burial.
(SINGING) The proportion is divine.
DAVE BROWN: So phi is 1 plus the square root of 5 over 2.
So we decided to be a bit clever, and we have got 1 in
this by the open string on the guitar, representing that.
And the other notes being played by the guitar are the
digits of square root of 5.
And then over 2, we go into half-time drums partway
through this, which I thought was quite clever, so.
[METAL MUSIC PLAYING]
BRADY: That's quite clever, isn't it?
DAVE BROWN: Yeah.
BRADY: You pleased with it?
DAVE BROWN: Yeah.
PHIL MORIARTY: Some people might
not consider it beautiful.
I think the way that the maths are embedded throughout the
song, yeah, has its own bizarre beauty about.
Yes.
[MUSIC PLAYING]
DAVE BROWN: And we do a similar thing for
the outro as well.
[RIFF PLAYS]
The 1 there is that [HUM]
top note.
Then we've got the chugs.
You remember what chugs are?
Doing square root of 5.
And again, half-time drums.
PHIL MORIARTY: Leibniz was a very famous mathematician,
developed calculus independently of Newton.
And he has this wonderful quote, which is that music is
the human mind counting when it doesn't
know that it's counting.
And that's great.
There are these fundamental links between numbers, between
maths, to music.
And it's great to actually embed those so tightly as we
do in this song.
BRADY: Well hopefully, by now, you're all dying to hear the
finished song.
I know I am.
I haven't actually got the final copy from Dave yet.
We're going to upload it here on the
Numberphile channel on Friday.
If you're watching this video after Friday, I'll have the
link below the video, and you'll be able
to find it, of course.
Also below the video in the description, I'll have a link
to Dave's channel.
You really should check it out.
He's a super-talented guy.
And I'll also have some information under the video
about these golden mean calipers, which were sent to
us from New Zealand.
They're lots of fun, and I'm sure you're all going to have
some questions about them.
And we'll be using them in some future videos we've got
coming about the golden ratio on Numberphile in the weeks
and months to come.
But for now, we'll hear the song on Friday.
[MUSIC PLAYING]