- [Announcer] This week on Sound Field.

Since the beginning of time a series of numbers has inspired the world around us.

This number can be seen almost anywhere you look.

It's called the golden ratio and you might have seen it before but did you know that you can also hear it?

(buzzing low tones) - Have you ever noticed how some pieces of music just seem to make sense?

The notes, the chords, phrases, the dynamics and harmony, they can all feel like they were meant to go together.

Well, many people believe that this isn't simply a coincidence but part of a natural order to the universe, something called the golden ratio.

To explain the golden ratio we asked our friend Joe from It's Okay To Be Smart to fill us in.

- The golden ratio is the irrational number Phi and like Pi, it doesn't end.

So instead of saying 1.6180339887 and so on, we'll just say Phi.

So what's interesting about Phi?

Take this golden rectangle.

It's golden because the ratio between its sides match Phi.

If you cut a square off a golden rectangle, you create a smaller rectangle with the same golden proportions.

And because this long irrational number made sense visually but couldn't be explained as a fraction, some ancient philosophers figured it must have a higher meaning.

They called it the golden ratio and later the divine proportion.

(dramatic voices) Which brings us to something called the Fibonacci Sequence.

This pattern starts with zero, then each following number is the sum of the two before it.

And what does that have to do with the golden ratio?

Well as the Sequence goes higher, the ratio between the numbers gets closer and closer to 1.618 or Phi.

Many believe the Sequence could explain growth in nature.

If you connect each corner of the squares with an arc you'll get a golden spiral.

Look familiar?

Well, a lot of people see these golden spirals everywhere.

(futuristic music) - I didn't know anything about golden ratio.

I was reading, trying to learn like, okay (laughs).

- In school I learned it as, okay, a piece of music has a golden section which is that point, that climactic, it doesn't always have to be dramatic but just something special always happens.

Music theorists have claimed to find the golden ratio in the works of many famous classical composers from Mozart to Debussy.

Some say the golden ratio and the Fibonacci Sequence are evident in Music for Strings, Percussion and Celesta by Hungarian composer, Bela Bartok.

For example, the opening xylophone solo in the third movement has a rhythmic pattern following the Fibonacci Sequence going from 1, 2, 3, 5, 8 and then back down 5, 3, 2, 1.

(chiming bell sounds) - So Bartok I think was being accused of being really cerebral in his music, so he was pretty notoriously silent about his work.

You don't see notes in the margin with these little details, right?

So a lot of people have said, well look, if he was doing this, he was using Fibonacci and the golden ratio, you know, why didn't he tell people or why wasn't it more obvious?

- Couldn't it just be that certain pieces that have that lineup with the golden ratio stand out and then music theorists gravitate towards that as an example?

- Yes, absolutely.

For example, the Celesta.

That comes in at bar 77 in the first movement and that has nothing to do with golden ratio or Fibonacci.

(beep) But the piece in the title is Celesta, right?

So that's really important, right?

So does that mean we discount all the other stuff?

I mean, I think you're right.

You have to look at the big picture.

- But in your opinion why should people care about the golden ratio?

- Well (laughs), so what we haven't talked about is how it shows up in nature.

So, for example, if you go out and look at flowers and you start counting flower petals, most of the time you'll find a Fibonacci number.

Think about, like, if you were gonna grow and plant lots of seeds on a flower you wouldn't just wanna equally spread them out.

As you got further away from the center there'd be too much space.

Nature doesn't want that, right?

Nature wants the sunflower to procreate so the more seeds the better.

It turns out the optimal angle of where they're arranging themselves is related to the golden ratio.

So put that all together and you've got kind of a nice, beautiful, like, mother nature.

What could be more beautiful than mountains and flowers and streams, right?

Perhaps that's why musicians have gravitated towards it in terms of, you're writing a piece of music and you have a climax in your piece, where are you gonna put it?

Are you gonna put it right in the middle?

No, you're gonna put it a little off-center.

So maybe you tend to gravitate towards something like the golden ratio.

- The climax of Bartok's first movement happens at bar 55 which is not only a Fibonacci number but also lands very close to the golden ratio.

("Music for Strings, Percussion and Celesta" by Bartok) Music theorists call this a Phi moment.

- Bartok isn't the only composer to have a Phi moment.

Finding one is simple.

Take the length of a song and then multiply it by 0.618 the inverse of Phi.

For example, take Under Pressure by Queen and David Bowie.

We have a total of 246 seconds times 0.618 which equals 152 seconds.

Now listen to what happens at that exact moment.

If you look hard enough, you'll start finding it everywhere.

Check out Drake's In My Feelings.

But were all these musicians writing songs with calculators by their side?

I doubt it.

Some say we find these golden moments because humans are just hard-wired to find order in the world.

- But sometimes the order of the Fibonacci Sequence can be mesmerizing like in this konnakol rhythm by B.C.

Manjunath.

(clapping and vocalizing) Manjunath wrote this as a tribute piece after the death of his father who had introduced the Fibonacci Sequence to him as a teenager.

This style of music is Carnatic music from southern India and is characterized by a very complex rhythmic system.

Manjunath used the first eight numbers of the Fibonacci Sequence to compose the intricate rhythms in this piece.

By the way, this is the Phi moment of this video.

(trumpet fanfare) (rapid rhythmic vocalizing) - I did write a piece using certain elements of the golden proportions and the Fibonacci numbers.

Should I play it for you?

It's really fresh, but okay.

- Oh, you're gonna play it live.

Oh, let's get it.

I wanna hear this, yes.

(rhythmic gentle piano) - So what I did was I just came up with a little motif and then I fleshed it out until I felt like it could go somewhere and something can change.

Then I knew, okay, this is the golden section and depending on the rules of the golden proportions I know exactly how much time is required until the end.

(rhythmic gentle piano) (fast arpeggios) Okay, I'll stop - Woo hoo hoo!

right there (laughs).

So obviously here, (fast arpeggios) it changes, right?

- Yeah.

- So I try to make it as obvious as possible.

But that is at the point where 200 sixteenth notes have passed and the whole piece has 324 sixteenth notes.

So that point at 200 - Where it takes from there is the golden section - Da da da da da da da.

or the Phi moment and this pattern, (fast arpeggios) I used the Fibonacci numbers so this has five sixteenth notes (slow arpeggios) then it goes to eight sixteenth notes (medium arpeggios) and then it goes to 13 sixteenth notes (laughs) (fast arpeggios) and then it goes back down.

- Ooo!

- I don't know.

So what was hard was it is has to end by, what, 324 sixteenth notes, right?

So it's like how I'm gonna end this (fast arpeggios) so I just bring back the pedal.

(fast arpeggios) (soft piano chords) I just kind of try to evaporate it but that was difficult - Nahre, Nahre, about this - Nahre.

because I was working - Nahre.

with the structure.

- Nahre.

But (laughs), - You are really the truth.

(laughs) You're really good at what you do.

- oh, thank you.

That was really tight.

- Using this type of format, this type of structure, is another way of adding a limitation to what you're doing, some sort of puzzle to work around so I found it really stimulating.

- People think of limitations and boundaries as negative words, however, when you are creative and have so many ideas coming to you, you kind of need those walls to create within.

- Exactly and it's so true.

Just the template aspect of it is very, very valuable as a composer.

Since you've heard it, can you help me turn it into a piece with perhaps some percussion - Yes.

or some drum sounds?

- Yes.

- Maybe something with clapping.

- Yeah, I got some sounds for that.

I got some stuff for that.

- Okay.

- I wanna, I'm excited to dance to that first section, to da da da da da da, da da da da da da.

(rhythmic vocalizations) (laughs) I was - Cool.

diggin' the build up.

- Cool.

I was diggin' that too.

(upbeat piano music) (fast arpeggios and clapping) Where do you notice the golden ratio?

What do you think of our mathematical composition?

Comment below and don't forget to subscribe.

(futuristic tones)