The Golden Ratio and Fibonacci Sequence in Music (feat. It’s Okay to be Smart)


– [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)

100 comments

Ive always known there had to be some sort of math involved in making music. I thought that itwas just my brain but it turns out i wasnt just making it up

432.. then they changed it to 440..why??
To upset the natural harmonics.. like the planets in our solar system and their individual resonance combining to give us the music of the spheres..earths is 5.83hz

that was pretty cool. As a visual artist I am quite familiar with the golden ratio. AS a budding musician, I was pleasantly surprised to see it yet again, showing its majesty of form.

harmony, dissonance, rhythms, and the transmission of emotional states through music, are not only to do with the golden ratio. Acoustics is essentially an aspect of physics, which is the exploration of nature and the laws of nature. The Fibonacci sequence is only a part of the story of music, not the whole story. Bear in mind also that the way we perceive music is partly cultural; sounds that may sound dissonant to one cultures collective ears sound perfectly fine to another cultures ears/taste. So, in summery there is some truth to what you say but it is not the WHOLE truth. As a musician, visual artist and teacher i have had many years to consider and discuss such things. To re-iterate, what feels right to the ear of a western musician and audience may sound all wrong to an eastern ear and vice versa. Not all of this is about the math, part of it is purely cultural; we can see this by comparing and examining the many and various musics of the world. I find part of what you say about the ideal time is a bit of stretch actually, not rooted in reality, but a reading of a pre-existing belief you have formed through your fascination with the math of music. Sometimes we simply want something to be true because it's 'beautiful' but that does not necessarily make it true. The universe, including sound and light, is not all beauty. When one looks closely, one sees that there is far more than what we as humans consider beautiful. Our senses are limited, there are all sorts of sights and sounds that are happening all the time outside of these limitations.

Mathcore is awesome. It kinda sounds disregulated, but is right where it belongs all the same. You can find the 4 4 in most of it.

I'm disappointed that a discussion like this didn't include any mention of the Pythagorean Solfeggio tuning frequencies, like Verdi's A = 432 hz, or their connection to the natural world, as opposed to the non-natural A = 440 hz frequency scale.

Hey Guys … great treatment of the Rhythm & organization of the music. And Really nice piano composition! One thing I'd be curious to see you bring up is the tone frequency of the notes in the melody or harmony and perhaps the overall tuning of the music. Perhaps there is a correlation between the tempo and frequency of the tones in a phrase or motif? Would love to hear your ideas on that. Thanks!

Fibonaccis are like the Musollini/Italian version of fiber-nazis, where yeah, you can have a schnitzel, but then you have to eat a whole bowl of broccoli stems and trunks. Uncooked. Without any butter.

Nothing new here. This information is readily available from sources that don't force the viewer to endure the annoying background music.
If U'v got something 2 say y not just say it?

None of this makes any sense logically. Just talking about applying math to everything. This is a waste of time. What are all you fools so lathered up about. You and I are so dumb for watching

I‘m a graphic designer and have studied the spiral for over 40 years. I have made hundreds of overlays and the Fibonacci spiral do NOT match nature’s spirals at all. Not even close except they’re both spirals. The angles are completely different… a lot different. Fibonacci spirals have just gotten a lot of PR that is undeserved.

Nice video, but people, PLEASE STOP making videos while SHAKING YOUR HANDS & THRUSTING/GESTICULATING THEM AT THE FRICKIN CAMERA 😞😠😠😠

There are evolutionary advantages to "lucking" into a Golden Ratio. Since the Golden Ratio can optimize (in some cases) the spacing of repeating systems, it's no wonder that natural systems that happened upon this ratio tend to stick to it. If by accident some plant has its leaves spaced in such a way as to gather the most sunlight, then it has an advantage over other plants that do not spend their energy as efficiently. Whether or not that advantage conveys reproductive benefits may or may not be, but when it does… that makes it a hard trait to change.
Any trait that affects reproductive health in an optimal way is going to be persistent… so it's no wonder that many living things approach this Golden ratio, especially when it comes to something like the compact spacing of seeds in a flower.

How about admitting, this cannot happen by chance. its designed, its perfect, its made by God to show his mark in everything. Notice it; because many before you didn't have the luxury of looking it up on the internet. Now that you know you better seek God.

Everybody in the this video, every single person, looks really delightful, fantastic people 🙂
But did you make this video 618 seconds long on purpose?

I'll try not to geek out here (not like I'm really a geek) but I can't help but think that the Fibonacci Sequence is almost the "Fingerprint of God" (and I'm not even religious). We see this almost everywhere we look. Sunflowers. Pine cones. Pineapples. Avocados. Roses. The mathematics describe the most pleasing of architecture and proportions. And…here too…it describes what sounds…proper…in music.
Anyone that has studied music to any degree knows how thirds and fifths influence the "feel" or "taste" of a musical piece. 3 and 5 being near the very beginning of the Fibonacci Sequence.
A coincidence? I think not. Somehow, I think that it describes what is in harmony with the Universe. And I think that good music (that which just inherently sounds pleasing to your soul)(sorry rappers but…that just ain't it) IS one of those things that brings us all closer…not only to each other…but closer to the rhythm of the Cosmos.

Sorry. Got a bit "over-wordy" again….
That's what I get for thinkin'….

The law in motion, sound, math, plant, biology…..everything. also law within law like fractals self replicating like us. The golden ratio is infinitely beautiful. It is law. "for all is law", Thoths wisdom, tablet III.

Having been a quantum physics major and currently a singer songwriter, I found this very enlightening. It's almost as if you can glean something of an individuals SPIRIT by seeing/hearing where and how they compose/play/sing. I feel in love with the black keys when I was little, my singing always a little off in the rightest way. By figuring out your natural inclination/ pattern you can figure out what type of flower you are in the world.🌼🌹🌸🌷

What an awesome presentation! Thank you for taking the time to put this together!
The musical piece that you created reminded me of a track from the film The Thomas Crowne Affair, the one with Rene Russo, so now I'm going to watch that movie now!
Thanks again for this stellar video as it completed my fine breakfast of Tea and pancakes!

who else here basically has.no idea what they were really talking about when breaking down the sequence of each song? I felt like I was listening to another language for the majority of this film and literally understood maybe 5% of the general theme of this video. sigh. smh

I absolutely love it! However, I do need to point out that 'motif' (at the 7 minute mark) is pronounced "mote eef"
(rhymes with beef) not motive, like the reason for doing something. Anyhow rock on!

omg can you please not talk during the actual song moments? very annoying because I want to listen to what you say and actually hear the music.

I knew about the golden ratio, but not how it can be found in music or used as an intentional tool. I look forward to hearing the finished piece.

Alchemy is an interesting subject that reflects on many of our social norms , gold is a dominant factor in the oscillating control of both money and in this day and age , digital currency or “ plastics “ . To say “ Divine Proportion “ is like saying “ Divine wisdom “ , in religious terms and so is “ Golden ratio “ , not just an excuse to indulge further in the mysteries of the natural environment and bring those mysteries into a place of “ interpretation “ . Going way of the mathematical relevance here but somehow it feels like an old “ Alchemical Trick “ that has lasted beyond its sell bye date of the 17th century when it peeked , even though the branch of it known as “ natural philosophy “ due to its lack of connection to the world of “ classical “ music is still quite a thriving subject matter given that music has a strong connection to physics . My view is that it’s actually about auditory communication , prediction and prophesy and that we have since the 11th century , learnt new forms of it , in new ways and with different tools created to do so . Devine proportion , Golden ratio and Fibonacci’s contribution to the number itself are all great examples of not just what the irrationality of certain scientific endeavours are , but the rational behind the origins of both music and its powers of communication .

Really a great idea!

The golden ratio is the most irrational number there is. Since consciousness arises out of the brains as a form of entropy, the golden ratio therefore ignites consciousness the most. It gives music the greatest impact possible from its structures. That is probably why composers gravitate to it.

In my own compositions I use a lot of math. I have written a program that tunes instruments while they are playing. It allows me to compose music in Just Intonation tuning in such a way, that I can modulate from one key to another. It is my aim in my compositions to be as natural as possible. That is why it almost always sounds a lot like New Age music, although it is slightly more complex.

Now that you have made me aware of the golden ratio to me, I will incorporate it more consciously. I shall also try to incorporate it in my animations.

Thanks for this great video!

A marginal thumbs up and good attempt by these young students to explain the fibonacci but I would have preferred something a little more old school to explain this to me and delve a little more in depth… 😊👍

Shame he put that drake kid with the likes of Freddie Mercury and David Bowie…..we are certainly regressing as a whole. A complete mess.

Is joe the guy who always walks bymy unicycle show in Washington square park and screams your not funny dude! Sure looks just and sounds like him

Really cool.
The sequence she plays @ 7:18 reminds me of Lyle Mays opening playing "The way up" Pat Metheny Group
https://youtu.be/HHceeuZz77Y

Just one piece of a giant puzzle that proves we are the children of the almighty creater GOD/JESUS…JESUS/GOD is REAL…Trust me JESUS IS REAL…I know with out doubt…If you want to know how I know go to my 4 video channel here on UTube…
Pastor Billy Romines…JESUS is everything with out JESUS you have NOTHING…Please READ THE HOLY BIBLE…You need to be saved and know JESUS…JESUS/GOD loves you…GOD bless you…Hearing brings faith…Hearing the word of GOD/JESUS…

accident is this,,notice the imperfection,,always ,,everywhere,,these people only rationalize ,their own being,,for a short period,,,lol …………….

It's the rythm to forget and learn something new, endless and forever faithful. It's the harmonic we want to be tuned in because we feel at home in it. Unless you like false disharmonious over the top blinding crap that makes you feel out of place so you run back home where you feel safe. Golden ratio is a map to find home and to stay home. Enjoy the neverending ride on these tracks

The Rhythms of Swing ("Jazz") also appear in a golden ration and what we call "Groove" in electronic music, the little offbeat sequences

Retreated inside from mosquito attacks at phi moment.

at
phi,
attacked.
it was fact:
mosquitos came fast.
cigs smoked, alas. we retreated.

And…..the note A is not harmonically compatible with nature at 440 hz…The golden ratio is at 432 hz…And the Nazi's were not respinsible(intended spell). As zionist media always portrays…In our world of pointing finger inversions its the ones pointing who are the liars…

I always knew the image of Arnold Schwarzenegger's & Carl Weathers' biceps from Predator 1 (from the "Dillon you son of a bitch" scene) showcased at 9:55 in this video was golden and created by god himself!

"A lot of people believe they see a pattern"…"a lot of people believe this pattern is in nature"… this guy is trying to be inclusive to idiots.

LOL! The Fibonacci Sequence does NOT start with 0! Why would it, it serves no purpose. It starts with Double One, which is GOD Elohim Echad, The Father and the Son !, !. Shalom to us only in Christ Yeshua.

Okay so this is creepy because I think it might be along the lines of where I find the climax or most important part of songs. I’ve thought about it for years but didn’t know how to explain it. Now I get to check a bunch of songs 😊

I apply this to my teaching methods and Art. My own music is rather simple but does apply very simple applications of the sequence. Ontario Ministry of Training, Colleges, and Universities Training the hand to draw employs the mind to hand. The human mind sees mathematics without perhaps even knowing it. The accuracy of mind to the hand becomes even more perfect with practice as we unwillingly apply mathematics using the Fibonacci sequence which is everywhere in life. Some people adapt to this mind to hand concept, sketching and painting or playing music, sports, etc. depending on the makeup of the individual's behaviors and DNA and other factors, better than others. There is a direct relation to mathematics in all things especially Medicine and the applications of physics. I have personally employed the Fibonacci sequence in my painting compositions and stone sculpting, as a result, since 1970 "to capture the human eye". Not a new formula for painting or Art composition but a good one in my opinion. John Dávid Hart Canadian Visual Artist – painter/stone sculptor – Teacher – Spaulding School Of The Arts. A method of medical therapy – Art therapy developed by myself and Psychiatrist Dr. Celeste Thirlwell, and colleague physicians, is to draw looking at a subject but intentionally try not to draw it. The Therapy relaxes an individual with Post Traumatic stress syndrome and builds new confidence as stress is relieved. Oddly enough the subject matter is conveyed in the sketch composition and direct relation to the mind observing mathematics is obvious. Art therapy can be employed for numerous medical conditions as a healing process. https://youtu.be/Z739TgnHtDE

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