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

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)


  1. So… you take this topic… and not even use the word Tool in the video? This has spiralled out of control.

  2. Fascinating! I think that this equation can be applied to figure skating routines to pieces of music where the music's golden ration phi moment has the visual aspect of the pattern the feet and movement of the skater in a Counterpoint phi golden ratio to the structure of the totality of the whole skater music routine into a more musical Mystical mysterious totality. Very interesting. I will be using this in presentation and interpretation of the dance to the music including my Flamenco pieces should be quite extrodinaire. Thx for posting. Bonl 💕

  3. This is Amazing. Love that little pice. This channel just became my new favourite thing in the world.

  4. What a great pianist.

    At the end when you are overlaying the pattern over certain pictures you are just finding patterns where there are none. Just because on tiny section of someones head is aligned with the overlayed pattern does not mean the patter is there. Just because someone is holding there arm at a certain angle does not mean there is a pattern there. That person has to hold their arm like that at some point.

    Now the pattern is found in nature a lot but you a really trying to make it fit where it doesnt at the end of this video.

  5. 3:11 College of The Holy Cross?

    Do they replace Astronomy with Astrology, Chemistry with Alchemy, and History with Mythology?

  6. The mix of science, numbers, nature, music, and the chemistry between people earned my subscription to this channel right this moment!!

  7. That keyboard piece brought one thought to mind: Tension! There was something about the percussive attack with the (I forget the Italian/Latin words – Ostinato? Pizzicato?) immediacy of the individual notes.

    Please discuss tension in music! Me and my ukulele want to know!

  8. This is truly one of the best videos I have ever seen on so many levels. I love your collaborative composition!!

  9. I'm working on a multicache geocache based on the Fibonacci Sequence in my area. In the process, I discovered the original settlers by instinct or intention landed in the golden spot surrounded by the golden geological rectangle. I may be using your video to help them to understand how to look for it as those numbers are where my clues will be found. 🙂

  10. how can you not use lateralus… smh it shows the incredible implications and applications of fibonacci and the golden ratio approximations, drake gets a spot tho so they got that going for them

  11. this video kind of has a kind of Inception-esque (as in the movie) load of phi moments that begin with the announced phi moment, followed by Nahre’s piano phi moment and then immediately at 8:08 we have the center moment of LA going “oooooooooooo!” Which was the best moment of the episode.

  12. I would really love to have a recording of that piano piece. Will it ever be released? Has it been already?

  13. The 'phi moment' of your tune is very tigran esque! Fantastic. You guys should do a video on his music really.. haha

  14. Worked for "On A Plain" by Nirvana! Well it was slightly after the .618 mark but I count it as a win.

  15. Hiya, chick playing keys. Do you want to jam? I dig! Already married and have a kid, so no, dont worry about romantic involvement even though you're attractive!

  16. Any composer will tell you that you aim for your climax to take place at the ⅔ point., which is obviously very close to phi. The reason you are taught this as a composition student, and the reason you see it in almost any piece you analyse, is because it works. But is it because of phi, or simply that you naturally want more time to build to something than you need to come down from it?

  17. This is like peeking at Coltrane's brain at work with all the musical math of Slonimsky and metaphysical of Sun Ra and Alice Coltrane going on in his mind and body.

  18. Not only does ratio between successive fibonacci numbers approach phi but all similar sequences of numbers, where the next number in the sequence is the sum of the two previous numbers, has this property. e.g. Starting with numbers 4 and 12, the sequence would go:
    16, 28, 44, 72, 116, 188, 304, 492, 796, 1288
    1288 / 796 = 1.6180904523 ~ Phi

  19. It’d be nice to tune to 432
    Have you both seen the doc
    Sonic Geometry, the language of frequency and form? It’s amazing

  20. U should contact indian classical musicologoist because everything has evolved from India. Especially in the field of music.

  21. Hi guys,
    I've got a PhD degree working on this.
    Check out the link below for related content

  22. I liked the piano players piece she did live and I’m looking forward to hearing iit with the added percussion they spoke of doing.

  23. Soundfield: what did you guys think of our mathematical composition?

    me: How do I put this lightly…… BRILLIANT!!!!!!!

  24. It is not that we understand is that this sound (vibration) to which every thing in existence is tuned to it but this is to where it starts lowest frequency but there is a lot you do not know about the vibration……………………………………

  25. I observe it in the dodecahedron and the other Platonic and Kepler-Pionsot solids and celebrate it during the 12 days of Phi Week, Aug 3-14, with Phi Day on 8/8 or ∞/∞. 😀

  26. I notice the golden ratio everywhere from our anatomies to pinecones. I want to experiment with rhyme schemes based in these numbers for poetry and rap. The funny thing is before I knew what either the fibonacci or golden ratio was I saw the golden rectangle in a closed eye vision. It seemed to directly tell me that everything is deeply interconnected, and since then I have been on a quest to learn and experience this universe. I have noticed a intimate connection between frequency and geometry. I am on a mission to more consciously understand and bridge the gap between sound and shape, frequency and geometry. We truly are all connected in a beautiful experience.

  27. Evidence of intelligent design. Nature rarely creates perfection and yet we find it from the smallest to the largest structures i the universe.
    Give your life to Jesus Christ. Believe and Pray: God, I know that I am a sinner and unless you save me I will be lost forever. I believe that Jesus Christ is the true Son of God, died on the cross for my sins and arose on the 3rd day. I accept Jesus as my Lord and Savior, in the name of Jesus, Amen.

  28. I just found the phi moment of Octavarium by Dream Theater it was at 14:49 and it was the exact time James LaBrie sings Full Circle. Coincidence?! Probably, but it just shows how good the song is that full circle is the phi moment of the song. It's like all linked and stuff or something lol

  29. First things first, cool video.

    About the use of a point of interest in song structures or musical structures near the golden ratio, I think is relatet with nature and is something that came from the ancient civilizaciones and it's been used in every form of art (sculpture, poetry, drama, arquitecture, etc…) including music. Aristoteles talks about a structure in poetry that kinda fits the golden ratio, so I think that from the very begining, humankind has been related to this through the observation of nature. Art mimics nature.

    I'm a great fan of mathematical compositions (I've made a few myself) and I recomend you to check italian composer Luca Belcastro. He writes using points of interest by dividing the length of his score using Phi in a pretty acurate way, and then dividing the secction from begin to Phi point, and the section from Phi point to the end in golden ratio and so on. He also uses mathematical permutations and other cool stuff. His pieces are really organic landscapes. Definetively check him out.

  30. I’ve also heard this ratio as “God’s Fingerprint”. As it is found trough nature dna the universe etc.

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