Writing music with the Golden Ratio/Fibonacci

Writing music with the Golden Ratio. Can it be done? If so, how? Also, we'll find out if playing guitar in A=432 Hz will heal your soul. And check out @samuraiguitarist take on the Fibonacci sequence!
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Hi, my name is Paul Davids! I am a guitar player, teacher, producer, and overall music enthusiast from the Netherlands! I try to inspire people from all over the world with my videos, here on KZbin.
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[@dalebodmer]

HELP, i watched Sammy G's video, at the end he said, "Check out Pauly D's video". i did. Paul said, "Check out Sammy G's video"... i'm stuck in an endless loop!

[@hanableclarkgod]

4 weeks is a long time for that loop! Watch this next kzbin.info/www/bejne/rZuYnaaYd9yLj5o

[@sonicoxthehedgehog]

damn me too

[@erikfinkel2717]

The mobius riff

[@joelconway8517]

A spiral if you will...

[@derstrassencalligraph7534]

You see the face of God. Now you trippin‘....or was it the other way around?

[@cilanto-2255]

I thought i was tripping when i saw samurai guitarist post the same concept at the same time lol

[@SamTahbou]

You were tripping, should have skipped those shrooms...

[@tinkerfox1663]

I know right?

[@bertgetner9397]

cilantro 22 You have just entered, Close Encounter's of the Paul kind!

[@ChangoFrett]

I see several youtubers post similar ideas or videos on the same topic on the same day or within a day or two way too often. Neely and Beato tend to do this but I've seen Signals Music Studio and Music Theory for Guitar post similar videos withing hours talking about the same topic. ...and they didn't collaborate beforehand.

[@ChangoFrett]

Which is why I specifically said "...and they didn't collaborate beforehand."

[@tatejones2783]

You mean to tell me after all this The rhythm of the universe Is quintuplet swing

[@theelectricant98]

was thinking this

[@elviukx10]

Always has been.

[@bullerfugl]

Shawn Crowder: 👀

[@GMatt193]

@@elviukx10 Always will be.

[@globalnomad4074]

HA HAH AH,,, AHHH YOU GOT IT

[@TheMusicalMedic]

This is also a clear demonstration of how drums drive music, it sounds really slow and wonky without the drums, with them it really brings it all together, and makes the piece sound more driven.

[@henrikpetersson3463]

And how drums also can bog the music. When the drums starts following along with the guitar, that's when the energy emerges.

[@MatthewScottmusic]

Sounds like an acid trip.

[@hectorvader4436]

Hey you here! When are we gonna have a tour on the new studio/home?

[@alextheguitarist7282]

Nice to see you here...man!!!

[@thatellipsisguy8984]

I get more of a brownie vibe from Paul than acid...

[@RvLicious69]

maybe acid has the golden ratio :O

[@goodnightmoonoo]

this video comes in waves

[@esjel9804]

Notice how Paul positioned himself using the golden ratio.

[@benbug11]

Paul Davids: "A432 is more in tune with the Earth" *Adam Neely has entered the chat

[@pyrotas]

The 432 Hz stuff, which I hope was just an informed joke, was a bit of a letdown.

[@OttosTheName]

Pretty sure it's a joke, he did once do a video about 432 hz years back if you want to find out how he feels about that whole debate, I can't recall what his conclusion was, but he seems pretty down to earth.

[@TheWrestlingFamily]

I just watched that video haha

[@Spectre-wd9dl]

432 is the magic number. Fun fact. If you multiply the dimensions of the great pyramid by 432,000 you get the dimensions of the earth.

[@ThorsShadow]

@@Spectre-wd9dl If you multiply any random number with any other random number, you get an equation. So magical. No, just mathematics. What you're saying is meaningless. There are a lot of important numbers, equations and mathematical concepts in nature. 432 is not one of them. Also, 432 is merely a multiple of 2. 2 is the amount of numbers in the binary system. Go binary, people. Stay tech.

[@DMSProduktions]

DOES this qualify as 'math' rock?

[@Joe-pi9bx]

Perhaps ratio rock?

[@josephtravers777]

All music is mathematics. Peace.

[@DMSProduktions]

@@josephtravers777 ;o)

[@aixide]

absolutely. Not the most common math rock sound with bright, twinkly riffs and tapping but I'd say this absolutely is math rock.

[@DMSProduktions]

@@aixide I thought as much!

[@dantee1138]

Tool fans looking with their third eye

[@morielchukrun5574]

Man you got me laughing to death😂

[@HM-2011]

Tool army soldier here and I couldn't agree more ;)

[@BasementGAS]

Fully agree. Spiral out. Was somewhat surprised that he did not mention this in musical evidence like he did with architecture.

[@Jvb18290]

My first thought when I clicked on this video was "I'm sure Tool will be mentioned..." :D

[@williaml.6922]

@@Jvb18290 I clicked on this video wondering how many tools would mention Tool.

[@joecordingley7071]

Intervals tend to sound good to our ears where the ratios of their frequencies are close to simple fractions, that is fractions with low numbers. The golden ratio is "the most irrational number possible", which means it is the number that is the most difficult to estimate with simple fractions. That would mean that an interval of frequencies equal to the golden ratio is the most dissonant interval that exists in nature.

[@scottystampley]

Joe Cordingley yeah like the scale locrian is from the word and sound loco!

[@Geert.Van.Boxelaer]

"Interference" by Richard Merrick, recommended. Let me know if you get it, I don't 🤓👍

[@maxibour]

The most beautiful part of your work is not the final result (sort of music i can hear if i were close to death...) but the way you create rules and use a concept as a protocol to make art. As a art’s teacher, i can describe your work as conceptual art. Your song may be played in fine arts or contemporary museum. You are a great artist, a great musician and yours videos are pieces of pedagogic’s models. Applause and respect. Great inspiration.

[@meadish]

The rhythm sounds like a slow moving hay cart pulled by donkeys. Guess that's how the universe rolls.

[@gabrieloalgo]

Call Ben Howard and Thom Yorke to finish that project.

[@mossmacarthur504]

the only way this should be played is on a vinyl, the groove being in the shape of the swirl formed by using the golden ratio.

[@connormatthews522]

This is so eerie, its like we're listening to the unspoken language of the universe that's suddenly given a voice

[@mr.generico386]

When sbr get animated, this should be the music that would play when gyro is teaching johnny the spin

[@yourbrooscar2613]

I was looking for this coment

[@boobeez8693]

Man he’s a math instructor now as well

[@9aarshsrivastava67]

Yup!! Seriously

[@outshimed]

These are very simple math concepts lol. You should have no trouble understanding ratios if you passed middle school math. The music part is what gets my head spinning.

[@notoriusdrifter40]

@@outshimed wow u too smart

[@kurdtacolbain731]

No. Math professors pronounce it "fee," not "fie," like sorority sisters.

[@kristiandelosreyes4466]

Damn when Paul played it with the drums it became a relaxing music that feels like you’re in a trip in outerspace

[@EatPieNProsper]

This felt like God pitching his idea for the universe.

[@christopherhasenberg1113]

The more layers you ADD to it, the closer to DIVine music you'll achieve. It may not be a big banger, but it's a certified MULTI-golden oldie... SUBbed, dude. Edit: fun fact: 1 mile=1.612 km

[@paperkid73]

This is so underrated wtf it’s great

[@bananaclipper9343]

Tool fans: tHe FiBoNaCcI sEqUeNcE mAn

[@AL-jg4pr]

Song from golden ratio: mozzarella rela rela rela rela Aside from jokes, real nice video mate.

[@santanafan1713]

I listened to the entire song. Genius....mindboggling beautiful. I can 100% imagine it being used as theme music for a movie.

[@tiggtiggs]

Imagine all music used the golden ratio, the rise in human consciousness would escalate, dramatically lulling humanity into the golden age, in harmony with one another. Sweeet. ✌️❤️

[@Excellerator420]

Tool-Lateralus title track

[@ninepinknails]

Tool army soldier reporting for duty.

[@Austin-fd4ep]

Ride the spiral.

[@hughneutron5303]

@@Austin-fd4ep tim the toolman is poking his head above the fence watching this

[@BoWeava]

✊ sry I'm late! 11:30's got sum Puscifer vibes to my ear.

[@BoWeava]

HOPE THIS IS WHAT YOU WANNEEED!

[@kittyirish1708]

Awaiting orders

[@quasar8744]

8:36 Paul: "sounds very ethereal" Ichika:excuse me?

[@pedromello3601]

Sounds like something Hans Zimmer would compose to a Nolan movie...

[@ConwayBob]

I love this kind of experimentation, Paul. A great way to break out of any rut in which we may happen to find ourselves. There does seem to be something magical about these mathematical ratios that are found all over the physical universe. Thanks for sharing.

[@Louis_Velliotes]

Having a music degree I know how much work you put into this. Cool stuff man!!

[@thorified7904]

Love it. Thanks for explaining and diving deep

[@sliiiin]

By far the most interesting of your videos, @Paul!

[@swoodc]

now we gotta broadcast this to space like tesla did so aliens can hear your fibonaci sequence

[@ciscobriano]

And then Jehovah’s like, “ cool you found some of my chords .”

[@surge263]

👽👩🏽‍🚀

[@ciscobriano]

Tesla found this? Hahaha but who put in their ? Evolution? 1+1 will be 3 in 1 million years? "Dont worry ill wait" but God is going to kill any retartad melennials who believe in,Aliens! Hahaha ! Wake up stupid. All of a sudden mainstream media is telling the truth? Pleaded God show no mercy

[@_RichardOrtega]

I love when music nerds get together and experiment with sounds. Cant wait to see Sammy G's video.

[@douglashenderson3799]

Completely fascinating, and beautiful too!

[@SebasHoning]

Love this!! Absolutely up my alley!

[@Bramble451]

It's funny you used 987, since "9-8-7" was the working title of the Tool song "Lateralus", from the time signatures of the opening riff; 9/8 - 8/8 - 7/8. Which led them to use the Fibonacci sequence in the lyrics when they noticed that.

[@thatguy5779]

Oh yeah tool in lateralus used the fibonacci sequence, in that tool song?????? Like the fibonacci sequence??? Like tool with the song lateralus?? By TOOL

[@Bramble451]

@@thatguy5779 Yes, I'm fully aware the large number of people bring up Tool's Lateralus. Un-wad your panties. I was making a more specific point about it. He used the specific Fib. number "987" in his own sequence. I found the coincidence of that and the fact that the same number in the sequence "987" is what resulted in Tool's use of the sequence. It seems like such a random number for them both to have landed on. I hear tea with honey is a good way to sooth the nerves. I suggest you try it out. Use decaf.

[@virtua954]

it’s such an amazing song. reminds me of a post rock masterpiece, like something that Godspeed You! Black Emperor! would make if they were happy

[@denglish5275]

Oh yeah I definitely here the influence from post rock here. Like God is an astronaut and explosions in the sky

[@derek.invyckb]

don't forget mono and red sparowes

[@Bbslue7]

What a beautiful sound, thank you. 🙏🏼💙

[@SimonAllen]

Incredible piece of music Paul, thankyou.

[@iseetheendisnear2416]

The Golden Ratio gets more accurate with every iteration of the logarithm. I’d bump those numbers up to the ugly, ugly decimal points for better accuracy. The problem with Golden Ratio music is that the sequence could go on forever. It’s kinda tough to come up with good ideas to use it in music.

[@napalmoffreedom]

11:54 - wooow,it's very magic)

[@jovanjovanovic6096]

This is mind blowing! Great research!

[@warlord_n_warheads7198]

Absolutely beautiful work Clap

[@micmupfel]

Spiral out!

[@hearthshinemusic2941]

KEEP GOING

[@charlespockert8948]

Except the Tool track was actually listenable...

[@wreams2964]

A=432: exists Adam Neely: you are fake. *walks out*

[@boazcohen7992]

SIMP

[@leanlute7507]

The complete song give me chills! Thanx

[@cafe.cedarbeard]

Good senses allow some of us to do this by feel, and focus. Like, good songs will have natural Geometry. Appllying the ratio to tempo is one great secret, even tho it's out it takes experience to understand. That's how you pop out the Swing, ubiquitous in most African music. Even if you don't study the math, craft worthy musical senses are an application of Nature's Geometry. You know, how in order to be in flow with music when it's music, stopping to think can sink the ship real fast. In other meditations I appreciate this discipline. Thanks for doing your thing.

[@sammycoppens5470]

I like both your songs and methods, only to me it feels like neither of you used a 'ratio'. You both turned the ratio in to a sequence... Which kind of defeats the whole purpose. Since we're using only 12intervals in an octave, we must repeat a note somehow. To me it seems the interval between the notes should change along a ratio for this experiment. Already music is kind of some sort of formula where between some notes are halve steps and others whole steps. And this formula implies things like root, (major/minor) third and quint form a chord. In short, I believe the ratio can be used to predict which note is the most natural after the one just played. But just like you divide your paper in pieces, you never cut on the actual same line, so same notes this close to eachother seams off. So maybe there is a projection of the golden ratio which forms a note sequences, or chord variatons (diminished, sus4,...) Or maybe when using a weird ratio, the usual notes should be forgotten and use a whole step between each interval, or something... Looks like this triggers me, just thinking outside of the box. Love the videos, Keep up the great work.

[@PaulDavids]

I do appreciate this comment but I actually use the ratio for the entire rhythm, song structure and for some ethereal soundscapes. For the melody I explored this route, but it's really hard getting something musical out of this! But feel free to try and share it with me :) That's the beauty of something like this, you can go wherever you want to go, to whatever place your think sounds cool.

[@xaviervangorp4862]

The way I see it is the ratio just works as a source of “randomness” in the creative process. Paul then manages to turn that random sequence into great music. But it is true that any randomly picked irrational number ( one that does not repeat in its decimal seq ) would have done the job just fine. Nothing special about phi ^^

[@xaviervangorp4862]

On that note can’t help but mention that most of the spirals shown on the pictures aren’t actually depicting the golden ratio but are simply another form of logarithmic spirals and of course given any shape and taking a couple points from it you can fit a spiral on such points.

[@MrStag-rq1lf]

8:43 Throw in a little Danny Carey and I think we got something

[@GIBKEL]

Paul.....That was simply beautiful and illuminating.

[@augustinsigrist9519]

Simply Amazing !

[@AMIR55312]

1:54 this gave it away 🤣🤣🤭

[@ananttripathi875]

Please read this: 3 minute 14 seconds is not equal to 100π... The fundamental unit of time is in seconds and 3:14 is 194 seconds. Also 3.14/1.6 coincidently came out to be 1.96... Actual calculation is 194/1.6=121.25

[@Staffy-jm3bc]

Anant Tripathi shut up

[@ananttripathi875]

@@Staffy-jm3bc bro any jee aspiring student would have said the same.

[@SchizoetryOfficial]

@@Staffy-jm3bc lol

[@ananttripathi875]

@Xavier Rios nerds like me are the reason you sleep peacefully in your home. We need to take care of every single calculation.

[@SchizoetryOfficial]

@@ananttripathi875 I mean, nerds are, yeah. But that kind of calculation is useless and just semantics that nobody cares about. I'm a nerd myself and I think it was kind of annoying lol

[@mysticmoderna]

Really outstanding project and I'm amazed with the outcome! You have a great personality too for these videos! Loved!

[@debdiemer3749]

I love the concepts! In some ways it’s like going where no music has gone before! Fabulous!

[@echot.2664]

This sounds like an indie movie's background music.

[@shafersongs]

Exactly.

[@quive5705]

Tusk, act 4. Awaken.

[@orange-cat00280]

This music is ethereal, I’m fascinated by the golden ratio and its use in art and music. Thank you for this amazing work!

[@zorbrian8294]

I actually got chills from your song. Awesome!!

[@bradwitt7190]

Excuse me. I see absolutely nothing about this in my Mel Bay guitar books.

[@reasonablequit7535]

Me a JoJo fan seeing no references: *sad cowboy spin noises*

[@softsquiddo]

I was looking for a comment like this. Thanks!

[@coolstarb.]

*cries in infite spin*

[@jingleskhanaudioproductions]

amazing approach. keep on experimenting!

[@cathalwhelehan]

I couldn't quite see where you were going with this at the beginning until you added layer upon layer to it and ended up sounding a little like Sigur Ros - fantastic!!

[@daddyofalltrades]

I'm sad Where is the timestamp guy ?

[@PaulDavids]

0:00 intro

[@comicjustplays2065]

Paul Davids lmaoooo, loved the video btw!!

[@keremkaya6915]

@@PaulDavids smooth

[@thatellipsisguy8984]

0:11 more intro 1:12 visual representation of the Golden ratio 1:23 applications and examples 2:35 432hz tuning, process 3:58 Sammy G collaboration Aaaaaaand that’s all... Edit: unless 5:08.13 works as a time stamp...

[@GeorgeSPAMTindle]

@@thatellipsisguy8984 ...

[@theforgottenviking]

Is this a new genre? If so, what's the name? Here's a coupe :) - Math Post-Rock - Atmathspheric

[@roma540]

Mathmathspheric?

[@timallen6025]

Who would ever go to college when this quality of education and fun inspiration is right here ?😀 Another great video appetiser thank you

[@soundguitar]

Such high quality. Wow, I aspire to someday teach as effectively as you, Paul. Thank you! :)

[@brockolee1476]

Everything is now a Jojo’s reference

[@goofysouffle9727]

As it should be

[@azfar188]

@@goofysouffle9727 Always has been

[@leoWithNoStyle]

these tempos reminded me a bit of math rock

[@sarahfairchild399]

Sound track for the creation of the universe!! Love it!!

[@_pinguu3401]

Superb mix!

[@JellyAcoustic]

So this is how being on LSD feel like

[@johnmcaleese8459]

No, not really.

[@stringsoul2655]

And adam neely made a video on "432 sounds bad" lol

[@theminiaturepaintingtutor7885]

The drums were added. I got chills. Excellent work.

[@smc8144]

I love it! I did a pretty in depth study of the Golden ratio a couple of years ago and it just floored me. Very cool tune here and fun to see music like this.

[@mrblablablabla]

Nerd! Interesting how this slowly went from 'this sounds like ass' to 'this is awesome!!' Almost like my emotional connection to the song got multiplied by phi with every change...?? ;-) (BTW, ik heb mijn profielwerkstuk voor wiskunde ooit over de 'gulden rede' gemaakt)

[@johnsonvarghese6524]

I’m so confused

[@088Noir]

It's f incredible man. I am blown away 25+ playing. Jesus...

[@TheFakeMikeLWatts]

I sincerely appreciate the openness, and absence of cynicism when presenting this material. Thank you.

[@davidjohnston710]

Paul, yes that is interesting. I always like the ethereal sound and spaciousness created by sustain and reverb. However, I thought this video was a bit “prettier”: kzbin.info/www/bejne/f3itlnqFrJ2HsLM. You certainly did a good job of explaining the rationale of what you did. The tonic of the chord A is of course A. Something about repeating the B note atop the A is annoying and dissonant to me. I guess I prefer sus2 and sus4 sounds for the feel of peace and harmony. “Feel the tension?” - indeed, it made me tense. Just me, I guess. If nature is based on one chord, then we are in trouble, no? Imagine if all chords are being played simultaneously in the universe - all possibilities at once?

[@rem9144]

Speakling of the golden ratio and fibonacci numbers reminds me of Tool - Lateralus. what are your thoughts on that song, Paul Davids?

[@JeffCloutier]

Having used this for woodworking design, I am so glad to see you do this with music!

[@kneeedeep5536]

you blew my mind once again man. This is BRILLIANT!

[@k00lkushy86]

Like Lateralus by Tool?

[@gothrung7276]

Tool's laterals uses the golden ratio aswell

[@gothrung7276]

This is, the fibinachi sequence

[@mikedunn9313]

They are both very closely connected. As the Fibonacci climbs the numbers added together they get closer to the golden ratio. It’s perhaps more accurate to phrase the question as “how are Fibonacci numbers, also known as the Fibonacci sequence, related to the golden ratio?” Either way, the answer is this: The ratio of each successive pair of numbers in the Fibonacci Sequence converge on the golden ratio as you go higher in the sequence. The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc., with each number being the sum of the previous two. The ratios of successive pair of numbers is thus as follows: 1/0=∞ 1/1 = 1 2/1 = 2 3/2 = 1.5 5/3 = 1.66666666666666… 8/5 = 1.6 13/8 = 1.625 21/13 = 1.61538461538462… 34/21 = 1.61904761904762… 55/34 = 1.61764705882353… 89/55 = 1.61818181818182… 144/89 = 1.61797752808989… 233/144 = 1.61805555555556… 377/233 = 1.61802575107296… 610/377 = 1.61803713527851… 987/610 = 1.61803278688525… The golden ratio is an irrational number with an infinite number of random digits that can be calculated as (the square root of 5 + 1)/2. To fifteen places this is 1.61803398874989. So in the sequence above, you can see that the ratio from each pair of numbers gets closer and closer to the golden ratio. Go further into the Fibonacci sequence to the pair of successive numbers of 14,930,352 / 9,227,465 and the result is 1.61803398874989, accurate to 15 places. That’s far more than enough accuracy for any practical purpose, but you can go further with the information provided here: www.goldennumber.net/fibonacci-series Also they both can be found in nature, art, and architecture. I feel the fibbanocci keeps you moving forward and out while also bringing you closer the the golden ratio, the center. No better way to find you center than to spiral out, keep going.

[@DzakiBean]

man that drum added so much impact

[@Azamra18]

I absolutely love you Thank You

[@dankay7982]

Ok, that was easy. Everybody knew this. The real question is: How does that apply to 0-3-5?

[@eliaturrin2476]

It's me or it sounds kinda like shoegaze?

[@Winterharbourmusic]

Yeah it does... and I love that

[@MrUniverse]

The fibonacci drum rhythm is a heart beat. Makes sense

[@AwaisZafar-Sony]

Paused at 11:07 ... Went back ... HIT that Like Button ... and went back :D This is one of the most profound experiments in acoustics ever. Unbelievably surreal and serene composition.

[@jsnhll02]

I came here because I listened to samuraigutaurist first.. her says you two were making a collab video, where he only uses fibonacci sequence, and you use only the golden ratio.. so at the end of each of your videos, there was no collaboration, and you and him used both fibonacci sequence and golden ratio. So I didn't get to hear anything I thought I would have. The lower numbers of the fibonacci sequence, do not match the golden ratio close enough for our human technology to match good enough for a good collab of music. You two should use higher numbers in the sequence, in order to match closely to the ratio. Also, one should only use the "fib sequence", the other using only the ratio. Then actually collab, and place each of your music together. The two of you seem mathematically and musically smart enough to do that. That's what I want to hear/see

[@taileenalvarez1626]

👍 yes. Really cool

[@lw216316]

Math proves there is intelligent design in the existence of the universe. The golden ratio, Pi etc... were not invented. They were discovered. Look at the works of Einstein and the other scientists who study the universe. They do their work using math.

[@vandykmail]

Wrong on so many levels.

[@pogikoshet9351]

Eric van Dyk how come

[@schmargle]

Sounds beautiful.

[@seamusjames9390]

You just found your key to that other dimension. I wonder how the universe behaves there . Please send the video soon , great job guys! Happy Christmas ☃️

[@ctturgeon5038]

This is subscription worthy... love your channel man.

[@jenluvz2dance]

This was absolutely amazing!!! Happy 2022 to you :) Stay curious!!!

[@jascha_huisman]

This is so nice, the vibe really reminds me of old arcade fire music! Love it 😻