Fibonacci sequence in music 

Also, Remember the Fibonacci Sequence 0, 1, 1, 2, 3, 5, 8, 13. It would be remiss if you did not count the first two values. 0 being silence, and 1 being the tonic of any given scale. What would that second "1" be? The second tonic of course, or the octave. And, within the primary octave of the sequence, you have the second, which gives us a 9th chord--the 3rd and 5th, giving us the major cord--and the 13th giving us the 13th chord. Read up on overtones as well. Fibonacci is there, too.

Bach was deeply involved in the application of the Fibonacci series in his compositions. Read the book "Form: The Silent Language" by Hugo Nordern.

All I hear is Bach BWV 846

Just to reiterate what @intervalkid said: SEVEN white keys, not eight! TWELVE tones, not thirteen! You can't just duplicate "C" whilly-nilly and make it part of the story. Why, then, don't you also duplicate C#, or B etc etc etc?!

I don't mean to be a troll but: Everybody doing math-music videos should understand that in music, the second is not the double the first, the eighth is the double of the first. That way they would do proper videos for once. Besides that, a basic western scale has 7 notes, not 8.

I'm sorry, but your responses were all given more than 4 months ago and were buried deep in the comments section, I didn't see them. If it's a question that gets asked often, put your answer in an annotation in the video so that everyone watching will see it. :)

I understand nothing.

The layout of notes on the piano has NOTHING, even remotely, to do with the Fibonacci Sequence. This is a forced relation.

7 white to 5 black. 8th is the 1st in next octave.

There a 12 diatonic notes in a chromatic scale before a note is repeated, not 13.

This only applies to C major scale played on piano. What if you started with any other note or used another instrument? None of this would apply to anything. We humans are good at finding patterns even where there are actually no patterns. I'm not saying there are no patterns in music, but what the video presented is not one of them. It's just a coincidence. Also, there aren't 8 white keys and 5 black keys. There are 7 white keys and 5 black keys. When you come back to C, you start another octave. You repeat the same note. You can't count that as a new note. And again, if you started with some other note than C, this wouldn't apply. If we started from C#, by the same logic there would be 7 white keys and 6 black keys. If you want something that actually applies to music, it wouldn't only apply to C major on piano. If it only applies to C major on piano, it's not a pattern. Also, even if all of what the video talked about was true, how would it actually apply to music? What does it have to do with anything? What do I do with this knowledge?

It's actually 5 black keys to 7 white keys. The 8th white key doesn't count because it's treated as an interval of equivalence. There is still a Fibonacci pattern here though, it has to do with moment of symmetry scales. (the pattern is 5, 7, 12, 19, 31, 50, 81... etc.) The idea is, if you construct a scale with an equal division of the octave with a number from the pattern, the "5th" generator of the scale will be in between the "5th" of 5 and 7-edo (equal divisions of the octave)

How many of u came here to listen the frequency and heard shit

This says nothing. And the music you play in the background has nothing to do with Fibonacci sequences. If one would make music out of the tones you indicate, the result would be very static and poor.

so when you play this on the piano, does the pattern of your fingers make a pentagram? Hmmm...

As several commentators have mentioned, the layout of the keys really has nothing to do with Fibonacci. If anyone's really interested in Music and the Fibonacci series, I did a video about how composers have used it here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yAyi8e5RDXw.html

This is just numerical mumbo-jumbo. There are 12 notes per octave, not 13, 7 white keys and 5 black. If you (wrongly) count the second octave key (cdefgabC), but you start on, say, F#, you have 6 black keys and 7 white.

The background music in the video is not related to the numbers and notes displayed on the piano keyboard.

13 NOTES TO A SCALE (PLUS A TONIC RESOLUTION) 5 BLACK NOTES 8 WHITE NOTES 8-5=3 3 SIDES TO A TRIANGLE ILLUMINATI MUSIC IS ILLUMINATI GUYS SPREAD THE WORD PEOPLE NEED TO HEAR THIS

there is seven white to five black! Cause your 8 belonges to the next octave.

There are 12 notes, not 13.

It's called the "syntonic tuning continuum" and it has certain properties such as producing a 5 note MOS (moment of symmetry) scale with 3 small and 2 large steps (the pentatonic, black key scale on the piano), a 7 note MOS scale with 5 large and 2 small steps (the diatonic scale on the white keys of the piano), a 12 note scale with 7 large and 5 small steps, a 19 note scale with 12 large and 7 small steps... (you should see where this pattern is going by now)

sounds almost exactly like the accompaniment of Ave Maria Bach version ?

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones. 1,1,2,3,5,8,13,21,34,55,89,144

So if I had an instrument tuned to 13 tone equal temperament, is that the Fibonacci sequence too? Or any combination of 8 notes + 5 notes? The pitches of the 12 tone chromatic scale are already a bastardized version of the first few harmonics of the harmonic overtone series. There's nothing "natural" about them, save for the octave which is essentially pure and the 5th which is tempered to be ever so slightly flat from pure. All of the other intervals are considerably out of tune from their natural counterparts in the overtone series. They only sound "ok" to us due to centuries of acclamation. I'm sorry, but it absolutely IS ridiculous to claim some kind of magical association between simply the number of notes we have in our western 12-tone equal tempered scale and the Fibonacci sequence. It could be ANY 12 notes tuned literally any old way we wanted and you'd still call it some magical mysterious "coincidence" ordained by the stars simply because it was "8 notes + 5 notes"? And yes, the whole "repeat the 7th note because the end is the beginning" nonsense is a complete farce. It's just an attempt to force the whole thing to make the sense that you want it to make - and give it all some kind of "deep" meaning at the same time. Honestly, the pitch relationships of the harmonic overtone series already follow a gorgeous pattern. But only a tiny, TINY fraction of those relationships are present in our 12-tone equal tempered scale. And Bach's music is inexplicably gorgeous and speaks to us on a truly deep level, but again, it's ridiculous to think you can distill the entire mystery down to "8 notes + 5 notes".

You're looking for a pattern resembling the Fibonacci sequence. But in a diatonic scale, the pattern is 12 (7+5), not 13 (8+5). And of course the 7 keys have meaning without the 8th. The 8th key tells the listener it's repeating, but it's nonetheless part of a new iteration. You could apply the same logic here to argue there are 8 days in a week - Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.

There are seven white keys actually

Guitars and pianos are both string instruments utilizing the same 12 note scale using strings which are not perfect because there is a compensation (or intentional error that cannot be avoided) across all the strings. That's why it is so hard to tune a piano. Both being stringed stringed instruments using the 12 notes scale, I'm curious what you think is more perfect about the piano than the guitar. The accidentals are put there VERY deliberately to form the major scale.

lol, the ratio of white to black notes is 5 to 7; You counted C twice.

Fibonacci starts with "0" as the first number, though that's usually disregarded in discussions about it. 0 + 1 = 1. Because of this, the first "C" has to be considered a zero, meaning that you have to count it at both the top and bottom. The Western scale as we know it is not complete until the 8th tone is played. It's like steps in a staircase: 7 steps between floors will require you to take 8 physical steps, otherwise you don't get to the top.

Very uninformative!

I am fascinated by the Fibonacci sequences and its many applications in life, and being a professional classical pianist and accompanist, I am also fascinated by numbers and numerology in music and the physics of sound. I'm sure that there are musical connections to the Fibonacci sequence, but I'm afriad that they are not here. The ratio of white keys to black keys on a keyboard instrument is not 5 to 8, it is 5 to 7, within the 12-note, not 13, chromatic system that we have inherited from our western musical ancestors. Out of the section of keys that is shown, the note c is depicted once on the bottom (left) and once an octave higher on the top (right), whereas all the other notes are just shown once (obviously). [Besides, If you take the next 13 notes, you would have to start with c-sharp and go to the next c-sharp. In that group of 13 keys there are 6 black keys and 7 white keys.] And, as rightly pointed out by Timrath, the system that has been handed down to us of white and black keys is truly arbitrary. I agree completely with Lauris Gatis Zarinovs, that the arrangement of keys has nothing to do with any musical substance, unless of course you are keyboard player and trying to figure out how to get the right fingers on the right keys at the right time in the right way to produce the desired sound. I haven't read the 764 comments, so I would assume (hope) that others have also pointed this out. By the way, the background music doesn't have anything to do with the the Fibonacci sequence either, as far as I am aware. It is the first prelude from the first book of preludes and fugues, Das Wohltemperirte Klavier, composed by Johann Sebastian Bach. The numerology in Bach's music is a fascinating subject, starting with the letters of his own name (H in German is B natural in English) but that is different than what is being claimed here!

I wasn't talking to you with this comment. I was replying to Brian Vasquez.

the note 8th is the octave version 1st , why you are counting it? please explain? i did not watch this full video, because of it

Keys on a keyboard are not music…

How about how it applies to mid eastern, indian, or eastern music? More steps between what western ears find "pleasant"

its Prelude N° 1 by Bach

and about the 432hz frequency?

This sounds like a famous piece, what is it's name?

7 are the number of days in a week, 5 are the number of fingers on a hand, the total number of keys counting naturals and flats is 12 same as the number of months in a year. The tonic can be any of the 12 notes of the chromatic scale. The"fourth" is always a fourth, no matter what the tonic is. The fact is that any musical work can be played or sung in any key. The reason the two numbers don't "add" correctly is that one note is counted twice.

Lateralus is nice

a 1 is an 8 in western music theory. and, yes, it completes the octave. to illustrate that 1 is 8, take a chord like Cmaj13 - it is a Cmaj7 chord (CEGB or 1,3,5,7) with a 9 (D), 11 (F) and a 13 (A). a 9 is also a 2. an 11 is also a 4. a 13 is also a 6. by that logic, it would follow that an 8 is also a 1.

Yeah this is grasping at straws...the c note is counted twice. Also you spent an entire minute reiterating your argument multiple times. You had about 20 seconds of content. Keep it concise!

The song you would like to be finished has very little to do with the overtone series, yet you want it to be continued. (I play the overtone flute and it has a wonderful harmonic feel up till the 16th overtone.) Without the octave (= 8 or 13) you won't have any experience of 7 or 12 though. You wouldn't enjoy this piece and ask for it to be finished. So the octave does it. There are lots of reasons why the piano-tuning is compromised. I would recommend M. Renolds book on this subject.

To the one's that think this is "stupid". Research the Fibonacci sequence before judging. It may help you to understand.

What song is this? BWV Prelude 1 in C Major BWV 846 from the Well-Tempered Clavier

this is not lateralus

That's what I thought too. I think the point was that the fibonacci sequence somehow made a pleasing major add9 chord or something. Would be interesting to see if adding up the bigger numbers in the same way would make up a chord useful for pop-artists.

Lets get the views to 11,235,813 ;-)

The 8th white key is the same as the 1st, they are both the note C one octave apart. There are a total of 12 notes, 5 + 7

this is the answer to all classical music...wow thats how they wrote such masterpieces in such a short time they had.

Why would you count consonants anyway? Their number vary from language to language and it surely doesn't match the number of tones. There are 5 basic VOCALS that match the 5 full tones AND (if you like) one of the numbers in the Fibonacci sequence...but number 5 can be found in many other contexts, so it doesn't prove your point anyway (and especially not with consonants)..if you still disagree, make sure to explain it, not only claim it, I'll be happy to receive a reasonable answer, thank you.

A great inspiration.

my mother was a piano teacher and taught me this at age 4 because I was having trouble reading the notes and insisted on looking at the keys because they looked like mathematics to me.

inb4illumaniti

Fibonacci sequence in music Hello, everyone. First, thank you all for watching this video. Seems I have been touching a matter of importance to you, regarding the 100.000 plus hits. There has been a lot of debate here wether the Fibonacci sequence can or can not be applied to music. It can. Since the thirteenth i.e. eight note HAS to be included. It is very typical for the Western, so called scientific mind, not to be able to look at one thing as the completion of one cycle AND the beginning of a new cycle. I'm sorry guys, but that's just what music is. Be as so called "scientific" as you can, as long as Bach's music touches you, you'll find yourselves on my side... Any musician would agree with me...

The premise this video is based on is wholly untrue. There is no ratio of 8 white keys to 5 black keys. The eight white key is the original notes octave and itself starts a new series of notes identical to the first except double their frequency. The ratio of keys in an octave is 7:5 which means that everything extrapolated from that assumption is just plain wrong. This pattern exists in music, but not here. Look at the series of harmonic overtones for example: A=440hz this value will be represented by 1. In the Fibonacci sequence you have this pattern: 1, 1, 2, 3 or in hz: 440((concert A), 440, 880(A above middle C), 1320 (2nd E above middle C). Here is where, if the person who made this video actually knew anything about music theory, they would start to see the harmonic overtone series developing. But I digress, this video is trash.

The guitar is my favorite instrument, but it is not meant to represent "pure" music. The piano is designed for the sole purpose of reflecting and containing pure music, with black keys being accidentals, or pitches that "happen" to be there.

Man, it doesn't matter if they made it legal in your state, stop smoking it! And learn some music.

Another note, relating more the the arguments and the actual topic: I think the problem is that the C was included twice; i.e. C,D,E,F,G,A,B,C,C,D,E,etc. and C,C#,D,D#,E,F,F#,G,G#,A,A#,B,C,C,C#,etc. it works like this, but you shouldn't count the C again, because it's the same note. Yes, it ends a cycle and begins a new one, but it's still the one same note - C (not C + C). And NB: Maths and Music barely work together. As said before, sucks when you have 4th+5th=8ve O-o

1,000,000 views

Some errors of methodology. Forget the number of keys, they don't really matter at all. You dealing with frequencies, so proportions must me drawn upon them and intervals. 1/1 unisson, 2/1 just octave, 3/2 just fifth, 4/3 just forth, 5/4 major third, 5/3 major sixth, 45/32 tritone and so on. Apply the Fibonacci's sequence in this framework.

WHAT THE HELL ???????????

Does anyone know a tutorial that shows how this is played with a top down video of the hands? That would help me understand so much better! I kind of understand what the numbered keys are conveying but this whole sequence is so hard for me to grasp with out seeing it played. Very Respectfully Corleone

1337

Does this only apply in C Major?

The music is the ‘prelude’ (introduction) to JS Bach’s ‘Prelude and Fugue in C Major’, #1 of his famous (and influential) ‘Well-Tempered Keyboard’ collection of ‘Preludes and Fugues’. It was later used by Gounod as the accompaniment to his setting of the words to ‘Ave Maria’ (the Catholic prayer ‘Hail Mary’ in Latin).

If you take 7 glasses and fill them with water exactly the amount according to Fibonacci sequence volume. You will have the basic music notes

Is this why the Ancient Egyptians called Music, Frozen Geometry?

This Fibonacci sequence in musique is copyright to M. Sylvain Lalonde from 2006, if you want to see the original concept visit harmoniedesspheres

Please, explain me, what does this video want to show us?

I'm not taking sides here, but I've been singing for much of my life and never have I heard of there being a significant difference between B# and C, or Cb and B. The fact is, one can divide an octave into as many tones as one wishes however certain fractions of division will sound better to the human ear than others. Western music does use the same system as a piano for the most part. The only true rule is that a tone will be half or twice the frequency as the tone it is an octave away from.

How did that drag for two minutes. All the video says is there's 8 white notes and 5 black per octave.

Humans invented the C major scale. There are no natural breaks between, say middle C (261.6 Hz) and an octave up (523.251 Hz), just the continuum of frequencies. "In Western music, scale notes are often separated by equally tempered tones or semitones, creating 12 pitches per octave. Many other musical traditions use scales that include other intervals or a different number of pitches."

NO, the song is not "the well-tempered clavier". The WTC is a collection of preludes and fugues, which are all different "songs" if you want to call it that way. The one playing in the background here is a prelude to the fugue that follows, it's in c-major and its "name" is BWV 846.

Try playing the first seven notes of any tonal scale. It will always sound un-resolved if you do not play the final eighth note.

The point is that music is able to capture the very essence of a philosophy that is directly tied to nature, it is humbling and awe inspiring because it glorifies God with some of the simplest yet most significant blessings known to man, music, nature, symmetry and sequence.

If there're 8 white keys (the C is counted twice), then you have 6 black keys (count C#/Db twice). Any way 7 white keys : 5 black keys as well as 8 white keys : 5 black keys have nothing to do with Fibonacci. You could also say that a pentatonic scale has 5 notes and the diatonic scale has 8 notes (Fibonacci!!), but of course if you say that the pentatonic scale has 5 notes, then a diatonic scales has 7 and not 8 notes.

I think there's no difference between black keys and white keys except for their shapes and colours... Why does the video says there's a pattern ? It's weird

Oh, no no no, not like that(!) The two ones come from the full sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. The reason why we're saying that the C shouldn't be repeated is that it's just one C. It acts like another note; e.g. In C major, the B is the 7th - C is the 8ve - the next D would be the 9th. Otherwise, C would be both the 8ve and the 9th (doubled...and this would screw even more maths in music). But, yeah, at least there's a bit of Fibonacci in it... :-)

the 8th is just the octave and would not count, because the note C is played twice. although you might consider fractals in the C Major scale. CDEFGAB EFGABCD GABCDEF BCDEFGA DEFGABC FGABCDE ABCDEFG a tool i use to find all the modes and chord tones. if you look there are alot of repeating patterns that note chord/scale relationships. this is just one iteration that can be repeated infinite times.

the real proportion of the fibonacci series can not be demonstrated on a western tuned piano. for example: the true frequency ratio of 2 to 3 would be a pure fifth and not a second of the equal temperatur.

Nothing about musical scales/modes is arbitrary. And the thirteen notes in an octave are not "equal parts" - each chromatic increase in frequency is exponentially greater than the last, such that one note is twice the frequency of the note an octave below - a ratio of 2:1; a fifth has a ratio of 3:2. None of this is coincidence, nor is it an approximation of nature. The systems of harmonics we use are a product of nature - what is pleasing (and otherwise affecting) to all humans intrinsically.

What is the song in the background?

Is there any relation to the Circle of Fifths?

Whats the name of this Bachs composition?

I think the authors should explain first, where there is the link between the F-sequence and the music scales .Normal audience will not understand this.

Ehat about f, a, and g? And thr black keys?

There are seven distinct keys in an octave. The eighth key is a repetition of the first, which is why it's referred to as one octave above the first note, and this key is the first key of the next octave. Put another way, if you go up white keys of a piano in eighth notes in 4/4 time (eight notes per measure), each measure will start on a different note. No matter how you slice it, a diatonic scale is not a repeating pattern of eight notes - unlike, for example a bebop scale, which is.

if you start from A# (Do = A#), then it would be 6 blacks and 7 whites.. how do you explain that?

In music we consider an octave as having 12 half tones (not 13). We do not count the octave because that is the 1st note of the next octave. I have been a musician for 27 years. Mathematics is what music is all about. Particularly the frequencies of the tones, but also rhythm. Lots of mathematical relationships in music. I just thought this video might have some valid info on a mathematical relationship in music that I was not aware of. Your point may yet be valid, I just don't see it, yet.

And, as Kratanuva said, this is just wrong. The octave is NOT included. That's why we talk about 12-tone scales, etc.

Could Fibonacci sequence be forming spherical waves of light? "Within every ocean of waves is always pressure at every point. Mass plasma field vector acting upon every point of space as inward waves come from a distance radius compressing+4-0-4+-decompressing two opposing vortices out of existence, or multiplying input+0/1-output dividing forming the sinusoidal wave medium density (space) at each point of space. Multiplied into time dilating inertial ref-frames within active cores of galaxies."

The 13th key is the first note of the next octave up. I.e. the root of the scale, transposed up an octave. In C major you can play a fibonacci-esque sequence by playing C, D, E, G, C (the root, first, second, fourth, and eighth). You should be able to do this for any of the chromatic scales.

Yes, we DO count the octave. All music depends on it!!! Listen to all tonal music and ask yourself whether you could appreciate it without the octave... It's like the Alpha and the Omega, you know? In case you don't know, I give up...

Of course an octave without the 8th note will sound unresolved. But patterns don't resolve; they repeat. That's the whole point. The idea with looking for golden ratios is to find _patterns_ of 8:5 or 13:8 or whatever. But in the western chromatic scale the pattern is 7:5 and 12:7.

Ave Maria by Bach / Gounod. What do you mean "no"?

We have a scale that equates to gradations of the 12th root of 2 as well as a set of whole-number ratios. However, we must remember that the western major scale has evolved over time (e.g., the dispute between Bb and B as the seventh). Nevertheless, you make a good point about the occurence and positioning of the # and b black keys on the pianoforte.

I don't know enough about the maths or music to comment on the connection between the two, but I do know this is beautiful. Thank you.

True..and in this case how comparable is the cycle C1-C2 with 1-10, when missing the originating 'unity' of 0? Also, to maintain the sequence the next note will be G# etc. Bottom line: 0-10 (decimal) and C1-C2 (octave) are cycles with positions therein, whereas Fibonacci numbers merely denote positions when number is applied to the golden ratio. Makes a nice pentatonic scale though :)