How Composers use Fibonacci Numbers & Golden Ratio | Composing with Fibonacci
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- Опубліковано 5 вер 2024
- In this video I discuss the relationship between the mathematical sequence known as the Fibonacci Sequence, as well as the Golden Section.
The Fibonacci Sequence was first proposed by Leonardo Bonacci in his 1202 book Liber Abaci -- the Book of the Abacus.
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Roy Howat's book on Debussy and Proportion: www.amazon.co....
Bela Bartok: An Analysis of His Music Paperback - 31 Dec 2000
by Erno Lendvai
www.amazon.co....
This talk PDF by Howat gives a good overview of what's available in his book:
symmetry-us.com...
The full score for the Chopin Prelude in C major Op.28 No.1 is available free on 8notes.com at www.8notes.com...
Thanks to Gavin Thomas for research and script writing.
I created an Indian raga in the 80s using the Fibonacci sequence to generate to intervals. I ended up with the rare but known Raga Bagh Kaush which scalewise is a mode of the very popular Raga Todi.
Fascinating!
Is it possible to hear your composition somewhere? If you could share a link it would be very welcome.
All that is irrelevant and outmoded. Serialism is the music of modern civilization.
Just taking a Math 101 class. This is my first introduction to the Fibonacci sequence. This video was amazing and very informative in explanation. Very beautiflully written.
I am an math teacher. We need to teach a lot more about stuff like this than calculation ad nauseum. No wonder so many people don't like math. They don't even know what it is
Patrick Leahey that's awesome. This is actually the first math class I haven't hated with the passions fires of hades. Totally an online class. It introduced me to so many areas I never dreamed in math. And I pulled out a decent grade. As a math teacher reach out to that one fringe kid that ekes by. You might change there world. Teachers rock.
This is SO GEEKY. I LOVE IT. And I have played Prelude in C when I was in college. I really enjoyed this video. I am trying to understand Fibonacci sequence to music and mathematics. This video put a smile on my face because Debussy is one of my favorite composers. This is going to make me study more on this subject. Please post more, and also anything connecting the classics to the sequence. Thank you so much
4:58 "(...) you are at the golden section(...)" Five minutes into a 8 minute video.
Glad you spotted that, I was proud of that. (only joking, well noticed!)
8 minutes and 3 seconds is not 8 minutes; 4:58 is not five minutes, so the system fails. Approximate is not good enough, it has to be exact to be proven.
Definitely good enough.
You are clearly not a mathematician.
I would say that the golden ratio is a mathematical formula that can be applied with expressionistic intent, and thus close enough is good enough in this case.
Intuitively I knew this for a while.
Nice to see it put into words and pictures.
The epic part of the song starts when the songs is 60/65% done.
Bartok's Music for Strings, Percussion and Celesta has some Fibonacci going on too, doesn't it? I remember having my mind blown in 20th century theory classes over that.
I think Bartok developed a whole composing technique based on the fibonacci sequence
I studied the choral music of Bartok - he uses the Golden Ratio all the time - both positive and negative.
Roy Howat actually gave a presentation on this stuff at my composition seminar. It's really interesting stuff.
Another interesting example is the first movement of Rachmaninov's 2nd Piano Sonata, where the main theme of that movement uses the fibbonacci sequence in semitones
F -> E (1) -> Eb (1) -> Db (2) -> Bb (3) -> F (5)
Arvo Part also uses the Golden Ratio in his compositions - the best example is in Magnificat. It’s a composition technique he learned from the time he spent studying Medieval Music - especially Dufay.
I came here after reading about how Debussy had believed to use the Fibonacci sequence in his music. I’ve been playing music for my whole life not even knowing this. This was real learning experience, Thanks!
Ended up here again after seeing another video on the Fseries. In the case of Chopin (and probably many others) I think there is no Fibonacci involved. Think of the piece this way:
melodies (and other musical structures) often come in lengths of two bars (or multiples). So, having an eight bar structure is nothing special. In the next eight bars something gotta happen, some deviation of the pattern (!) setup in the first eight bars. If the change were to happen right away at bar 9 we would think of it as a second theme but that's not what The Romantic Soul was after: something new isn't as surprising as something familiar that suddenly (when it gets repeated) takes an unexpected turn.
So, where to put the twist? If the music is strongly structured around the harmony it is usually at the first bar after the first half of the structure. So that would mean at bar 5 (OMG another Fibonacci number!). So that would be bar 13. And where is this point at the next eight bars? 8+8+5=21. So, nothing special, nothing metaphysical, no numerological juggling.
Well, it's not like the flowers and shells and trees in the wild are consciously planning out these sequences either. The point is that they emerge *naturally* in nature. So, the fact that what makes sense musically is also aligned with the sequence fits the whole idea. Sure, it's not metaphysical or numerological, but it's certainly a "special" feature of our reality. At least, that's my take on it.
There was so much care and interest put into this video, it does Fibonacci proud.
John Chowning's 'Stria' (1977) is the best example of the golden ratio in music so far, in my opinion. The golden ratio is baked into the timbre and tuning of the piece and it sounds totally different - it ain't no weak sauce trick where you have to count bars!
Really like the topics you adress! This is only the second video I've seen at your channel but I'm already curious for the third one. Up next: The cutting edge of jazz swing theory!
A strange thing; This concept of neat ratios of bars in music divided with important sections, I've actually thought about this even before seeing this video. This is the first time I've heard of the concept of adopting the Fibonacci sequence into music. It makes a lot of sense.
This is fabulous and it strikes me funny that someone with such a logical mind should have a shade that is askew in the background.
The mathematician Charles Henry was the one who taught Debussy the golden ratio concept.
Very nice video. Thank you
I just checked where the climax is in Canon in D (my favorite piece) and I'll be doggone it is so close to the golden ratio. Amazing!
The golden mean is the ideal section. The proportion itself is the guidance to beauty. Music, being art expressed in series of repeated frequencies, should follow this majestic sequence in order to exist at its utmost quality.
It's all totally incredible! Intertwined in nature, music, and art is totally fascinating. Something is going on here.
the Fibonacci numbers are used when building a guitar, to set the frets. The fret on a guitar have a changing ratio of length. I didn't do it myself but was told about it by someone who builds guitars.
www.liutaiomottola.com/formulae/fret.htm
Doesn't refer anywhere to that idea, I suspect it is a fanciful notion.
I made a set of large wind chimes using one inch diameter steel pipes, the formula for tuning them to each other was made using the concept 'the twelfth root of 2 is the same as 2 raised to the 1/12th power'!
It worked rather well.
I’ve been binge watching all these videos, they’re fantastic!
Actually, no I don't feel the Chopin example audibly lines up with the Fibonacci sequence. Yes the first section is 8 bars long, but I don't hear the audible event happening on the 8th bar, I hear it on the 9th bar when the cycle repeats. 9 isn't in the sequence.
Oh ho! Maestro David just sent me into an altered aesthetic consciousness with Debussy!
The only reason I watched this clip, is because I found out by chance, that my compositions, and each movement in them, were structured almost exactly around the golden ratio - I was struck by this discovery, so I decided to investigate this topic a little further, and I took Beethoven's music and found out that he too based it around the ratio of Phi... I must say though, that only those movements that I wrote in minimalist and atonal styles where not structured in Phi ratio. Thank you David for making this clip about this topic and making me feel a bit less weird about myself.
NERD ALERT! or as other people call it, the notification bell! You have my type of nerdness! Thank you!
Here's a fun general rule of thumb I keep in the back of my mind... suppose you're constructing a three-large-section piece, and the first big part is Z measures in length. If you make the second big third Z x 0.618 bars long, the third big third (assuming it's Z measures long) will begin at the Golden Section of the work. This helps me a great deal, though I don't necessarily stick to it religiously. And for what it's worth, I've always believed that musical composition is closer to architecture than "math."
Lateralus by Tool. best use of fibonacci and golden ratio in music. works so well.
.. and of course, π (pi) pops up every time we play a round *ba dum tss* but seriously ty for posting : )
Chopin's prelude also has a 5 notes motif and a 3 notes accompaniment ;)
1:48 As a mathematician, I find it troubling that you jump from natural shapes to beauty without reason or evidence. Everything in nature "looks" beautiful, including cancer cells. Finding the same curve repeatedly in natue is a product of confirmation biases.
Before Fibonnaci (which is not his nickname, but a name given by scribes and scholars many decades after his death so as not to confuse with the more famous Leonardo), the western world was obsessed with pi. Later obsessions revolved around other numerical ratios and their corresponding geometrical curves.
There is no inherent "beauty" in one curve in nature and absent in another. All curves are beautiful when looked in the right way. Paccioli wrote entire theses out of whole cloth about how he uncovered the mathematical secret to beauty in painting and architecture. That secret he thougt was the fib ratio. Luckily for us, his own roommate for several years, who was also an artist, didn't think beauty can ever be reduced to a math formula. That roommate happened to be Leonardo di Vinci.
So if you don't mind, I'd suggest you stop the b.s.
Cheer up bud.
Avocado Pirate: Well Put!
Great video explanation.
I am quite a distant relation to Bonacci and very happy to find your video !
It works well for the point where the recapitulation begins in' common practice period' music...Simply because 50/50 symmetry leaves the recap sounding too long...and generally recaps are more 'compact', so in a way if you were to stretch out the musical material in time, the sides would be equal
Perhaps you’re familiar with Karl Berger (jazz piano/vibe/composition). He taught and expressed the application of the Fibonacci approach to melody. That is to use it in any way produced thoughtful sound results. Thanks for the musical education restart !! Fantastic insights !!
This is very close to Adam Neely's work, great ! :D
Here's a rather direct occurence of Fibonacci Numbers in music:
The number of rhythms consisting solely of 16th notes and 8th notes (and no breaks) corresponds to the fibonacci numbers for a given rhythm length:
Rhythms of lentgh 1/16: 1 possibility (just one 16th)
Rhythms of length 2/16: 2 possibilities (two 16ths or one 8th)
Rhythms of length 3/16: 3 possibilities (three 16ths or 8th-16th or 16th-8th)
Rhythms of length 4/16: 5 possibilities
Rhythms of length 5/16: 8 possibilities
and so on...
This is analogous to the number of possiblities to walk up a stair with a given number of steps if you only allow yourself to take either one or two steps at a time.
If you allow the rhythms to include dotted 8ths as well, then you get the tribonacci numbers instead.
What about Lateralus by Tool?
I came here after watching a video by Paul Davies where he composes a song usig Golden Ratio (and having a cool/strang conversación with a visual artist who considered Paul Davies work as "nonsenses" because of the way he aproaches golden ratio. It will be great to know you opinion on what Paul did, I think he created a groundbraking rhythmic pattern that reminded me microrhythms. Also listen to Luca Belcastro, he uses golden ratio as a tool to place musical events through a piece creating organic musical landscapes.
Great video.
Also... Is the add placed near the golden ratio?
I wonder if the time between notes in a ritardando might be Fibonnacci based. As a piece slows down more and more, we approach it as feel, but maybe that feel is a subconscious representation of the Fibonnacci Sequence. I'm just spit balling.
Fascinating stuff, no doubt. Can't wait for your next video.
many thanks!
Good show old chap! Very good indeed!
You not only answered my question, but caused me to think of many others!
Thank you so much for that!
JMM
What about the major pentatonic scale? 1, 2, 3, 5, 6, 8. Remembering that a 13th is just a 6th up an octave. 1, 2, 3, 5, 6, 8 vs 1, 2, 3, 5, 8, 13. Also look at a bass clef.
Keep the geeky stuff coming! Loving it!
I tend to pan instruments at 38% and 62% when 100% is too wide. I was experimenting with ways of dividing the stereo field that felt as spatially "defined" sounding as dividing into 5 equal parts and that was the winner. 38% and 62% seems to be more spatially distinct than using multiples of 33.3 (0%, 33%, 67%, 100% L/R) but that's probably more to do with brain knowing theyre "Golden Ratio Certified" numbers than anything I actually hear lol.
I have been thinking very much about composing a piece using this ratio; In fact it has been constantly on my mind of late. I want to find the corresponding colours and shapes for a design for the artwork too. I have bordered on a fixation with this as someone who heard a piece I had written for a gig said "I get it you used the Fibonacci sequence, cool man". Hmm I thought and left it, being busy at the time, but returned later to investigate this idea. It is true although not planned that way; the piece was in 3 movements, it's timing was 5/8 and it's speed 140 not quit 144, it reached the peak at 83 and had 21 chord changes. I guess that qualifies, As the pc i had it on has died I am going write another, having lost the original. It was a very sad loss, i was very proud of that piece. ( I thought i was smart writing in B flat minor 7), for a more orchestral/jazz sketch that grew out of all proportion. Great video, thanks i have been re-invigorated.
When I was in school the maiden with the flaxen hair was used as the example to show this. It works down to beat numbers in that piece.
sound is a spectrum not just time. This topic can have more dimensions
Applying the fibonacci sequence to music is like trying to apply complimentary color theory to sound. It's just not applicable. The sequence and the ratio are about VISUAL balance. We do not perceive the movement of time the same way we perceive visual information.
you are so profoundly off........you have no idea.
That was a great video. Now I know how to compose music. I'm off to my drafting board & slide rule to lay out my next unappreciated neoclassical peace/I mean piece.........
Brilliant presentation. I am working on sounds created by ancient structures such as pyramids and stone circles etc.
I can imagine the Beatles sitting around discussing how to incorporate these concepts into 'She Loves You' and 'I Want to Hold Your Hand'. No..actually I can't.
It's the choice between "Do I incorporate mathematical discipline into my songs in the hope that one specific formula might unleash beautiful melodies or do I just record what pops into my head?" Fortunately for us, The Beatles went with the latter.
Fabulous video. Thank you. I have just subscribed.
Nice geekiness for me Bruce, I'll see if I can squeeze that into 10" cutdowns! HNY BTW ;-)
The existence of the Golden ratio in nature had to do with efficency, but I agree that it is related in how we experience visual beauty. However, I don't see the connection you're making between Fibonacci and music. Choosing one of those numbers to place the musical climax is completely arbitrary, as I see it. Maybe regarding the frequencies or rhythm?
Maria José Garicano well I suppose it depends on how we experience time . If using the golden ratio in architecture makes sense where we experience the whole thing at once (premise) does it also apply to something we experience over time ? You could argue that climatical point of sonata form is around 2/3 of the way through when the recap starts - does the exact ratio matter? And Hollywood comedy romances films of 90 minutes usually have a dramatic point 20 - 30 minutes from the end - slightly more than 2/3 of the way through. May be in a temporal art form the past get psychologically compressed so that is why it needs to be slightly later ?
Very interesting. Thank you
1:43
Not a series, it's a sequence.
David, just reminded me of a lecture on Beethoven’s Fifth by the late David Osmond Smith, our tutor at Sussex, in which he showed how the climax of the first movement occurs on the golden section. My memory is hazy as this was in 1987 so I might have the info wrong but nevertheless it struck a....chord ( sorry)
Can any one adduce any examples of great music that DO NOT exemplify Fibonacci sequences? Would the lack of any identifiable presence of the sequence preclude these works from being great music? In other words, would we be mistaken in our love for them?
In short, composers may use any number of esoteric rationals for the structure of musical works, but these rationals are, in the final analysis, irrelevant to the appreciation of the music as an auditory phenomena.
Best explanation on that subject
So helpful thank you!
Dig it!!! great food for thought. But can not all divisions of natural phenomena be measured using any systematic numerical scale? With equal time sequence between events.
Music is not the most mathematical. The complete spectrum for sound is known. Try making something that needs an element not discovered yet. We need better math to create the rest of the elements on the periodic table of elements. But I get your point.
This is quite amazing.
If the Fibonacci sequence is truly the natural order of things then it's only logical that highly talented people would chance upon it in structures especially in creating art forms of a mathematical nature such as music.
This is very inspiring fundamental stuff.
This is quire wonderful. I'm working on using golden ratios in time to provide a structure for free improvisation. I always come to your videos when I'm working out a concept..
Why can't it be applied to scales, chords or notes?
Thank you for your knowledge!
Is there a divine chord?
insightful video, thanks
Does the crooked blind have some Fibonacci significance?
I think you'd better count the slats on each side and work out the meaning!
So the den's apparent randomness is in fact elegantly composed....
Great vids by the way
...something like that! Thanks for watching!
that was very interesting- thankyou
Really nice your channel, I hope that youl grow to have more suscribers.
many thanks!
Glad I found this! (I thought I had already seen all your videos, but this one must've fallen through the cracks)
I'm going to be writing a theory paper this month where I test out some of Roy Howat's analytical approach on a Debussy piece that isn't one of the ones discussed in his book. We'll see if I can find these ratios in it, and if so, I'll have to see if I'm forcing it or not...
Im almost certain Clare De Lune was made the same way it has a Fibonacci sequence
thx a lot
Very nice
What about intervalls? The overtone series works with multiples, but what intervall do I get, when I take the golden ratio of the frequence of a tone? Maye we could this to construct an alternative harmonic system?
I'm willing to bet there's an Adam Neely video about that.
thank U man.
Very Impressive!!!!
Gábor Kósa is composing in a system based on golden section: the golden sixth is used to periodize the scale, divided into 9 equal tones. The property of the golden section means that when a golden sixth (with frequency ratio Phi) is played, then the first difference tone is a golden sixth lower than the base of the original interval, thus reinforcing the period bounds of the infinite scale. one of his pieces can be heard at
ua-cam.com/video/Uq2uqXSIojw/v-deo.html
Thanks....
nice video
Most interesting...but PLEASE: The sequence of numbers 1, 1, 2, 3, 5, 8, 13, etc was described by Fibonacci around 1200 AD. However, the Indian mathematician Pingala found the sequence at least 1,000 years before Fibonacci...(probably 200 BC).....while analyzing Sanskrit poetry.!! Fibonacci pinched it!!
It's very doubtful that a 12th century European could have had access to Pingala's work. (Perhaps you know how Fibonacci could have, and can share that here?) So, probably not "pinched", but discovered independently.
@@memereference2545 More likely pinched.The numbers originated in Ancient India and were taken by the Arabs to Europe. Also, Newton and gravity.
Well said.
well said to Eric Fairman
@@jsmith3980 Again, if you have evidence of 12th century European access to Pingala, please provide it. Arabic (Indian) numerals and Fibonacci sequences are not the same thing, and transmission of one does not equal transmission of the other. Which is just common sense.
Golden! Thanks!
I don't care about the theory. Just the cute rabbits
I'd say about 95% of most music has an 8 bar intro...
all that is not compleetely true. the golden section/ratio is not only ratio and for sure not main in nature. people know other sequences as we call it silver bronze etc sequences/ratios and all of them have their place in nature harmony if you wish. But maybe for the peoples body golden ratio may be more accurate but bronze and silver look more ellegant for me.
Though all such seq. share the same method.
Pn=N*Pn-1+Pn-2
"n" is the position of number you callculatin'
In Golden ratio N=1. Silver N=2 bronze N=3 etc any you like.
thanks, as always :)
fascinating omg can't believe there is so much maths on music
love this channel
interestingly enjoyable
Keep it up! Great!
Coincidentally, I almost smelt the rabbits. Not kidding.
Came here expecting to see Tool, but oh well I keep forgetting that I watch videos dedicated to actual composers
I am slightly disappoint that the video isn't 610 seconds long...
the Golden Spin
dig
I was reading da vinci code and I ended up here
Mathematicians always talk as if numbers are the real thing, as if they came first and everything else followed according to their dictates. Maybe if you are a theist and your god is a mathematician that would make sense. Like words and brush strokes, math is just another language used to describe phenomina in the natural world that already existed before the language was created. You don't say that birds became yellow or brown as a result of the words yellow and brown. Hence, a composer does not have to know anything about math for the music to reflect the phenominon described by math. That composer could also access that phenominon simply by direct interaction with the natural world in which that phenominon exists and always has, long before the language called math. We humans are like kids who learn about something after looking through a rolled paper "telescope" they created, and then want to explain the thing to everyone else because they assume that their discovery is the first time anyone has ever run across that thing. And they think the rolled up piece of paper they used to observe it is magic and somehow created the thing they observed. We really need to get over ourselves.