The Fibonacci sequence in music

A few weeks back there was a really interesting article in the Guardian newspaper (UK) about the Fibonacci sequence and applying it to music. The article was written by Vijay Iyer an American of Indian descent , who writes and performs on piano. After reading the article I checked out his track “Mystic River” on the Historicity album. It’s seriously good and you can hear it on Spotify if it available in your country.
http://www.guardian.co.uk/music/2009/oct/15/fibonacci-golden-ratio - the article
http://open.spotify.com/album/3I3uK5mo0uvj4TnSCxS2zk - link to Historicity

I realise the Fibonacci sequence might not have any application to Irish Trad. (Or does it? It seems to have come up before in previous discussion on this board.) Mathematics and music seem to have an affinity.

I think there is no inherent linking between those, while you can see math all over the music, this article seems to force a mathematical construct on music. If this works out (i can’t listen to it, i trust you on the quality), it’s due to a good musician rather than the inherent beauty of the fibonacci numbers. for some actual examples of ratios close to phi you can read
http://en.wikipedia.org/wiki/Golden_ratio#Music
but mind the citation at the end of the paragraph

In the opinion of author Leon Harkleroad, "Some of the most misguided attempts to link music and mathematics have involved Fibonacci numbers and the related golden ratio."

PS: forgive me for citing wikipedia, but it sums my opinion up quite well.

Lawrence Blatt has an album for guitar out that claims to be based on Fibonacci numers, etc. Seems more or less like a gimmick to me.

"… this article seems to force a mathematical construct on music." I’m 100% with TMB on this.

Artists and architects often deliberately use the Golden Ratio (the end result of Fibonacci series) when designing their works, with results that are usually very satisfying to the eye, even if only appreciated subconsciously. But playing music - no. How many of us think about maths when playing music? Working out a bit of Fibonacci to put swing into reels?

Some composers today may play around with mathematical techniques, and composing using a music editing program certainly makes the process easier, but such artificiality is obvious in the end result. There’s nothing new in this, btw; in the Renaissance there were composers who played around with the most incredible cross-rhythms and time signatures - which are next to unplayable as written - and even Mozart apparently devised a method for composing minuets by rote, but perhaps as a joke.

I know someone who used the golden ratio in working out what swing to make his cubase play a reel. Sounded bloody awful, as you’d expect. He said so himself.

I think that most music is a product of convention and instinct … two very uncomfortable bedfellows to science and mathematics.

@llig leahcim
I agree about convention and instinct. Although I think that you can see math behind a lot of what "instinct tells me", like the intervals in just intonation. What my ear tells me is pleasant has certain mathematical properties (very simple fractions). But I do think that such observations might be interesting, but shouldn’t be part of considerations when making music (apart from deliberate experiments, but as lazyhound pointed out you will hear it in the end result).

My dog could do the integral calculus necessary to calculate the trajectory of a biscuit and catch it in his mouth.

But this was in fact a "product of convention and instinct" - not a conscious mathematical calculation.

Music is probably best done the same way.

There was an interesting theory that brains were using complex calculus when performing tasks like catching balls. But experiments disproved it. I remember one where they had a really good slip fielder. They measured the speed of the neural connections and how that they are able to pass information to muscle movement etc., and found that even if that brain had the calculation capacity, it lacked the speed with which to use it in such circumstances. The only explanation for the ability to catch a ball at such high speeds is that the brain is estimating where the ball might be and pre-empting. And it can only do this after much much practice. Though how much is actual hard-wired-to-your-dna instinct is a different matter. I suspect more so with a dog than a human. (maybe a dog would have better luck batting against Shane Warne)

However, it’s interesting to note that much of science and mathematics is counterintuitive. Probability is a good example and casinos make much use of it. In roulette, if black comes up 10 times in row, everyone puts their money on red, even though it’s 50/50 that red will come up (discounting the green of course). And I’m always amused by the statistic with the national lottery where the odds are much much better if you don’t bet until the very last minute. Not because you have a greater chance of winning when the numbers are drawn, but because you’ve less of a chance of dying in the mean time.

I always thought that music was sort of God’s clue for us as to how He creates

If you buy all that quantum mechanics and particle wave duality of light stuff, and throw it on the fire with the equivalence of energy and matter and then boil it down in chicken fat, you get to the idea that all the matter in the universe is energy at some sort of resonance (Sum of the Histories is what Dick Feyneman calls it) and so…

everything you see around you is simply God whistling a tune

I’m not sure what tune it is. It sounds sort of like the Merry Blacksmith, but the B part is different and its in a different key

but the point is that it isn’t music and math that are so related

its music and nature that are related, and we humans use math to try and find patterns in both

Very nicely put, Nate.

That’s what I was about to say Nate.

Except that I thought the tune was Old Hundredth.

Strangely enough you can increase your Lottery ‘expected winnings’ simply by choosing numbers above 31. This is because a lot of people include birthdays in their chosen numbers, so if you do win (with numbers below 32), there’s a bigger chance that you will be sharing the prize.

“…but the point is that it isn’t music and math that are so related
its music and nature that are related, and we humans use math to try and find patterns in both…”

Oh, that’s good. I’m gonna quote it today.

pattern and repetition in a pleasing sequence, we love it:

http://www.youtube.com/watch?v=DfJa3IC1txI&feature=related

play video

http://www.youtube.com/watch?v=RqRd555v0Hg

play video

http://www.youtube.com/watch?v=ukyHLv8Ulg0&feature=related

play video

I certainly hope God is a better musician than I am!

Nice links Dujera Dubh. Have you seen these?

http://www.michaelbach.de/ot/index.html

we’re always looking for the patterns, consciously or unconsciously, that’s why the music is so powerful:

http://www.youtube.com/watch?v=4xRIOwP_CEc&NR=1

play video

thanks, sash, I can see I will have hours of fun with that!!

These are pretty good too.

http://ericbigas.com/fractals/index.html

That’s if your eyes haven’t gone all funny like mine just did, Duijera Dubh!

"everything you see around you is simply God whistling a tune"

🙂

I am going to ponder that one today.

It’s not your eyes, sash! moooohahahaha!!

seeing how the thread is going visual here are some grand drawings;
Kseniya Simonova’s Amazing Sand Drawing
http://www.youtube.com/watch?v=vOhf3OvRXKg&feature

play video

Thanks to everyone for contributions on fibonacci, maths, music etc. Some interesting links too. I was interested also to find out people’s views of Vijay Iyer, as I have just discovered him through that article. Great track below (but not fibonacci influenced as far as I know).

http://www.youtube.com/watch?v=pOBhrnOzwXw&feature=related

play video

I just read the article and it strikes me as pretty darn close to nonsense.

It is irrational. ;)

One of my favourite books is mathematical writer Underwood Dudley’s _Numerology, or, What Pythagoras Wrought_, in which he states the Law of Small Numbers: there are not enough small integers to carry out the many tasks assigned to them. Dudley handily debunks many of the mystical properties associated with the Golden Ratio as well. (Yes, the GR comes up a lot in math. No, the fact that an approximation of the GR appears when you inflict some contrived sequence of computations upon the measurements of the Egyptian pyramids doesn’t mean anything, and in particular, is not proof of the existence of God.)

Anyway, this bit from the linked article says it all: "The goal is that you perceive the "short-long" division of the cycle the same way in each case. ***Thankfully the ear is forgiving***: because we expect and even crave continuity in our perception, our listening brains help smooth things out."

In other words, this music sounds decent not because of its connections to the Fibonnacci sequence, but IN SPITE of them. (In other words, what TMB said in the first comment in this thread - I am amused that the article’s author, who praises the composition, seems to agree with that!) A composer’s lofty mathematical intentions are overridden by our subconscious notions of what music should sound like.

Pity, because there are plenty of legitimate connections between math and music. (I heartily recommend _Music: A Mathematical Offering_, available in its entirety here - http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html - for those so inclined. It focuses more on sounds than music per se, and the author is careful to note that he is not attempting to deconstruct or quantify the emotional appeal of music - something that the Fibonacci composer, the author of the linked article, and too many contemporary music theorists, do in abundance.)

TDM, many thanks for the Music-A-Mathematical-Offering link. It’s a very useful update on my old copy of Helmholtz.

TDM - Thanks for mentioning Dave Benson’s book. My other half is a mathematician and he has now put it on his Christmas list.