What is the relevance of the Fibonacci Sequence?

So I read up on the fibonaci sequence (sic, though i really don't care.) So they say its a ratio that exists, and is a "golden ratio." Most of the stuff about it is bullshit, concerning, say, spots on ladybugs and the number of drones in a hive, the seasons, and whatnot, because the natural world is far fom being as well-proportioned as Pythagoras would have one to believe. But even if, say, there is truth to the golden ratio, or whatever it is, what relevance is it to music? Does it magically make one's music pretty?

I remember this guy claimed Debussy used it, though he was proven to be bullshitting. And even when composers do use the golden ratio, and "say" they use the golden ratio, I don't get how that added mysticism does anything to make the music any better than if it was ignored? It's just a number. What's so special about that ratio as opposed to say 4:2345 or 234:12384535?

Maybe I am far from being a mathematically minded person, but break my ignorance, I just don't get it ;)

So I read up on the fibonaci sequence (sic, though i really don't care.) So they say its a ratio that exists, and is a "golden ratio." Most of the stuff about it is bullshit, concerning, say, spots on ladybugs and the number of drones in a hive, the seasons, and whatnot, because the natural world is far fom being as well-proportioned as Pythagoras would have one to believe. But even if, say, there is truth to the golden ratio, or whatever it is, what relevance is it to music? Does it magically make one's music pretty?

Actually, it isn't bullshit, it's fact. Lots of nature conforms to mathematical sequences. Pine cones, for instance, are rooted in the fibonaci sequence. Lots of biological processes are governed by timers that operate, in some cases, on prime numbers like cicadas. The number of drones in a hive is controlled by the colony and is highly organized, just not in the usual sense.

Actually, it isn't bullshit, it's fact. Lots of nature conforms to mathematical sequences. Pine cones, for instance, are rooted in the fibonaci sequence. Lots of biological processes are governed by timers that operate, in some cases, on prime numbers like cicadas. The number of drones in a hive is controlled by the colony and is highly organized, just not in the usual sense.

And those facts and others are precisely why I love nature, it always finds ways to surprise you ;)

And those facts and others are precisely why I love nature, it always finds ways to surprise you ;)

Oh, that's certainly true!

The way I look at it, you have to choose a career in which you're constantly surprised and fascinated by new input. Nature never ceases to amazing me.

On a side note, relating to fascinating issues, Will, did you realize you have several thousand genes for smell in your body that you can never use? Talk about fascinating, we're walking around with extremely wasteful DNA!

A good house-keeping gene or two was never a waste ;)

I'll try to explain without a pic, which can be tough... (and no, I won't borrow one from wiki, everyone can go to wiki and check for "golden ratio").

So the idea behind the golden ratio comes from the ancient greeks, I believe (btw, modern greeks have nothing to do with their ancient bloodlines, and I hate nothing less than people going about for ancient greece and things they did and how this reflects what greece is today and blah blah. ;)).

In geometry, the ancient greeks had an obscession to do things the simplest way possible, without measuring. So the golden ratio, is actually one of the geometrical/mathematical problems, that needed solving with only a tape (not a measuring one), and a diabitis (how do you call that in british? that makes circles?). Pretty tough thing to do.

Golden ratio is a certain point in a straigh line, which devides the line into two unequal parts: a and b (b being the smaller one), let's assume. In order for that to be a golden ratio it needs to be : b/a=a/a+b. There are only two points in that line that correspond to that simple rule, and it's the golden ratio. In maths, it is approximately 5/8 (or 8/5 actually, but the 5/8 is mostly used).

It is met in nature in various forms and people, because of the fibonacci series, which connects directly that that, have used it extensively, from the Parthenon to A4 pages (where 2 A4 pages equal 1 A3? and so on... the principal is the same).

In music it is mostly (but not exclusively) used in the form, where a climax or a division of parts, or something simmilar is at the golden ratio of the whole piece. The fibonacci series, being a series of numbers, 1,1,2,3,5,8,13,21,etc can provide many uses as well. Maybe the way that a series progresses in the octaves, maybe the way that voices are inputed, maybe something else, dunno...

The difference to having 61% (the golden ratio), to some other percentage, I don't think that it can be proven really. It's mostly good fun and maths for the composers who like that. Plus it takes perfect performance to get it right in timing issues. However I do think that without the golden ratio, to another point, maybe there would be less "driving" of the piece, and thus less sense of "architecture".

No idea if it helps...

There was a study that asked people to draw a "nice" rectangle (well-proportionned or so). On average, it was gloden proportion. Greeks built temples based on this proportion they called divine.

Anyway there is a book somewhere that explain how bartok used fibonacci and other sequence to build some works....

I know a composer using this technique to write music.

It is not my prefered music, but it sounds very homogeinous, somehow, which is not expected....

Bartok has used many techinques apart from that! In many works. And other composers as well

Berio, Ligeti, etc. (Can't name works for a specific reason and I apologize for that).

A composer using this technique to write music: Nikolas Sideris teeheehee

homogeinous: Can you explain this a bit better? homgenous, means with all the voices moving at the same time, in contrast to using counterpoint. I can't see much relation to the golden ratio, or the fibonacci series...

To those interested I posted a work, where I use in the form the golden ratio principals: http://www.youngcomposers.com/forum/continuity-solo-piano-cd-7914.html#post107259

I remember reading once that the "golden mean" as it's called, as a ratio is applicable to the shape of the inner ear, and that consonants resonate because of it and dissonances don't.

I never use it for creation of music. Some people incorporate it into their trading (stocks, bonds, commodities etc) - but wouldn't feel comfortable doing that.

Weird. It sounds like something I'd instantly discredit... but I'm intrigued. I think I'll actualy wait a read about it before slaming on it.

Weird. It sounds like something I'd instantly discredit... but I'm intrigued. I think I'll actualy wait a read about it before slaming on it.

Ugh, what is it with people?

Things you may feel like instantly discrediting are often true. Science is not common sense. You should have learned this stuff in school!

Here's more info about the sequence in question:

Fibonacci numbers also appear in the description of the reproduction of a population of idealized bees' date=' according to the following rules:

* If an egg is laid by an unmated female, it hatches a male.

* If, however, an egg was fertilized by a male, it hatches a female.

Thus, a male bee will always have one parent, and a female bee will have two.

If one traces the ancestry of this male bee (1 bee), he has 1 female parent (1 bee). This female had 2 parents, a male and a female (2 bees). The female had two parents, a male and a female, and the male had one female (3 bees). Those two females each had two parents, and the male had one (5 bees). This sequence of numbers of parents is the Fibonacci sequence.

This is an idealization that does not describe actual bee ancestries. In reality, some ancestors of a particular bee will always be sisters or brothers, thus breaking the lineage of distinct parents.[/quote']

Fibonacci sequences appear in biological settings' date=' such as branching in trees, the spiral of shells, the curve of waves, the fruitlets of a pineapple, an uncurling fern and the arrangement of a pine cone. Przemyslaw Prusinkiewicz advanced the idea that these can be in part understood as the expression of certain algebraic constraints on free groups, specifically as certain Lindenmayer grammars.

A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979. This has the form

[img']http://upload.wikimedia.org/math/f/2/e/f2e452edabf5bed52aaeca6c6eaf2f4c.png[/img],

theta = n times 137.5^{circ}, r = c sqrt{n}

where n is the index number of the floret and c is a constant scaling factor, and is a form of Fermat's spiral. The divergence angle, 137.5

Ugh, what is it with people?

Things you may feel like instantly discrediting are often true. Science is not common sense. You should have learned this stuff in school!

maybe it's the application to music that he is talking about?

maybe it's the application to music that he is talking about?

Even that gets covered in our basic theory and history classes.

Even that gets covered in our basic theory and history classes.

Things you may feel like instantly discrediting are often true. Science is not common sense. You should have learned this stuff in school!

stating that "the earth is flat" makes me want to discredit it instantly... does that make it true?

and I could remind you that music is not science.

music is not common sense either.

As a musician, my own instinct is likewise to be retiscent of anything "science-based" in music. Other than the analysis of accoustics or the construction of musical instruments, I can't say I am particularly open-minded to the introduction of "scientific principles" into the creation of music, except in the most superficial way.

Science and music together generally have a sad tendency to create emotionless and arid music.