Ruy Lopez

From Hawkingfan:

A lot of composers use them in structuring the form of their peices as well.

Sorry, I know very little about paintings but music, yes. Can you give an example of how a musical piece is structured according to Fibonacci nos. and ratio. I would really love to see this.

I play by ear on the piano modern pieces by Brian Adams, Elton John, Sinatra, Lennon etcc. But I also read notes and play Mozart, Beethoven, Chopin sonatas and other lesser pieces. Am also familiar with the structures of all 9 Beethoven and some of Mozart's symphonies. You can use any of them as an example.

Thanks in advance. (that is if it's not too much of a bother)

Ruy Lopez

From liquid;

So what's being claimed on the back of that? Or are you merely asking how the maths works? I apologuse if I'm missing the obvious!

Not sure what you mean but I sort of felt technical analysis or charting was being misrepresented in your post. But probably half of all people react the way you did; I've seen it so many times. Is this what you mean?

Don't be concerned about it anymore and enjoy your flight and destination.

Jesse

There's a theory which I saw mentioned on the show The Human Face hosted by John Cleese, that the most beautiful faces are the ones that most closely approximate a certain ideal which is built up out of various golden ratios (for example, the theory claims that the most beautiful ratio of nose width to mouth width is the golden ratio). Here's a website about this theory which also shows pictures of the "mask" they use to overlay on pictures of real faces and see how closely they match the ideal:

http://www.beautyanalysis.com/index2_mba.htm

And here's an article from "The Human Face" show's website:

http://tlc.discovery.com/convergence...cles/mask.html

Another site with more examples of the mask applied to faces from photographs and from art:

http://goldennumber.net/beauty.htm






And here's a page where someone morphs their real face to more closely approximate the proportions of the mask, you can judge for yourself whether the morphed version is more attractive:

http://www.frickell.com/oldancient/face.html

I don't know how this theory is viewed by others who study the psychology of beauty, though.

Hawkingfan

Check out the score for Bela Bartok's "Music For Strings, Percussion, and Celeste", First Movement. Pay attention to the measure numbers that are Fibonacci numbers (8,13,21,34,55, etc.)
But it is debated quite a bit on whether or not Bartok was actually aware of the Fibonnaci series. It may be a coincidence. But the correlation is still there whether he knew it or not. I don't think he ever mentioned it in any of his writings or conversations. But even if it is subconcious, it makes sense, because the piece's form really sounds "natural" divided up like that. Give it a listen. It's pretty uncanny.
There is no hard evidence to prove that the pre-twentieth century composers used them. Subconciously, I think most composers put a "climax" at right around 0.618 in their pieces (I know that's generalizing a bit).

But in the twentieth century and in the post modern era composers can use the Fibonnaci in order to give them some idea on how to structure their piece, especially in writing in a free form. You can divide the "intro" into a certain number of measures (or seconds) that correspond to a Fibonacci number, the "first theme" into another number, "variation" or whatever into another number, etc...
This type of composition is taught in a lot of modern schools. The composers that do this are not famous and you probably wouldn't be able to get any scores.

And I didn't check out your URL, so I may be repeating something, but you do know that the piano keyboard is designed according to the Fibonnaci series? For every ONE octave C to C, there are TWO black notes grouped together, followed by THREE black notes grouped together, making a total of FIVE black notes for every C octave, and then there are EIGHT white notes, making for a total of THIRTEEN notes total.

I highly recommend checking out the Mondrian and Rothko paintings. Check out the "boxes" that Mondrian makes and see how they relate to one another, not much their position, but their size. The Rothko stuff is much more obvious.

Ruy Lopez

Thanks for taking the trouble Hawkingfan. I found Bela Bartok's "Music for Strings..." in this site;

http://www.midiworld.com/bartok.htm

but it contains only the 2nd and 4th movements. I'll have to go to a nearby music store for the CD and score. I think it's available.

Your comment,

This type of composition is taught in a lot of modern schools. The composers that do this are not famous and you probably wouldn't be able to get any scores.

seems to say a lot. It is the difference between real geniuses and us, the 99.9% of the population. We need a formalized pattern of instruction and a generally accepted mode of thinking. Even Bartok's music does not impress me like the awe that I get from Mozart's 40th Symphony. I guess I have to use Fibonacci when and if I try to compose.

You are right about the piano keyboard--- it's 1, 2, 3, 5 and 8. And also with the observation that human's apply selective thinking; it's there sometimes but often it's not there. I'll also investigate Mondrian and Rothko.

From comments on the board and the links I have read, Fibonacci numbers/ratios have something to say about what we perceive to be "naturally beautiful or pleasing". The observation applies also to the biological world where, in addition, a Fibonacci arrangement seems to optimize life functions with space requirements.

And from the viewpoint of financial investing, there are indeed applications; one of which is the "retracement ratio" which I know how to handle. I suspect there are more in this area because Fibonacci numbers seem to be the basis of two of the most well known and successful practitioners, William Gann and Ralph Elliot.

These two lived during the roaring 20s and depression years. But again, a word of warning. The "genius"of these two people cannot be transferred to the avid average Joe through a seminar or course on their supposed methods. They are gone and what we have are inadequate copycats. I do not understand their methods nor even bothered to. I might give it a try.

Goliath

Ruy Lopez,

The Golden Ratio shows up in a lot of places in mathematics. Also, IIRC, there is a quarterly journal that only publishes papers dealing with results about the Fibonacci numbers.

I am a graduate student working towards a PhD in Mathematics. My area of interest is Commutative Algebra (specifically Factorization Theory of Integral Domains), so neither the Fibonacci sequence nor the Golden Ratio show up in my area of specialization.

Sincerely,

Goliath

Ruy Lopez

Thanks Jesse and Goliath.

Hawkingfan

I think we hit the jackpot with Bela Bartok. When I googled "Bela Bartok Fibonacci Numbers", I found out how Bartok used the golden ratio in the piece you suggested as well as in other compositions. Also got to listen to the 1st movement.

The jackpot for me is the fol. link;

http://www.americanscientist.org/iss...bs96-03MM.html

"Did Mozart Use The Golden Section?"

One critic says that Bartok consciously used the golden ratio in "Music for Strings, Percussion and Celesta". According to him, it is too obvious and exact. Others say Bartok never said that he did use the ratio.

The Mozart article involves an analysis of many of his sonatas by John F. Putz, a mathematician. Putz concluded, without great conviction, that where Fibonacci appeared in Mozart's sonatas it was most probably intuitive. In one set of sonatas, the correlation is .99 but in others around .93 but with wide individual variances.

Now there is work to be done. I will probably set aside Bartok, for now, because I already know how he did the "Music for Strings..". Intend to analyze two of Mozart's piano sonatas because I already play them by memory and I have the scores. Listen to Sonata in C Major K545. Go to "Piano Sonatas Section" and select no. 16 Allegro by Gary Lloyd

http://www.classicalmidiconnection.com/cmc/mozart.html

My playing is not as good but similar to the artist as I have played this close to a hundred times.

This 8th Sonata by Beethoven is clearly my favorite. It's the Adagio Cantabile "Pathetique" played by Mike Turner. I'll analyze and tear this apart. Have played this over a hundred times and never tire of it.

http://www.classicalmidiconnection.com/cmc/ludwig.html

If only for this, the thread was worth it.

Ruy Lopez

I checked the following for Fibonacci ratios because I have their written scores as well as I play them from memory.

1)Beethoven sonata no. 8 (Pathetique) adagio cantabile

2)Mozart sonata in C Major no. 16 allegro

3)Mozart piano concerto no. 21 andante (Elvira Madigan theme)

Only Mozart's Sonata in C Major showed the .618 ratio quite accurately. The ratio of the principal and secondary theme measures to the development part is .622; while the ratio of development measures to total measures is .616. These ratios follow the procedure of others doing similar analysis.

It looks like Beethoven never heard of the ratio; he's too far off. Mozart's concerto movement is similarly off field. It appears, as Putz has concluded, that Mozart may have followed Fibonacci ratios only on sonata form.

Putz, a mathematician but not a musician, made guarded conclusions because that is the nature of his trade. I feel confident, as a piano player who can feel the mood of the composer, that Mozart had the ratio in mind when he wrote Sonata in C Major.

But then, what makes music beautiful? It's definitely not the Fibonacci ratios. Beethoven's 8th sonata and Mozart's 21st piano concerto are among the most beautiful melodies and harmonics I have ever heard.

I leave this topic wide open.