Re: Re: Golden Section and


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Posted by Chris R on February 29, 2004 at 01:09:16:

In Reply to: Re: Golden Section and posted by Rick Denney on February 28, 2004 at 23:44:25:

Another thing to note is the inverse of the "Golden section", also known as the "Golden proportion", is .6180339... You get this when you look at the ratio of the numbers in the Fibonacci series, 2/3=.667, 3/5=.6, 5/8=.625, 8/13=.61538 etc. This ratio of almost 2 to 3 is found everywhere in nature. From the number of petals on a flower, to snowflakes, to the inherent proportions in the human body ie. the three parts to our fingers, arms, and legs. There are two smaller parts and one large part. Or even the position of our eyes on our face which is essentially two thirds the way up. Granted, we are all made differently but this ratio seems to hold in a general sense for us.

This ratio has been found found in many great composer's works, especially Bach's. If you listen some of his music you'll begin to realize that the mood of the piece changes about 2/3 of the way through, it goes into a minor tonality if the piece starts in major or vice versa. This can even be applied to very large works like St. Matthew's Passion where the smaller movements portray this ratio as well as the work as a whole. Who knows if Bach was thinking about these things when he composed. Or maybe it just came naturally to him? Could this be why he is considered the greatest composer ever? But, who am I to judge...There's also one last thing to note with Bach's relationship with this ratio. Bach was a devout Lutheran. The Golden proportion is found when looking at the cross. The "crossbar" is located about 2/3 up the height of the cross. Interesting....

I know that this ratio is used in visual art as well. Paintings and sculptures frequently have this ratio but it usually goes unnoticed to the casual viewer. Artwork seems more pleasant to look at for some reason when it applies the ratio. There is an inherent beauty to this ratio in both art and music which is something us aesthically oriented people can look for.

There are many things you can look at when concerning the Fibonacci numbers. I think it's such a fascinating sequence. There are many things to consider when looking at them, like Rick pointed out and what I attempted to point out here.

I know this post didn't really comment on the Golden mean but I thought it would be relevant when discussing Fibonacci numbers. I just thought I would throw out that tidbit of information to my fellow tubists.

Chris "just about as nuts as Rick and Sam right now" Rubenacker


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