Determining the golden section?

[Johnmasters]

quote:

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Originally posted by:

erich_zann

And for those that want to explore the number even more, don't

forget Mario Livio's book "The Golden Ratio".

I'm sure that there are tons of pages out there written on the

subject, but for the price (used under 10 bucks), it might provide

some interesting reading for some of you........

Johnmasters - Quote: "For the antiquing people: natural damage

should eventually approach a fractal nature."

I am very intrigued by this statement. Maybe you could start a new

thread explaining the practical applications/techniques...? Or PM

me and I'll give you my email.

Very curious indeed.......

(Thanks to all for the very informative thread !!!)

E.

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It was a kind of joke, but in principal would seem correct. The idea is that the same sort of patterns would be seen at any level of magnification. (Because natural damage is random) But in practice, naturally damaged instruments are not infinitely old.

I really find it hard to believe in any kind of exotic "design" beyound some simple proportions. The Greeks did not like straight lines, and I understand that. There is a way to find PI with the Great Pyramid, but the explanation is a simple one. If you want to draw a new pattern to suit your own tastes, why not just get tracing paper and draw an original. You can then erase and redraw certain curves, recopy etc, until you get a smoothly curving shape you like. By "smoothly curving" I mean that a the radius of curvature of a line should vary in a pretty "smooth" way.

[David Tseng]

>>The last statement is VERY profound. If your number system is not

true, (last statement) Einstein theory of relativity won't work neither. Don't you believe this? >>

I do not understand what you are talking about.

[Torbjörn Zethelius]

Surely you know about proportional dividers:

http://www.weems-plath.com/upl..._files/large.4548.jpg

They're ancient. You can find most proportions with it, both rational and irrational.

[Ken Pollard]

Irrational dividers? But you could certainly get very close.

We have the basic problem: we can describe violins (or the universe) mathematically. Does that imply that the violins were created from a mathematical basis? In another thread on Stewart-Pollens book, Manfio transcribes a bit on the creation of the templates lacking any formal design markings. Quite interesting.

One exercise I had my math students do was to measure various objects to see if their aspect ratios were close to the golden ratio. Many things, doors, paperback books, photos, are fairly close. Is this because the Golden Ratio was used? Maybe, or maybe it just looks good, or fits well in the hand.

The spiral of the chambered nautilis, often used in golden ratio texts, follows the Golden Ratio/Fibonacci pattern fairly close. Mathematically based design? Or is it because this particular math describes how things grow? As the chamber gets longer, it gets wider. Which comes first? And is our math the only way to describe it? Like the old saying, when all you have is a hammer, everything looks like a nail.

I really don't know. But lacking some evidence to show that violin design comes from the math, rather than being described by it, I think the burden of proof is on those that claim such math was used. One could just as well claim the design came from a good eye for proportion and a good physical intuition & experience.

It is fun to think about, though.

[Fellow]

Hi David Tseng,

Einstein theory was based on a foundation of deep mathematics, in particular, (your) number system.

That statement is assumed to be true in the number system (my professor said)

Theory is thery, we all doing approximation in pracice (work). For example, there is no

perfectly straight line, only "nearly perfect" straight.

[David Burgess]

Ken, that's a really nice post.

Music and pitch easily lend themselves to mathematical description, but how much music is really of mathematical origin? Are any composers really thinking in those terms prior to putting the music they hear in their head onto paper?

[Guest]

David Burgess - Google Joseph Schillinger...He created and taught a

mathematical based system of musical composition. ( "The

Schillinger System of Musical Composition" ).

So, yeah sometimes it seems that the numbers come before the

notes.

E.

[David Burgess]

OK Eric, I should have chosen my words more carefully.

My mother taught college music theory, so I'm aware that it's been tried, and also that math might be said to be incorporated when choosing a tempo or time signature for a specific application such as dance.

Couldn't we correctly say it's much more the exception than the rule?

[Collin]

Not to mention the Schoenberg method (although it's not rooted in equations....) and fractal music (which is).

[Michael_Molnar]

I thought this thread was about the Golden Section. So let me redirect the thread. I encourage you ADD'ers to start a new thread since you cannot keep focus. Don't be offended: Your new topic is very interesting, but doesn't belong here. Thank you.

Back to the thread on hand:

Finding the Golden Section in a design is like finding pi in that design.

(Read that again so you might understand what I meant.)

These are natural arithmetic ratios.

They are ubiquitous.

I hope you know what that means, namely that his thread is pointless.

[Ken Pollard]

Given that the thread is pointless, it seems ok to wander in various directions. Even a blind pig will find an acorn from time to time.

One Einstein quote goes like this:

"It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure."

Or maybe the thread's not pointless. Simply because pi or the golden ratio appears naturally, does not imply that it could not be knowingly factored into the design of a musical instrument or a painting or a symphony. To say that the golden ratio was not a conscious part of violin design seems as extreme as saying it was.

Just as we can find composers that use math to create music, there's bound to be violinmakers who use math to design instruments. Lots of possibilities. Asking if for examle, Bach used math for music or if Stradivari did for violins, is what I think folks are considering here.

[pandora]

Actually, pigs have a very keen sense of smell (remember truffles?) and probably use that to find acorns.

[Ken Pollard]

Ok -- a pig with a head cold...

[Collin]

quote:

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They are ubiquitous.

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If the golden ratio & pi are ubiquitous, how can one not

go off topic? Going off topic is like adding the odd gouge mark to

a scroll, or leaving a dissonance unresolved - it provides

interest.

quote:

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I hope you know what that means, namely that his thread is

pointless.

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It's anything but pointless - back to the music analogy: Ignoring

the golden ratio in design is akin to playing Beethoven on a

Theremin - it doesn't work. Likewise, playing Beethoven with

perfect equal temperment doesn't exactly work either - remember the

first finger phenomenon? Point being, seeing as the golden ratio

isrelatively  ubiquitous, and contributes to beauty, it

doesn't hurt to use it as a contributor to design. Remember the

Greeks?

I'll just ignore the "I hope you know what that means" bit - along

with "you ADD'ers".

That said, let's get back to the topic at hand.

[David Burgess]

Personally, I'm more of an OCDer than an ADDer, but what I'm really wondering is who wrote the rules defining what's on topic and what's off?

So which came first, the chicken or the egg?

Did someone come up with the idea for the golden ratio and then start applying it to design, or did it come about by observing things of beauty, and attempting to come up with a system to explain and reproduce it?

[COB3]

"Did someone come up with the idea for the golden ratio and then start applying it to design, or did it come about by observing things of beauty, and attempting to come up with a system to explain and reproduce it? "

David, the obvious and correct answer is "yes!"

[polkat]

I started this thread with a very simple approach to a question I had in reference to Alvin King's paper on cremonese F hole placement. He finds the golden section of the centerline down the top plate and uses that as a reference to position his F holes. He claims that the old masters used the method. I simply wanted to know how to find the golden section of a line so I could try the same method. GMM22 gave me a usable answer. I certainly didn't mean to stir up a can of worms, but I don't understand why people are saying the thread is pointless??? Sorry if it is.

[Melvin Goldsmith]

Polkat

It is a good thread

[Darren Molnar]

""""""""""""""'Did someone come up with the idea for the golden

ratio and then start applying it to design, or did it come about by

observing things of beauty, and attempting to come up with a system

to explain and reproduce it?

"""""""""""

 I think the idea comes from pythagarus or one of

his followers so the best thing would be to ask one of them. Thats

a little bit before my time, David,how old are you now a-days?

[Guest]

polkat - asking a simple question on this forum and opening a can

or bucket of worms is, in my opinion, what makes maestronet such a

valuable resource !

thanks for starting such an interesting thread.

E.

[Fellow]

If we look at a rectangle ( a card board for example) with sides 1 to r (golden ratio), we

are plaesed. Why? I think if it (rectangle) is too close or too far, we find ourselves hard

to see it, We are pleased because it is easy to see. Little focusing is required. So it is " prospective thing.....(golden ratio)"

Prospective means it has something to do with the separartion of our eyes (left and right eyes).

If we cover one eye, then "Golden ratio" does not mean a thing. Just my thinking. Right?

[Torbjörn Zethelius]

Many ratios are pleasing to the eye. The golden section is quite clumsy in it's pure form IMO.

Luca Pacioli was probably one of the first to write about the "Divina Proportione". His book was published in Venice in 1509, so it was "hot" in Andrea Amati's days.

[Bacon]

David in response to "Music and pitch easily lend themselves to mathematical description, but how much music is really of mathematical origin?"

The treatises on music and instruments presented in the 15th ,16th, and 17th centuries lead us directly into the world of math and proportion.

Of The origin of the design only moderns can guess but their is plentiful information of the period to indicate this marriage of music and math , so much so that they were not looked as but two arts but one.

By the time Stadavari was on the scene the design was flexible but established. Concerning archings perhaps we should look greater toward the contributions of his second father in law , a great mathematician of the day. I seems to me that is when the changes begin.

[Ken Pollard]

I'll claim complete ignorance on the second father-in-law angle, Stephen. Can you post any more info?

[David Burgess]

"Bacon", one could legitimately claim that music is math. My proposition would merely be that Mozart wasn't thinking in this context when scribbling notes on paper.

Was music originally created by math or analysis, or were these things imposed upon it at some point?

People love to figure things out and come up with systematic explanations for things, myself included. Has it ever been otherwise?