Golden mean in guitar design

[architype]

Do any of the Luthiers out there use the Golden Mean in the design of their instruments? I'm aware that the musical scale is directly tied to the golden ratio of 1.618 and the Fibronacci series aproximates this ratio...(1 1 2 3 5 8 13) and also that violin design has been proportioned on this ratio.
Do any of you guys base your body width to length and body length to overall length or is this inherent in the design in order for the instrument to function musically?

See attached:

http://www.goldennumber.net/music.htm

[Burton LeGeyt]

I use it. Usually I will draft a set of numbers off of the scale length, or the nut to body join dimension, and work loosely off of those. The one hard one is for most of my instruments the waist is at the golden mean of the body length.

I don't use it for sonic purposes, I think of it as an aid for a pleasing set of visual proportions.

[architype]

Originally Posted by Burton LeGeyt

I use it. Usually I will draft a set of numbers off of the scale length, or the nut to body join dimension, and work loosely off of those. The one hard one is for most of my instruments the waist is at the golden mean of the body length.

I don't use it for sonic purposes, I think of it as an aid for a pleasing set of visual proportions.

I would be interested to see your drawings, unless it is giving away trade secrets. It would give insight into the complexity of the process. You can't just start cutting wood on day one...there has to be a plan.

[Burton LeGeyt]

I'm afraid you might be dissapointed in the drawings, they aren't as detailed as you might imagine. I have seen people's drawings (and attempted a few myself when I started) who did calculate all the curves off of a golden ratio and spend a ton of time finding all the relations that would allow it to still look like a guitar. I am not doing that, I just work up a set of numbers and roughly draw those in and then fudge my outline around them.

It might be something like I start with the distance from the nut to the body for a 14 fret guitar. That distance is approximately 14.25 with my scale length.

Working forward and back from that number I get:
.79, 1.28, 2.08, 3.36, 5.44, 8.80, 14.25, 23.05, 37.30

I can see that some of those numbers can correspond well, for example I could use 3.36 for my headstock width or neck depth but the other ones would be outside normal sizes. I got around this by calculating the mean between each of those numbers. This gives me, for instance, 8.80, 10.88, 12.16, and then 14.25. Those numbers match up better and I can get some usable numbers that I might use for my waist, or upper bout. In the end, though, this seems too much like an abstraction to me, I am working too hard to make things fit into a shape I want to maintain.

I am not saying it doesn't have a place because I very much think it does. It is just that I haven't found a way to practically apply it beyond very simple relationships, like where the waist falls on the body. I studied it enough to know that randomly applying it to different sections is not an elegant use of it and since I find the whole study almost a study of elegance itself I want to learn more before attempting a more complete design. An example of a complete design would be from a book I read in school explaining how some gothic cathedrals were built around the ratios within a single chord. The architect expanded on those ratios to "color" the design the same way a musician would choose a key to color the composition. I was fascinated by this (building as music!) and humbled by the level of dedication these artisans had to thier craft.

There has to be a plan, yes, but there also has to be experience to guide the planning. The plans and designs will continue to evolve just as the skills to complete them will. I feel this all the time in my own work.

I hope that helps, and is not too long winded. This is a favorite subject of mine and i wish I had more concrete help to offer.

[Archtop Guy]

There was a recent article in Fretboard Journal about Erich Solomon, who uses the Golden Ratio in his designs. I played some of his guitars at Healdsburg and they deserve all of the accolades they get.

After noticing the small variations in guitar shapes myself, I measured my loved L-5 a while back and found the golden ratio matched the upper bout width to the waist, and the lower bout to the upper bout. This may have something to do with why these designs are so timeless.

[architype]

This has always fascinated me. When I read about the Golden Mean in high school for a report on Greek mythology I was already setting my sights on being an Architect, so this information was illuminating. It took some of the randomness out of design.
I too use the ratio when I am designing a building, but it can sometimes be restricting, and function and budget typically will rule at the end of the day.
It is a tool that helps when I'm trying to refine a design. If I can get those relationships to work, then I think it just makes for a more asthetically pleasing project.
I love the beauty and simple elegance of guitars, but I always wondered if I superimposed the ratio over the shape, where would the lines fall? Maybe I'll measure my guitars and go through this exercise for the fun of it.

[Howard Klepper]

Of interest [warning: deflationary cynical content]:

http://www.maa.org/devlin/devlin_05_07.html

http://www.emis.de/journals/NNJ/Sharp_v4n1-pt04.html

http://www.laputanlogic.com/articles...1647-4601.html

http://goldenratiomyth.weebly.com/

[architype]

Originally Posted by Howard Klepper

Of interest [warning: deflationary cynical content]:

http://www.maa.org/devlin/devlin_05_07.html

http://www.emis.de/journals/NNJ/Sharp_v4n1-pt04.html

http://www.laputanlogic.com/articles...1647-4601.html

http://goldenratiomyth.weebly.com/

Interesting stuff. None of these sources deny the fact that it does turn up in nature, (maybe not all of the places that have been proported), and that it is a proportioning tool, (one of many), that has been used certainly since the Greeks. In fact the first link boils it down to a he said she said argument...he essentially says OK it does show up in Architecture, Music and Painting, but prove that they did it on purpose. The fact that it keeps turning up seems to be enough to suggest that it was intentional.
I don't worship it, but I do use it to design with, (when it is appropriate), and I like the proportion that it produces.

[Haans]

No...........

[Howard Klepper]

Originally Posted by architype

Interesting stuff. None of these sources deny the fact that it does turn up in nature, (maybe not all of the places that have been proported), and that it is a proportioning tool, (one of many), that has been used certainly since the Greeks. In fact the first link boils it down to a he said she said argument...he essentially says OK it does show up in Architecture, Music and Painting, but prove that they did it on purpose. The fact that it keeps turning up seems to be enough to suggest that it was intentional.
I don't worship it, but I do use it to design with, (when it is appropriate), and I like the proportion that it produces.

I think he said that there is no evidence at all that it was used by the Greeks, or purposely used by anyone until the 16th century. He and the other writers show that one has to arbitrarily define boundary points in order to "find" it in Greek architecture.

You earlier said that the musical scale (which one is that?) is derived from the Golden ratio. Can you explain that? All I can find is some numerological hand waving about how in an untempered scale the notes are in simple proportions, and the Fibonacci series generates a lot of simple proportions, so QED. And the stuff on violin chooses certain points on certain violins as the places to measure from, which then, with a bit of fudging, turn out to have the right ratio. Or have some of the other ratios in the Fibonacci series.

This is the way numerology works. You start with the conclusion, and then project it onto things until you find something that fits it. Or fits it closely enough. It's the way people find that history was predicted by the ratios used in the pyramids, etc. etc. In fact, it can be proved that anything can be a mathematical model of anything else; you just need to find the equations that will map one on to the other. I can splatter paint on the wall and find all sorts of interesting things modeled by the positions and sizes of the drops.

To be sure, Phi is a nice ratio, like many others. It can be used as a design tool. Like many others, and nicer than most. Does its use produce an especially good sounding guitar? No reason to think so. Which is not saying that someone who uses it won't make especially good guitars.

Here is someone having fun with numbers: http://www.thedailybeast.com/article...d-symbols.html

[nashrb]

Originally Posted by Howard Klepper

I think he said that there is no evidence at all that it was used by the Greeks, or purposely used by anyone until the 16th century. He and the other writers show that one has to arbitrarily define boundary points in order to "find" it in Greek architecture.

You earlier said that the musical scale (which one is that?) is derived from the Golden ratio. Can you explain that? All I can find is some numerological hand waving about how in an untempered scale the notes are in simple proportions, and the Fibonacci series generates a lot of simple proportions, so QED. And the stuff on violin chooses certain points on certain violins as the places to measure from, which then, with a bit of fudging, turn out to have the right ratio. Or have some of the other ratios in the Fibonacci series.

This is the way numerology works. You start with the conclusion, and then project it onto things until you find something that fits it. Or fits it closely enough. It's the way people find that history was predicted by the ratios used in the pyramids, etc. etc. In fact, it can be proved that anything can be a mathematical model of anything else; you just need to find the equations that will map one on to the other. I can splatter paint on the wall and find all sorts of interesting things modeled by the positions and sizes of the drops.

To be sure, Phi is a nice ratio, like many others. It can be used as a design tool. Like many others, and nicer than most. Does its use produce an especially good sounding guitar? No reason to think so. Which is not saying that someone who uses it won't make especially good guitars.

Well put Howard. Like the OP I too am an architect but I don't use the golden ratio as a design tool. I have found over the years that, like most "rules" in life, they just don't hold up when the rubber meets the road. There are so many variables that are driven by factors outside of a mathematical ratio that rigidly applying a ratio or another other hard and fast rule often yields results that appear contrived. Reminds me of the George Carlin routine where he talks about how people believe in horoscopes...says here "Today is a good day to ask for a raise"...yeah, if I had a job I WOULD ask for a raise!

Rob

[runamuck]

I, for one, do not think the Golden Mean, is all that golden.

It's been some years since I've fooled around with it as a
designer and that's because in many, many cases it simply
is not aesthetically pleasing, in my opinion.

Jim McCarthy

[architype]

Geez guys...ask a simple question and everybody gets all out of whack. I never said it had magical powers...just wanted to know if any of you guys used it. Here is the attachment that explains it, (in terms of music), better than I ever could.

http://www.goldennumber.net/music.htm

I'm no music theorist, so if there is information there that is incorrect or stretching it a bit I'd be interested to know.
If you want to analyize the facade of any building you have to start some where. Do you start w/ the centerline of the columns, the outermost edge of the columns, the overhang of the cornice...so yes there are many places the can be called arbitrary, but the overall proportion of let's say the Parthenon is close to or approximates a golden section. Your eye does the rest.
We weren't there when they built it, so all we have is the ability to analyze it after the fact. Given the other complexities of that particular building, ( the entire base is a convex curve along both sides, all the columns tilt inward slightly to make a kind of parralax correction from the point of view of the main approach, there is a slight bulge, or "entasis" in the columns to give the impression of carring weight), the golden section would be the simplist of techniques applied to the design.
As I said, I use it as a tool. It isn't the starting point, but more of a way to check myself. I was just wondering if you guys did the same.

[Howard Klepper]

Originally Posted by architype

http://www.goldennumber.net/music.htm

That site is a good example. It is utter nonsense. Phi never even appears there as a scale generator (being irrational, how could it?). Many of the "Fibonacci ratios" it claims are not even in the Fibonacci series. It gets the ratios used on calculating the tones of an untempered 12-tone scale wrong. But there are those pyramids, which must prove it!

"A432 was often used by classical composers and results in a tuning of the whole number frequencies that are connected to numbers used in the construction of a variety of ancient works and sacred sites, such as the Great Pyramid of Egypt."

As I said, nothing wrong in using phi in your work.

Short answer to the original question is no. But If you measured some things on my guitars, I bet you could find something that approximated phi as well as the Parthenon's facade does. Incredible building, BTW. One of the greatest sights in the world. I got all ferklempt seeing it.

[architype]

Howard, I defer to your musical knowledge since I can't even read music and play by ear.
I agree that you can usually manipulate the numbers to get the answer you want, but I am also humbled at the beauty of what the ancients were able to acomplish given the technology and resources they had available to them. I also get a feeling in my chest when I enter a beautiful space whether it is Notre Dame or Fallingwater. I get that same feeling when I hear a beautiful piece of music, Johann Bach to Jackson Browne. The same as when I look at a beautiful piece of sculpture or a custom made guitar.
I guess there will always be an intangible element to beauty that is beyond analysis and maybe the mystery of it is what makes us persue it even more.