Is there a special ratio for a ukulele's body dimensions?

I working on my own body for new ukes I will soon be making. Is there a specific ratio for the body shape, meaning upper bout, lower bout and waist widths? I have one I currently like, it has a narrow waist, like the old Hawaiian ukes but not quite as narrow. When I made violins I recall something about the "golden ratio".

Has anyone used specific ratios to design their own body or did you just base it on aesthetics?

You might want to look at Robert Mottola's site and get his "G" Thang program..... very good for guitar design..... see no reason why it want work on a ukulele.

http://liutaiomottola.com/formulae/gthang.htm

Blessings,

Kevin

Golden Ratio
1.6

Try to resist re-inventing the uke. Look at the shapes that work and why they work. If you make the waist tight like the vintage ukes, you are limiting the top vibrating surface and sound for design. If that's what you want.... well there you go. A radical design will appeal to a limited number of people which means a limited number of sales. Good luck.

Koa Soprano said:

Is there a specific ratio for the body shape, meaning upper bout, lower bout and waist widths?

Click to expand...

Yes, but whatever you do, don't tell the pineapples.

Duane has some good advice about not re-inventing what is known to work well.

At the same time, check out these pics. My brother recently made me this divider (out of the blue) for my birthday. It's a gage that maintains the golden ratio. In the pics it is set against the bouts and waist of a pretty typical uke -not a narrow waist. Hmmmm... 1.618 ratio. How about that? All show a clear 1.618 ratio.

This one show the ratio in terms of bout-to-waist-to-bout layout.



These two show the relationship between the width of the lower bout and the waist. The gage was not adjusted between the two shots.



And these two show the relationship between the waist and upper bout -notice that the width of the waist shows a 1.618 ratio with the CENTERLINE of the upper bout.



Seems that you can stick with the tried and true, and still be "golden".

Note: I did not build this uke. Just grabbed it and the gage to see if I could answer the question in the original post because I happened to have a tool to do so.

If 1.6 was good enough for Pythagoras and Leonardo Da Vinci, it is good enough for me

My design isn't as narrow as the old ones. I just got a 1920s Hawaiian "Echo-Uke" and it's 3-3/8" at the waist. A Martin I brielfy had measured to 4" at the waist, my design is 3-13/16". It's based on the Larrivee body but as narrow in the lower bout as a martin. I just don't want to directly copy someone else. When I built guitars I always had original designs.

That's a neat tool tobinsuke.

Beau Hannam Ukuleles said:

If 1.6 was good enough for Pythagoras and Leonardo Da Vinci, it is good enough for me

Click to expand...

Right on! I just got my number from Wikipedia... Math is not my strongest suit, which may explain my fondness for gages No correction or disrespect intended - my experience as a machinist has led me to go three or four decimal places.

tobinsuke said:

Right on! I just got my number from Wikipedia... Math is not my strongest suit, which may explain my fondness for gages No correction or disrespect intended - my experience as a machinist has led me to go three or four decimal places.

Click to expand...

hahha- My maths sucks too, or is it two? When i design things i take the longest part, and divide it by 1.6 to get the smaller section, such as the lower and upper bout portions.

The classical guitar upper and lower bout widths are based on it as is the location of the waist. If fact, if it looks 'right' it is probably based on or close to the Golden mean.

I like traditional & historical shapes, but I also like to "draw a line and look at it" to see if it pleases.

Kevin, you're right about Mottola's G Thang tool. We've been using it for years... It works just fine for both guitar and ukulele design. But....

the G Thang tool will not stop you from creating designs that are out of balance according to the "golden ratio" (1:1.618034) or designs that simply don't look good.

Just as a note of interest, the numbers in the Fibonacci sequence also approximate the golden ratio:
2:1 = 2.000000
3:2 = 1.500000
5:3 = 1.666667
8:5 = 1.600000
13:8 = 1.625000
21:13 = 1.615385
34:21 = 1.619048
55:34 = 1.617647
89:55 = 1.618182
144:89 = 1.617978
233:144 = 1.618056
377:233 = 1.618026
610:377 = 1.618037
987:610 = 1.618033
1597:987 = 1.618034
2584:1597 = 1.618034
4181:2584 = 1.618034
6765:4181 = 1.618034
and so on...

Once the ratio is reached at 1597:987 it remains stable at 1.618034 (rounded to 6 decimal digits). Anyway, 1.618 'll do me just fine most of the time.

One of the nice things about the Fibonacci sequence is that is shows how the ratio of the smaller portion to the larger portion is the same as the ratio of the larger portion to the whole (i.e. the sum of the two). In other words a:b as b:[a+b]. Or 0.618:1.000 as 1.000:1.618. Yeah!

erich@muttcrew.net said:

One of the nice things about the Fibonacci sequence is that is shows how the ratio of the smaller portion to the larger portion is the same as the ratio of the larger portion to the whole (i.e. the sum of the two). In other words a:b as b:[a+b]. Or 0.618:1.000 as 1.000:1.618. Yeah!

Click to expand...

Thanks for pointing that out. I was about to mention it. 1 : 1.618 describes only the 2 dimensional world. .618 : 1 : 1.618 goes 3D! and, .618 : 1 is just as useful as the converse. I have used this math in many ways in my various designs, and look forward to learning it's application in ukes more.