Golden Mean: Post 4

Golden Mean, Golden Rectangle, Golden Spiral

Golden Rectangle & Golden Spiral

Photo by Sophia Darby

"The musical instrument in this picture, like many other instruments, contains the golden ratio in a variety of places within its structure. In the violin, one example of the golden ratio is the proportion of the top of the violin to the bottom of the neck and the measurement from the neck out to the side of the upper bout. This also creates a golden rectangle if you extend the lines into space." -Kelsey Goodwin

Cellos present the golden ratio between their neck and body, thus demonstrating divine proportions, which is a exalted term for the appearance of the number 1.618033, represented by the Greek letter phi (ϕ).

Violins, violas, and cellos were all eventually designed using the golden ratio in order to improve the acoustics of the instruments.

I've overlaid the successive golden rectangles and their corresponding segments of the golden spiral onto Sophia's image in order to show this (skewed to a small extent due to the slight angle of the image).

This ratio is also evident in the lengths of the cello's different segments - The length of the neck plus the length of its body divided by the length of its body is equal to all of the following: 

the length of the body / the length of the neck

the length from the top of the body to the second 'tip' on its side / the length from the bottom the peg box to the bottom of the neck

the length from the top of the body to the second 'tip' on its side / the length from the top of the body to the first 'tip' on its side

the length from the top of the body to the first 'tip' on its side / the distance between the two 'tips' on its side

To view the original blog post click here