# Bass Clef and the Golden Spiral

Discussion in 'Miscellaneous [BG]' started by canopener, Nov 21, 2004.

1. ### canopener

Sep 15, 2003
Isle of Lucy

Any relation?

Discuss.

2. ### Floating teetH

Jun 29, 2004
Southern USA
Pretty close.

3. ### Sonorous

Oct 1, 2003
Denton, TX
Golden spiral?

Explain.

4. ### Hambone

Mar 18, 2000
Atlanta/Loganville
The figure you see drawn is a plot based on the "golden ratio" and is a series of "golden rectangles" that form a figure called a "whirling square".

The golden ratio (also called the "divine proportion") is seen when figuring the ratios of distances in simple geometric figures. I don't know the alt symbol on the keyboard for this but it is shown as a lower case "o" with a slash through it. I'll just call it X for our purposes. If you take a rectangle with the ratio of 1:X, X is defined so that if you partition off a square and a rectangle, the new rectangle will be another "golden rectangle". Continue this process with each new rectangle and the plot of each successive point on the squares will fall on a logarithmic spiral.

The Golden numbers are something close to 1.61803 and .61803.

This actually has a use in music. I found this in the Radio Shack book on making stereo speakers. Turns out that if you don't have ANY idea of the dimensions and ratios to use to make a speaker cabinet - to use the golden ratio will yield a box that won't create standing waves. So that would be like this: Pick the Width of your cabinet - let's say 10". The height would be 10" x 1.61803 or 16.18" tall. The depth is figured as 10" x .61803 = 6.18" deep. That should make a speaker cabinet that sounds decent.

But be warned, I am NOT the guy to really explain this stuff. There are many TB'ers that are way better at math and geometry than me and they will help you further if I didn't do the job.

5. ### Marlat

Sep 17, 2002
London UK
OTOH, if you turn the Bass clef on its side, it looks a lot like the face of a sock puppet. Maybe that was the inspiration?

6. ### Hambone

Mar 18, 2000
Atlanta/Loganville

Without one shred of fact to back it up, I would guess SURE!

Math and music have always had strong connections and it wouldn't surprise me if it turned out that whatever time in history the bass clef began to be used was also a time when math knowledge was increasing. Maybe the Rennaissance? I don't even know when Fibonacci (sp) was doing his thing but that is the source for the numbers behind the spiral.

7. ### Hambone

Mar 18, 2000
Atlanta/Loganville
Damn! You're right.

Hey, forget all that stuff about golden ratios and log this and that. I like the sock puppet definition better.

8. ### Floating teetH

Jun 29, 2004
Southern USA
I can explain the similarity. The golden rectangle has been considered aesthetically pleasing for a long time. It can be found in ancient architecture, not to mention all sorts of other 'tings (I learned this in geometry from a video that used disney characters). So since the golden spiral implies that shape, it isn't surprising that a similar spiral would be chosen for a symbol, since it's supposed to look cool.

A wrinkle just formed on your brain.

disclaimer: a wrinkle did not just form on your brain.