The Sound of the Golden Mean
Click here to listen to the sound of the Golden Mean
These two tuning forks, when listened to together, create the Golden Mean ratio. Listening to this ratio has a healing effect on us (the frequencies of the two tuning forks are 414.2Hz and 256Hz).
The Golden Mean
The Golden Mean (or Golden Section), represented by the Greek letter 'phi', is one of those mysterious natural numbers that arise out of the basic structure of our cosmos. Phi appears clearly and regularly in the realm of things that grow and unfold in steps, and that includes living things.
The decimal representation of phi is 1.6180339887499.
You can find the Golden Mean in a number of places. If you start with the numbers 0 and 1, and make a list in which each new number is the sum of the previous two, you get a list like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... to infinity>
This is called a 'Fibonacci series'. Leonardo de Pisa (circa 11801240 AD), better known as Fibonacci, discovered the uniformity of ancient harmonic wisdom. He realised that the natural branching, flowering, and spiralling forms in nature follow the same uniform laws found in musical scales.
If you then take the ratio of any two sequential numbers in this Fibonacci series, you'll find that it falls into an increasingly narrow range: 1/1 = 1 2/1 = 2 3/2 = 1.5 5/3 = 1.6666... 8/5 = 1.6 13/8 = 1.625 21/13 = 1.61538... 34/21 = 1.61904... and so on, with each addition coming ever closer to phi (1.6180339887499...).
Rectangles formed from the golden section creating the spiral pattern found in nature
If you have a rectangle whose sides are related by phi (say, for instance, 13 x 8), that rectangle is said to be a Golden Rectangle.
If you divide the above rectangle's long side according to the Golden Mean you will produce the square that you see on the right of the rectangle. If you then divide the central line inside the rectangle according to the Golden Mean you will create another square in the top left hand corner of the rectangle.
If you continue dividing the next line inside the rectangle you create a smaller square in the bottom left hand corner of the rectangle. If you continue this dividing and then draw a line through all the points that you have divided you will end up with a spiral pattern (see above).
This pattern, created by the Golden Mean is found in snail shells, spiral nebulae of galaxies and the petal arrangement of daisies and roses. The Golden Mean proportions were used in the construction of the Greek Parthenon and the Egyptian Pyramids. Since the Renaissance, the Golden Mean has been used extensively in art and architecture, it figures for example in the Venetian Church of St. Mark built early in the 16th century.
It has become a standard proportion for width in relation to height as used in facades of buildings, in window sizing, in first story to second story proportion, and in the dimensions of paintings and picture frames.
The Fibonacci series relates to all of the musical intervals, which comprise beautiful chords. The following table shows some Fibonacci ratio musical chords using the fundamental tone A:
A 
A 
D 
F 
E 
C 
E 
C# 
F# 
C# 
D 
F 
root 
octave 
4th 
aug.5th 
5th 
min3rd 
5th 
3rd 
6th 
3rd 
4th 
aug.4th 
1/1 
2/1 
2/3 
2/5 
3/2 
3/5 
3/8 
5/2 
5/3 
5/8 
8/3 
8/5 
The Fibonacci ratios were also utilised in sacred temple architecture, including the towering Gothic Cathedrals. Guillaume Dufay (c. 14001474) from the Netherlands composed music for the dedication of Florences cathedral of Santa Maria del Fiore in 1436.
His musical piece was based on the Fibonacci series of tones, which corresponded to the dimensions of the cathedrals dome. These musical temples were part of the medieval renaissance of sacred geometry, Hermetic mysteries and the flowering of art and music.
The French architect LeCorbusier noted that the human body when measured from foot to navel and then again from navel to top of head, showed average numbers very near to the Golden Ratio. He extended this to height compared with armspan, and designed doorways consonant with these numbers.
Studies have shown that the patterns of tree branching adhere to the Golden Mean proportion, although again not exactly, while the dendritic cracking in certain metallic alloys which occurs at very low temperatures is Golden Mean based.
Mike Kay found that many of Mozart's sonatas divide into two parts exactly at the Golden Section point. Was this a conscious choice or did he do this intuitively? His sister said he was always playing with numbers and was fascinated by mathematics (American Scientist March/April 1996).
Divine Proportions and the Golden Mean
If the top of head to belly button = 1 then belly button to bottom of the feet = 1.618
If the shoulder to fingertip = 1 then the ideal height of man or woman = 1.618
Each succeeding finger bone is 1.618 the length of the preceding finger bone.
The distance from elbow to wrist is 1.618 the distance from wrist to fingertip.
All beautiful faces regardless of race, age, sex, and other variables conform to the Divine Proportion.
Reproduced from  www.facialbeauty.org/divineproportion.html
