Phi 1.618* | the Divine Ratio
Greek philosophers considered the Golden Mean to be the middle between two extremes, one of excess and the other of deficiency.
According to legend, the Greek Philosopher Pythagoras discovered the concept of harmony when he began his studies of proportion while listening to the different sounds given off when the blacksmith’s hammers hit their anvils. The weights of the hammers and of the anvils all gave off different sounds. From here he moved to the study of stringed instruments and the different sounds they produced. He started with a single string and produced a monochord in the ratio of 1:1 called the Unison. By varying the string, he produced other chords: a ratio of 2:1 produced notes an octave apart. (Modern music theory calls a 5:4 ratio a "major third" and an 8:5 ratio a "major sixth".) In further studies of nature, he observed certain patterns and numbers reoccurring. Pythagoras believed that beauty was associated with the ratio of small integers. With this discovery, the Pythagoreans saw the essence of the cosmos as numbers and numbers took on special meaning and significance. The symbol of the Pythagorean brotherhood was the pentagram, in itself embodying several Golden Means.
The Golden Ratio in the World