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The Golden Ratio
Transcript of The Golden Ratio
Pyramid If you divide a line into two parts so that the longer part divided by the smaller part or the whole length divided by the longer part. You will find the golden ratio. Golden Ratio in Rectangles
If you divide the length of the rectangle by the width, you will get the golden ratio 1.168 etc. The ratio of height of the pyramids face to half the length of the base is 1.618. The Egyptians referred to this as the Sacred Ratio. In the above picture 'b' is half the base, 'h' is the height and 'a' the slanted height. The ratio b:h:a equals the golden ratio (1: : ) The way that the ancient Egyptians placed the Sphinx and the Pyramids of Giza are based on the Fibonacci curve. The Sphinx relating to the rectangles turned out to be the precise curve. The layout of the Sphinx and Great Pyramid The Golden Ratio in Music The Golden Ratio in Musical Scales Musical Scales are based on the Fibonacci number system. A scale consists of 8 notes. The 5th and 3rd notes create the foundation of the chord. They are based on whole tone (2 steps from the root tone - the first note of the scale). It was found that it was pleasurable to listen to strings tuned into small numbers (1,2,3,4,5...). Golden Ratio in Musical Instruments In history there has been many people that used the golden ratio in the creation of musical instruments. Stradivarius used the golden ratio to make sections of masterpiece violins. These violins had perfect tonal qualities. Also some people like Jody Espina used the golden ratio in creating her saxophone mouthpiece. Every aspect of the mouthpiece was made with the ratio in mind. This created huge projection and no ringing. Also, the golden ratio is in speaker wire design. Each wire is the golden ratio to the others. The reason for this is it is the key to vibration control. The strands are placed with every strand coupled to each other. This creates a silenced conductor creating the purest sound. Golden Ratio in Speakers The Fibonacci number sequence is: