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The Golden Ratio

In the Great Pyrimad and Music

Gina Teixeira

on 11 September 2012

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Transcript of The Golden Ratio

By Gina Teixeira The Golden Ratio What is the Golden Ratio? The Golden Ratio is found in many things such as Music, Art, Architecture, Nature and Advertisement. In music it is found in instruments and scales. The Golden Ratio or The Golden Mean is a very significant number. It is approximately 1.618. This number is found in many things including Art, Music, Nature, Architecture and many other things. The Fibonacci Number Sequence is also related to the golden Ratio. The main idea of the golden ratio is to use a balance. This balance we see all around us, because it is in things naturally. This balance is put into use into many different things, such as art, architecture or nature. This balance of proportion makes the object more appealing to the eye. The main idea behind it If you were to take a cross section (a right angle triangle) out of the great pyramid, called Egyptian Triangle, you would get the golden ratio. This is because the ratio of the slant height to the distance of the center of the bottom is 1.618... The Golden Ratio in relation to the Great
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:
To find the next number in the sequence you add tether the two numbers before it. For example we got 2, by adding 1+1. Then 3 is found by adding 2+1. Fibonacci number sequence Now that I have looked into the Great Pyramid in relation to the Golden Ratio, I believe that the Ancient Egyptians did know about the Golden Ratio. I think this because, I believe that without knowing it you can't just make something the perfect proportion. It could happen but its highly unlikely. Also, in my research it says that the ratio of the height of the face to half the base length is 1.618... When finding this information it says that the Egyptians called this the Sacred Ratio. If the egyptians were to call it something then they must have knew about it. Reflection and Evaluation This video is a musical interpretation of what the golden ratio sounds like. The way that the ratio is translated into music was starting at middle C is : C = 1, D = 2, E = 3, F = 4, G = 5, A = 6, B = 7, C (octave higher) = 8, D (octave higher) = 9, and no note is played for zero. Bibliography http://books.google.com.au/books?id=FMYCsT-cZDUC&pg=PA133&lpg=PA133&dq=the+main+idea+behind+the+golden+ratio&source=bl&ots=bgc5Sam0BS&sig=93dyl0QxVFOP2q44NvhenG6_Bi4&hl=en#v=onepage&q=the%20main%20idea%20behind%20the%20golden%20ratio&f=falsehttp://www.mathsisfun.com/numbers/golden-ratio.htmlhttp://www.goldennumber.net/acoustics/http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htmhttp://www.goldennumber.net/phi-pi-great-pyramid-egypt/http://mathematics.knoji.com/interesting-facts-about-the-golden-ratio-in-nature-art-math-and-architecture/http://www.jonathandimond.com/tafe/documents/Intro%20to%20Golden%20Section.pdfhttp://www.goldennumber.net/music/http://www.google.com.au/imgres?q=golden+ratio+great+pyramid&um=1&hl=en&sa=N&biw=1277&bih=611&tbm=isch&tbnid=xBm8Ety9u8EedM:&imgrefurl=http://www.jaesonjrakman.com/Cydonia%2520101/PAGES/PAGE10nmsldi7f87f.htm&imgurl=http://www.jaesonjrakman.com/Cydonia%252520101/Cydonia%252520101%252520Pics/city-gm.gif&w=300&h=300&ei=B0pIUPCGHO-ZiQe66YCQCg&zoom=1&iact=hc&vpx=804&vpy=122&dur=234&hovh=225&hovw=225&tx=114&ty=104&sig=106843090732386897303&page=2&tbnh=129&tbnw=129&start=18&ndsp=25&ved=1t:429,r:4,s:18,i:144http://www.mathsisfun.com/numbers/golden-ratio.htmlhttp://www.mathsisfun.com/numbers/fibonacci-sequence.html
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