![]() Ned Kahn’s “Cloud Arbor,” located in Pittsburgh, PA Many of Ned Kahn’s other sculptures incorporate suspended fog or clouds, and I was curious about the process of their creation. The position and intensity of the light changes depending on the time of day during which it is observed. Kahn uses a material called a diffraction grating in his “Prism Tunnel” sculpture in order to create a fascinating, ever-changing light display. The most well known example of this phenomenon is the dispersion of white light into its constituent colors. Light refraction is simply the bending of light by a foreign medium, which changes the speed of the wave 6. Most people encounter light refraction at some point or another during their lifetime, whether in the form of Pink Floyd’s “The Dark Side of The Moon” album cover, or the rainbow that appears when light shines through a faceted piece of glass. Pink Floyd’s famous “Dark Side of The Moon” album cover Ned Kahn’s “Prism Tunnel,” located in San Marino, CA For example, the creation of Kahn’s “Prism Tunnel” display in San Marino, California required some basic knowledge about light refraction. Because Kahn’s work focuses on the scientific natural processes in the world, most, if not all of his displays require a basic understanding of related scientific concepts. Find out how here.Just like the exhibits at San Francisco’s Exploratorium that inspired Ned Kahn’s artwork, Kahn’s own work involves numerous scientific concepts and applications. Some people think this is one of the reasons it sounds so good.Īs well as being used to craft violins, the Golden Ratio that comes from the Fibonacci Sequence is also used for saxophone mouthpieces, in speaker wires, and even in the acoustic design of some cathedrals.Įven Lady Gaga has used it in her music. The Golden Ratio can be found throughout the violin by dividing lengths of specific parts of the violin. ![]() Stradivari used the Fibonacci Sequence and the Golden Ratio to make his violins. There's a reason a Stradivarius violin would cost you a few million pounds to buy – and its value is partly down to the Fibonacci Sequence and its Golden Ratio. Read more: To save the sound of a Stradivarius, this entire Italian city is keeping quiet Hailed as the master of violin making, Antonio Stradivari has made some of the most beautiful and sonorous violins in existence. The first movement as a whole consists of 100 bars.Ħ2 divided by 38 equals 1.63 (approximately the Golden Ratio)Įxperts claim that Beethoven, Bartók, Debussy, Schubert, Bach and Satie (to name a few) also used this technique to write their sonatas, but no one is exactly sure why it works so well. The exposition consists of 38 bars and the development and recapitulation consists of 62. In the above diagram, C is the sonata's first movement as a whole, B is the development and recapitulation, and A is the exposition. ![]() The Golden Ratio in Mozart's Piano Sonata No. Let's take the first movement of Mozart's Piano Sonata No. Mozart arranged his piano sonatas so that the number of bars in the development and recapitulation divided by the number of bars in the exposition would equal approximately 1.618, the Golden Ratio. Development and recapitulation – where the theme is developed and repeated.Mozart, for instance, based many of his works on the Golden Ratio – especially his piano sonatas.Įxposition – where the musical theme is introduced The Fibonacci Sequence can be seen on a piano keyboard.Ĭomposers and instrument makers have been using the Fibonacci Sequence and the Golden Ratio for hundreds of years to compose and create music. Starting to see a pattern? These are all numbers in the Fibonacci Sequence: 3, 5, 8, 13. In a scale, the dominant note is the fifth note, which is also the eighth note of all 13 notes that make up the octave.A scale is composed of eight notes, of which the third and fifth notes create the foundation of a basic chord. ![]() Eight are white keys and five are black keys. An octave on the piano consists of 13 notes.The Fibonacci Sequence plays a big part in Western harmony and musical scales. Leonardo da Vinci's use of the Fibonacci Sequence in 'La Gioconda' (Mona Lisa). ![]()
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