Mathematics and music, two seemingly opposite disciplines. In the first case, the common feeling of belonging to the driving cold, rational and abstract. The latter, of course, calls to embrace the emotion and art. So what do these two things have to do with each other?
Music in one of its most basic form is concerned with changing the quality of time. This creates what we interpret as rhythm and melody. Here mathematics is its place of entryin the scene.
Fibonacci series (named after Leonardo of Pisa) is an infinite sequence of numbers so that each new number is the two previous numbers in the sequence of the sum. For example, 0, 1, 1, 2, 3, 5, 8, … etc. are the Fibonacci numbers, 1 = 0 + 1 2 = 1 + 1 + 2 3 = 1, etc. .. The relationship between a number of his ex in such a sequence is called a Fibonacci ratio, and converge to a single threshold constant, the golden section. The golden ratio is often in the musicalCompositions. Many great works in the history of the golden ratio have inadvertently share their compositions used symmetrically on the golden section. It 'very important as a tool for the structural organization of music. An example is Handel's famous chorus, "Hallelujah," which consists of about 94 measures. The entrance of the famous trumpet solo is done between 57 ° and 58 measures, just 8/13ths (such as the golden section) of the road for the entirePiece of music. Many other studies have shown that Mozart's piano sonatas and the relationship between exposure and Reprise in sync with the golden-section.
It 'does not mean that many great artists and musicians, and began to think about mathematics when they create their works, but rather that the harmony and beauty of nature in mathematical proportions and that the investigation of the structure and symmetry of objects deeper understanding of different mathematical beauty,Art, emotion and life.
Music in one of its most basic form is concerned with changing the quality of time. This creates what we interpret as rhythm and melody. Here mathematics is its place of entryin the scene.
Fibonacci series (named after Leonardo of Pisa) is an infinite sequence of numbers so that each new number is the two previous numbers in the sequence of the sum. For example, 0, 1, 1, 2, 3, 5, 8, … etc. are the Fibonacci numbers, 1 = 0 + 1 2 = 1 + 1 + 2 3 = 1, etc. .. The relationship between a number of his ex in such a sequence is called a Fibonacci ratio, and converge to a single threshold constant, the golden section. The golden ratio is often in the musicalCompositions. Many great works in the history of the golden ratio have inadvertently share their compositions used symmetrically on the golden section. It 'very important as a tool for the structural organization of music. An example is Handel's famous chorus, "Hallelujah," which consists of about 94 measures. The entrance of the famous trumpet solo is done between 57 ° and 58 measures, just 8/13ths (such as the golden section) of the road for the entirePiece of music. Many other studies have shown that Mozart's piano sonatas and the relationship between exposure and Reprise in sync with the golden-section.
It 'does not mean that many great artists and musicians, and began to think about mathematics when they create their works, but rather that the harmony and beauty of nature in mathematical proportions and that the investigation of the structure and symmetry of objects deeper understanding of different mathematical beauty,Art, emotion and life.
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