«golden section" - a concept rather mathematical and study it - the task of science.This division certain magnitude into two parts in such a ratio so as bolshaya part will relate to low as a whole larger.This ratio is equal to the number of transcendental F = 1.6180339 ... with amazing properties.
method golden section - a search function values at a given interval.This method is based on the principle of dividing the length of the so-called golden ratio.The most widely he had received to find extreme values of the solution of problems related to optimization.In addition to mathematics, the golden section method is used in various fields ranging from architecture, art and ending with astronomy.For example, the famous Soviet director Sergei Eisenstein used it in his film "Battleship Potemkin", and Leonardo da Vinci - when writing his famous "Mona Lisa".
golden section method is used in music.It turned out that music works very common this golden proportion.In the early 20th century, at a meeting of the Moscow musical circle was made by a message containing information about what is the use of gold
culmination of many pieces of music is not in the center and slightly offset to the end product in a ratio of 62:38 - it is the point of the golden ratio.Doctor of Arts, Professor L. Mazel noticed vosmitaktnye studying music of Chopin, Beethoven, Scriabin, in many works of these composers climax, usually falls on the weak beat of the fifth, which is the point of the golden section - 5/8.L. Mazel believed that almost every composer - follower harmonic style, you can find such musical structure: five bars and three lifting stroke of descent.This suggests that the method of golden section was actively used by composers consciously or unconsciously.Probably, such a structural arrangement of the highlights of the musical composition gives the harmonic sound and emotional.
Serious study of musical works for display in their golden ratio undertook composer and musicologist L. Sabaneyev.He has studied about two thousand works of various composers and concluded that approximately 75% of the golden section is present in a piece of music at least once.The largest number of works that meets the golden proportion, he noted from composers such as Arensky (95%), Beethoven (97%), Haydn (97%), Mozart (91%), Scriabin (90%), Chopin (92%), Schubert (91%).The most closely he studied etudes by Chopin and came to the conclusion that the golden ratio was determined in the 24 sketches of 27. Only three etudes of Chopin golden proportion has not been found.Sometimes the structure of the musical work included both the symmetry and the golden section.For example, many of the works of Beethoven divided into symmetric parts, and each of them appears golden section.
So, we can say that the presence of the golden section in a piece of music is one of the criteria for the harmony of a musical composition.
